Answer:
38%
Step-by-step explanation:
Given that X,the hours per week the music student practice follow a normal distribution.
X:N(8,4)
We have to find the percentage of students who practice between 6 and 10 hours.
6<x<10 implies converting to z
We know z = (x-mean)/sigma = (x-8)/4
Hence 6<x<10 is equivalent to (6-8/4)<Z<(10-8/4)
= |z|<0.5
From std normal table we find this area equals = 0.1915+0.1915
=0.3830 = 0.38 (rounded off)
Hence required percentage = 0.38x100 = 38%
Final answer:
To determine the percentage of music students practicing between 6 to 10 hours, we convert these hours to z-scores and use the standard normal distribution table, which reveals that approximately 38.2% of students practice within this range.
Explanation:
To find the percentage of music students who practice between 6 to 10 hours per week, we can use the properties of the normal distribution. We first need to convert the range values to z-scores using the formula Z = (X - μ) / σ, where X is the value from the data set, μ is the mean, and σ is the standard deviation.
Converting 6 hours to a z-score:
Z = (6 - 8) / 4 = -0.5
Converting 10 hours to a z-score:
Z = (10 - 8) / 4 = 0.5
Now we use the standard normal distribution table to find the probability corresponding to these z-scores. The area under the curve between z-scores -0.5 and 0.5 gives us the desired percentage. Looking up the z-scores in the standard normal distribution table, we find that the area between these scores is approximately 38.2%. Thus, 38% is the closest option provided.
What is the solution set of {x|x<-5} n {x|x>5}?
[tex]\{x|x < -5\}\ \cap\ \{x|x > 5\}=\O[/tex]
Look at the picture.
The common part does not exist.
Which is another way to express the problem 1 - (-7)
1+7
because when there are two negatives together you turn it into a positive and add
1 + 7
Because two negatives makes a positive. Hope this helps!
How is graphing (0,12) different from graphing (12,0)
By graphing the given points we understood that (0,12) is on the y-axis and (12,0) is on the x-axis.
We need to explain how is graphing (0,12) different from graphing (12,0).
How to plot the point on the cartesian plane?Given a point, (a, b), you plot the point in the Cartesian plane by finding the number a on the horizontal, or x-axis; then you trace directly up or down from that spot, moving parallel to the vertical, or y-axis until you reach the height of the number b.
Now, plot (0,12) and (12,0) on the Cartesian plane.
In the graph plotted we can see (0,12) is on the y-axis and (12,0) is on the x-axis.
Therefore, by graphing the given points we understood that (0,12) is on the y-axis and (12,0) is on the x-axis.
To learn more about the points on the x-axis and y-axis visit:
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Find the missing number to complete this division fact. 63 ÷ ∎ = 9
Hello AskMeBosh
The missing number in this equation is 7
This is because 9 * 7 is 63
So your answer would be 7
:)
63/7=9 the missing number is 7
recipe for banana oat muffins call for 3/4cups of old fashion oats you are making 1/3of recipe how many cups of oats should you use
The full recipe for the banana oat muffins requires 3/4 (or 0.75) cups of old fashion oats. But you are planning to make only 1/3 of the recipe.
To find the amount of oats required for 1/3 of the recipe, we need to multiply the amount required for the full recipe (3/4 cups) by the proportion of the recipe you are making (1/3).
Let's start with the full amount, which is 3/4 cups of oats. Then, we are going to use only 1/3 of this amount. So, we multiply 3/4 by 1/3.
The result of this calculation is 0.25.
So, you will need 0.25 cups of old fashion oats to make 1/3 of the banana oat muffins recipe.
46 out of 310 seniors graduate with honors. What is the ratio of seniors graduating with honors to the total number of seniors
Final answer:
The ratio of seniors graduating with honors to the total number of seniors is 46/310, which simplifies to 23/155.
Explanation:
To find the ratio of seniors graduating with honors to the total number of seniors, you would divide the number of seniors graduating with honors by the total number of seniors. In this case, 46 seniors graduate with honors out of a total of 310 seniors.
Therefore, the ratio is 46/310, which can be simplified to 23/155 when reduced to the lowest terms.
Adam invests $6139 in a retirement account with a fixed annual interest rate compounded continuously. After 17 years the balance reaches $8,624.97. What is the interest rate of the account? Help! Working out required.
Answer:
2.38% annual interest rate
Step-by-step explanation:
We have the initial value that is $6139 and the final value that is $8,624.97 the initial value is a 100% and the final value is 100%+17x% where x is the annual interest rate, then:
[tex]\dfrac{8624,97\cdot 100\%}{6139\cdot (100\%+17x\%)}=1[/tex]
[tex]\dfrac{8624,97\cdot 100\%}{6139}=100\%+17x\%[/tex]
[tex]\dfrac{862497\%}{6139}-100\%=17x\%[/tex]
[tex]140.49\%-100\%=17x\%[/tex]
[tex]40.49\%=17x\%[/tex]
[tex]\dfrac{40.49\%}{17}=x\%[/tex]
[tex]2.38\%=x\%[/tex]
To find the interest rate of the account, you can use the formula for continuous compound interest, which is A = Pe^(rt). By plugging in the given values, you can solve for r and find that the interest rate is approximately 1.77%.
Explanation:To find the interest rate of the account, we can use the formula for continuous compound interest:
A = Pe^(rt)
Where:
A = final balanceP = initial investmente = Euler's numberr = interest ratet = time in yearsGiven that Adam invested $6139 and the balance after 17 years is $8624.97, we can plug in these values and solve for r:
8624.97 = 6139 * e^(17r)
Divide both sides of the equation by 6139:
e^(17r) = 8624.97 / 6139
Now, take the natural logarithm (ln) of both sides:
ln(e^(17r)) = ln(8624.97 / 6139)
Use the logarithmic property ln(e^x) = x to simplify the equation:
17r = ln(8624.97 / 6139)
Finally, divide both sides of the equation by 17 to solve for r:
r = ln(8624.97 / 6139) / 17
Using a calculator, we find that the interest rate of the account is approximately 0.0177, or 1.77%.
Learn more about Finding interest rate using continuous compound interest formula here:https://brainly.com/question/28524037
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a store is selling a hat at 55 percent markup. the store originally paid $16 for the hat. what is the retail price for the hat
$24.80 is the new retail price for the hat
Answer:
$24.8
Step-by-step explanation:
Hello, i think I can help you with this,you can easily solve this by using a rule of three
Step 1
define
the retail price for the hat will be the originally paid value plus 55%, it is equal to 155% of the original price
if
$16 ⇒100%
$x? ⇒155%
the relation is
[tex]\frac{16}{100}=\frac{x}{155}\\solve\ for\ x \\\frac{155*16}{100}=x\\x=\frac{2480}{100}\\ x=24.8[/tex]
the retail price is $24.8
Have great day.
how can i use variables to describe real world problems
A variable can be used to represent an unknown amount. Then you write an equation using the variable and based on the information you are given, and you solve the equation to find the unknown amount.
Here is an example.
Mary has money in a bank account. She received $20 for her birthday. She deposited the $20 in her account. After the deposit, she was told the account had a balance of $85. How much money did she have in the account before depositing the $20?
We don't know the amount she had before depositing