a) The probability that a randomly chosen student completes the activity in less than 29.9 seconds is approximately 0.1292.
b) The probability that a randomly chosen student completes the activity in more than 40 seconds is approximately 0.3085.
c) The proportion of students who take between 29.4 and 39.1 seconds to complete the activity is approximately 0.3839.
d) 95% of all students finish the activity in less than approximately 49.816 seconds.
a) To calculate the probability of completing the activity in less than 29.9 seconds, we need to find the z-score using the formula z = (x - μ) / σ, where x is the given time, μ is the mean, and σ is the standard deviation. By looking up the z-score in the standard normal distribution table, we find the corresponding probability.
b) Similar to part (a), we calculate the z-score for completing the activity in more than 40 seconds and find the corresponding probability from the standard normal distribution table.
c) To determine the proportion of students taking between 29.4 and 39.1 seconds, we calculate the z-scores for both values and find the corresponding probabilities. Then, we subtract the smaller probability from the larger probability.
d) To find the time at which 95% of students finish the activity, we use the z-score corresponding to the 95th percentile (1.645) and calculate the time using the formula x = μ + z * σ.
Understanding the probabilities and proportions in relation to the normal distribution helps in analyzing the performance and characteristics of students in physical activities.
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Complete question is in the image attached below
what is half of half of half of 8?
Answer:
I believe it is 1
Step-by-step explanation:
half of 8 is 4
half of 4 is 2
half of 2 is 1
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
у— пинь
7.
Graph y= 4x-3
Answer:
какие?
Step-by-step explanation:
You and your four friends go to the Cheese cake Factory. You all split the bill evenly. If
each person's share was $11.50, how much was the original bill?
Answer:
$57.50
Step-by-step explanation:
you+4 friends = 5 peope or 5 checks
$11.50 each for five people
11.5x5=57.5
Original bill=$57.50
I NEED HELP WITH THESE QUESTIONS
The answers to all parts is shown below.
Using Pythagoras theorem
1. (r+2)² = r² + 4²
r² + 4 + 4r = r² + 16
4r = 12
r= 3
2. (r+8)² = r² + 12²
r² + 64 + 16r = r² + 144
16r = 80
r= 5
3. (r+9)² = r² + 15²
r² + 81 + 18r = r² + 225
18r= 144
r= 8
We know the tangent drawn from external points are equal in length
1. x = 22
2. x+12 = 3x
x= 6
3. 5x-4 = 2x + 2
3x = 6
x= 3
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If a polynomial f(x) has a remainder of -6 when divided by x-5, what is f(5)?
Answer:
Step-by-step explanation:
The answer is just 5
f(5)=5
Tres anuncios luminosos se encienden en diferentes intervalos, el primero cada 4
segundos, el segundo cada 10 segundos y el tercero cada 12 segundos. Si en este
momento se encuentran en operación. ¿Cuántas veces coinciden encendidos en los
siguientes 4 minutos?
Usando proporciones, hay que los anuncios luminosos coinciden 4 vezes en los siguientes 4 minutos.
¿Qué es una proporción?Una proporción es una fracción de la cantidad total.
Considerando el mínimo múltiplo comun de las duraciones de 4, 10 y 12, los anuncios luminosos coinciden a cada 60 segundos = 1 minuto, porque:
4 - 10 - 12|2
2 - 5 - 6|2
1 - 5 - 3|3
1 - 5 - 1|5
1 - 1 - 1
Asi, los anuncios luminosos coinciden 4 vezes en los siguientes 4 minutos.
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Find the slope of the line passing through the points (-6, 4) and (-6, -9).
Answer:
There is no slope.
Step-by-step explanation:
Following the formula for slope,
y^2 - y^1
-------------
x^2 - x^1
when inputting our values, we get -13/0. We cannot divide by 0 and because the 0 is in the denominator, it means that there is no slope.
let |g| 5 15. if g has only one subgroup of order 3 and only one of order 5, prove that g is cyclic. generalize to |g| 5 pq, where p and q are prime.
To prove that the group g is cyclic, we analyze the possible values of the order |g|. We consider the cases for each possible value and demonstrate that in all cases, g is either cyclic or leads to a contradiction.
For |g| = 1, 2, 3, 5, or 7, the groups of these orders are always cyclic.
If |g| = 4, 6, 8, 9, 10, 12, or 15, we show that g cannot have the required subgroups. Assuming g is not cyclic, we find an element x of order 2 and additional elements y, z, w, etc., also of order 2. This contradicts the given conditions since g would be isomorphic to Z₂ × Z₂ or have more than one subgroup of order 3 or 5.
For composite orders |g| = pq, where p and q are prime, we generalize the analysis. By Cauchy's theorem, g has elements of order p and q, and since there is only one subgroup of each order, they are cyclic. We show that the intersection of these subgroups cannot have an order of pq, leading to a contradiction. Hence, g is cyclic.
Therefore, in all cases, g is proved to be cyclic. QED.
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4(x + 2) = 4x + 2
Are these two Equivalent
Answer:
no they're not
Step-by-step explanation:
4(x+2) = 4x +8
4x+2= 4x+2
Answer:
No they are not equivalent
First we would have to solve 4(x+2)
In order to solve this we need to multiply. So 4×X is equal to 4x. 4×2=8 Therefore when solving Its 4x+8..and 4x+8 is not equivalent to 4x+2
adam, benin, chiang, deshawn, esther, and fiona have internet accounts. some, but not all, of them are internet friends with each other, and none of them has an internet friend outside this group. each of them has the same number of internet friends. in how many different ways can this happen?
(a) Therefore, the range of possible values for "x" is 1 to 5. (b) Summing up these values, we get 5 + 10 + 10 + 5 + 1 = 31. Therefore, there are 31 different ways this can happen
To find the number of different ways this can happen, we can consider the number of internet friends each person can have. Since each person has the same number of internet friends, let's denote that number as "x". We can then create equations based on the given information:
1. Some, but not all, of them are internet friends with each other: This means that at least two people are internet friends with each other, but not everyone is friends with each other. This implies that the minimum number of internet friends any person can have is 1, and the maximum number is 5 (since there are 6 people in total).
Therefore, the range of possible values for "x" is 1 to 5.
2. None of them has an internet friend outside this group: This means that each person's internet friends must be within this group of 6 people. So, the number of internet friends each person can have is limited to the remaining 5 people.
To find the number of different ways this can happen, we need to sum up the possible values of "x" and calculate the corresponding combinations. For "x = 1", we choose 1 person out of 5 remaining people, giving us C(5, 1) = 5. For "x = 2", we choose 2 people out of 5 remaining people, giving us C(5, 2) = 10.
Similarly, for "x = 3", "x = 4", and "x = 5", we have C(5, 3) = 10, C(5, 4) = 5, and C(5, 5) = 1 respectively. Summing up these values, we get 5 + 10 + 10 + 5 + 1 = 31.
Therefore, there are 31 different ways this can happen
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To estimate the product of 21 x 78, what is the best way to round the factors? (2 points)
20 x 80
30 x 70
20 x 70
30 x 80
Answer:
20x80
Step-by-step explanation:
21 is closest to 20 and is rounded down, 80 is closest to 78 and rounded up so the closest and most logical estimate is a: 20x80.
An elm tree is 3 1/2 times as an apple tree. The Apple tree is 10 2/3 feet tall. How tall is the elm tree?
Answer:
37 1/3
Step-by-step explanation:
10 2/3 * 3.5=37 1/3
The height of the elm tree is \(\mathbf{37\frac{1}3}\) feet
The given parameters are:
\(\mathbf{Apple = 10\frac 23\ ft}\)
An elm tree is 3 1/2 times as an apple tree.
So, we have:
\(\mathbf{Elm = 3\frac 12 \times Apple}\)
This gives
\(\mathbf{Elm = 3\frac 12 \times 10\frac 23\ ft}\)
Express as improper fractions
\(\mathbf{Elm = \frac 72 \times \frac{32}3\ ft}\)
Expand
\(\mathbf{Elm = 7 \times \frac{16}3\ ft}\)
\(\mathbf{Elm = \frac{112}3\ ft}\)
\(\mathbf{Elm = 37\frac{1}3\ ft}\)
Hence, the height of the elm tree is \(\mathbf{37\frac{1}3}\) feet
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a simple random sample of 40 items resulted in a sample mean of 25. the population standard deviation is 5. what is the standard error of the mean? (round your answer to two decimal places).
The standard error of the mean is approximately 0.79 (rounded to two decimal places).
Define standard error ?
The standard error is a statistical term that measures the variability of a sample mean or an estimate of a population parameter from its true value. It is the standard deviation of the sampling distribution of the mean. In simpler terms, the standard error measures how much the sample mean varies from the true population mean. A smaller standard error indicates that the sample mean is more likely to be representative of the population mean, while a larger standard error suggests that the sample mean may not be as reliable.
The formula for the standard error of the mean is:
\(SE = \frac{\sigma }{\sqrt{n}}\)
Where σ is the population standard deviation and n is the sample size.
Substituting the given values:
\(SE =\frac{5}{\sqrt{40}}\)
SE ≈ 0.79
Therefore, the standard error of the mean is approximately 0.79 (rounded to two decimal places).
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i offer you a gamble in which you win $1200 if a card randomly drawn from a standard 52-card deck is red and you lose $1200 if the card is black. what is the expected value of the gamble?
The expected value of a gamble can be calculated by multiplying the probability of winning by the amount you could win and subtracting the probability of losing multiplied by the amount you could lose.
In this case, we are given that if a red card is drawn from a standard 52-card deck, you win $1200, and if a black card is drawn, you lose $1200.
First, let's determine the probability of drawing a red card from a standard 52-card deck. In a standard deck, there are 26 red cards (13 hearts and 13 diamonds) and 26 black cards (13 spades and 13 clubs). So the probability of drawing a red card is 26/52, which simplifies to 1/2 or 0.5.
Next, let's calculate the probability of losing, which is the probability of drawing a black card. Similarly, the probability of drawing a black card is also 26/52 or 1/2.
Now, we can calculate the expected value using the formula:
Expected value = (probability of winning * amount won) - (probability of losing * amount lost)
Expected value = (0.5 * $1200) - (0.5 * $1200)
Expected value = $600 - $600
Expected value = $0
Therefore, the expected value of the gamble is $0. This means that, on average, you neither win nor lose money in the long run by playing this gamble.
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And can you please show your answer thx
Answer:
y=4x is the answer
Step-by-step explanation:
7/10 × 1/3 × 5/11 Write your answer in simplest form
Answer:
7/66
Step-by-step explanation:
Given problem,
→ (7/10) × (1/3) × (5/11)
Let's solve the given problem,
→ (7/10) × (1/3) × (5/11)
→ (7 × 1 × 5)/(10 × 3 × 11)
→ 35/330
→ 7/66
Hence, the answer is 7/66.
Solve for x thanks!!!!!
Answer:
x=5
Step-by-step explanation:
Since the angle with the expession and the one that has a measure of 58 and corresponding, they have equal measure. This helps us write an equation-
12x-2=58
now, solve
-2+2=0, 58+2=60
12x=60
12x/12=60/12
x=5
hope this helps:)
please crown me brainliest!!!
Answer:
12x-2°=58°
12x=58°+2°
=60°
x=60÷12
=5
A man of mass 60kg runs with a constant velocity. He has kinetic energy of 750j. Calculate his velocity
Answer:
the velocity of the man is 5 m/s.
Step-by-step explanation:
The kinetic energy of a moving object is given by the equation:
K.E. = 0.5 * m * v^2
where
K.E. is the kinetic energy
m is the mass of the object
v is the velocity of the object
In this problem, we are given that the man has a mass of 60 kg and a kinetic energy of 750 J.
So,
750 J = 0.5 * 60 kg * v^2
Solving for v:
v^2 = (2 * 750 J) / 60 kg
v^2 = 25 J/kg
v = sqrt(25 J/kg)
v = 5 m/s
Therefore, the velocity of the man is 5 m/s.
the mean weekly usage in our sample is 25.3 hours per week. the expected expense of a machine being used 25.3 hours per week is $ 2966.19 incorrect: your answer is incorrect. hundred. since this expected expense is greater correct: your answer is correct. than the cost of the maintenance contract, the maintenance contract is correct: your answer is correct. advisable.
Based on the given data, the expected expense of a machine being used 25.3 hours per week is $34.22 hundred.
To calculate the expected expense of a machine being used 25.3 hours per week, we need to first find the regression line for the given data. We can use statistical software or a calculator to find the regression line, which is:
Annual Maintenance Expense = 7.99 + 0.79(Weekly Usage)
Using this regression line, we can plug in the mean weekly usage of 25.3 hours to find the expected expense:
Annual Maintenance Expense = 7.99 + 0.79(25.3) \(\approx\) 34.22 hundred dollars
Since the expected expense of a machine being used 25.3 hours per week is greater than the cost of the maintenance contract, which is $3,200 per year or $32 hundred dollars, it would be recommended to purchase the maintenance contract.
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Complete Question:
Jensen Tire & Auto is deciding whether to purchase a maintenance contract for its new computer wheel alignment and balancing machine. Managers feel that maintenance expense should be related to usage, and they collected the following information on weekly usage (hours) and annual maintenance expense (in hundreds of dollars).
Weekly Usage(hours) | Annual Maintenance Expense
13 17.0
10 22.0
20 30.0
28 37.0
32 47.0
17 30.5
24 32.5
31 39.0
40 51.5
38 40.0
If the maintenance contract costs $3,200 per year, would you recommend purchasing it? Why or why not? (Round your answers to two decimal places.)
The mean weekly usage in our sample is 25.3 hours per week. The expected expense of a machine being used 25.3 hours per week is $ __________ hundred.
It is not 21.47 or 34.74.
Helppp meeee plzz. Thank you
Answer:
midpoint is (−6,11 over 2)
Evaluate
p
+
(
−
q
)
−
2
p
Multiply and simplify if possible. (2sqrt3x -2)(3sqrt3x +5)
show work
The expression is simplified to give 2(9x + 2√3x - 5)
How to determine the valueFirst, we need to know that surds are mathematical forms that can no longer be simplified to smaller forms
From the information given, we have that;
(2√3x - 2)(3√3x + 5)
expand the bracket, we get;
6√9x² + 5(2√3x) - 6√3x - 10
Find the square root factor
6(3x) + 10√3x - 6√3x - 10
collect the like terms, we have;
18x + 4√3x - 10
Factorize the expression, we have;
2(9x + 2√3x - 5)
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Write down the two inequalities that define the shaded region in the diagram
The two inequalities that define the shaded region in the diagram are:
y ≥ 4 and y < x
How to Write Inequalities that define the Shaded Region?For the solid vertical line, the slope (m) is 0. The inequality sign we would use would be "≥" because the shaded region is to the left and the boundary line is solid.
The y-intercept is at 4, therefore, substitute m = 0 and b = 4 into y ≥ mx + b:
y ≥ 0(x) + 4
y ≥ 4
For the dashed line:
m = change in y / change in x = 1/1 = 1
b = 0
the inequality sign to use is: "<"
Substitute m = 1 and b = 0 into y < mx + b:
y < 1(x) + 0
y < x
Thus, the two inequalities are:
y ≥ 4 and y < x
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how many student wear spectacles?
Answer:
12
Step-by-step explanation:
This is a rather simple one is it not? We know that there are 40 students in the class and 30% wear spectacles. Your current answer (30/40) is wrong unfortunatly because it assumes that it is 30% of 100 as a percent is percentage of 100 (eg. 30% is 30/100).
Expression: 30%*40.
Converting the percent to a decimal (30/100), we get 0.3.
Then simple multiplication, 0.3*40 which is 12.
Which function is nonlinear? Y=4x+9 y=7/x-6 y=x-6/7 15 points
Answer:
The answer is y = 7/x -6.
Step-by-step explanation:
A linear function is one where x and y are both to the first power. Using this knowledge, let's look at the options that we are given.
y = 4x + 9
In the above equation, both x and y are raised to the first power, so we know that this equation is linear.
y = 7/x - 6
In the above equation, y is raised to the first power, but x is not. Since x is in the denominator of a fraction, it actually has a power of -1, which makes this equation nonlinear.
y = x - 6/7
In the above equation, both x and y are raised to the first power, making the equation linear.
Therefore, the correct choice is y =7/x - 6.
Hope this helps!
14% of americans like to only cook and 48% of americans like to only shop, while 85% enjoy either cooking or shopping. what is the probability that a randomly selected american enjoys both activities?
The probability that a randomly selected american enjoys both activities is 23 % .
Given :
14 % of americans like to only cook and 48 % of americans like to only shop, while 85 % enjoy either cooking or shopping .
14 % = 0.14
48 % = 0.48
overlapping is 85 % = 0.85
P ( A ) = 0.14
P ( B ) = 0.48
P ( A and B ) = 0.85
we know that,
P ( A or B ) = P ( A ) + P ( B ) - P ( A and B )
= 0.14 + 0.48 - 0.85
= 0.62 - 0.85
= -0.23
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What is the y-intercept of the function f(x) = 4 – 5x? * 4 points -5 -4 4 5
Answer:
the answer is 4
Step-by-step explanation:
Answer:
h ey ew h he h dhv h d h h h j hd v 8 9
Step-by-step explanation:
Seeds cost for a farmer are 40$ per acre for corn and 30$ per acre for soybeans . How many acres of each crop should the farmer plant if she wants to spend no more than 2400 on seed? Express your answer as a liner inequality with appropriate nonnegative restrictions and draw its graph
Given that:
- The seeds cost is 40$ per acre for corn.
- The seeds cost is 30$ per acre for soybeans.
- The farmer wants to spend no more than $2400.
• Let be "x" the number of acres of seeds for corn and "y" the number of acres of seeds for soybeans.
You know that the total amount of money has to be less than or equal to $2400. Therefore, you can write the following Linear Inequality to represent that situation:
\(40x+30y\leq2400\)You can rewrite it in another form by solving for "y":
\(\begin{gathered} 30y\leq-40x+2400 \\ \\ y\leq\frac{-40x}{30}+\frac{2400}{30} \end{gathered}\)\(y\leq-\frac{4}{3}x+80\)Since the number of acres cannot be negative:
\(\begin{gathered} x\ge0 \\ y\ge0 \end{gathered}\)• You can identify that the boundary line is:
\(y=-\frac{4}{3}x+80\)It is written in Slope-Intercept Form:
\(y=mx+b\)Where "m" is the slope and "b" is the y-intercept.
In this case, you can identify that the y-intercept is:
\(b=80\)In order to find the x-intercept, substitute this value of "y" into the equation and solve for "x" (because the y-value is zero when the line intersects the x-axis):
\(y=0\)Then, you get:
\(0=-\frac{4}{3}x+80\)\(\frac{(-80)(3)}{-4}=x\)\(x=60\)You can identify that the symbol of the inequality is:
\(\leq\)It indicates that the line must be solid and the shaded region must be below the boundary line.
Knowing all this information, you can graph the inequality on the Coordinate Plane (Remember that the values of the variables must be greater than or equal to zero. Then, you must shade with a different color the region in which "x" and "y" are greater than or equal to zero).
Hence, the answer is:
- Linear Inequality:
\(40x+30y\leq2400\)- Nonnegative restrictions:
\(\begin{gathered} x\ge0 \\ y\ge0 \end{gathered}\)- Graph:
what are the answers
Answer:
I use app called math
way
Step-by-step explanation:
Let theta be an acute angle of a right triangle. Find the values of the other five trigonometric functions of theta.
The exact values of the remaining trigonometric functions are listed below:
Case 3: cos θ = 3 / 5, tan θ = 4 / 3, cot θ = 3 / 4, sec θ = 5 / 3, csc θ = 5 / 4
Case 4: sin θ = √11 / 6, tan θ = √11 / 5, cot θ = 5√11 / 5, sec θ = 6 / 5, csc θ = 6√11 / 11
Case 5: cos θ = 8√73 / 73, sin θ = 3√73 / 73, tan θ = 3 / 8, cot θ = 8 / 3, csc θ = √73 / 3
Case 6: sin θ = 1 / 2, cos θ = √3 / 2, tan θ = √3 / 3, sec θ = 2√3 / 3, csc θ = 2
How to find the exact values of trigonometric functions
In this problem we find four cases of trigonometric functions, whose exact values of remaining trigonometric functions must be found. The trigonometric functions are defined below:
sin θ = y / √(x² + y²)
cos θ = x / √(x² + y²)
tan θ = y / x
cot θ = x / y
sec θ = √(x² + y²) / x
csc θ = √(x² + y²) / y
Now we proceed to determine the exact values of the trigonometric functions:
Case 3: y = 4, √(x² + y²) = 5
x = √(5² - 4²)
x = 3
cos θ = 3 / 5
tan θ = 4 / 3
cot θ = 3 / 4
sec θ = 5 / 3
csc θ = 5 / 4
Case 4: x = 5, √(x² + y²) = 6
y = √(6² - 5²)
y = √11
sin θ = √11 / 6
tan θ = √11 / 5
cot θ = 5√11 / 5
sec θ = 6 / 5
csc θ = 6√11 / 11
Case 5: x = 8, √(x² + y²) = √73
y = √(73 - 8²)
y = 3
cos θ = 8√73 / 73
sin θ = 3√73 / 73
tan θ = 3 / 8
cot θ = 8 / 3
csc θ = √73 / 3
Case 6: x = √3, y = 1
sin θ = 1 / 2
cos θ = √3 / 2
tan θ = √3 / 3
sec θ = 2√3 / 3
csc θ = 2
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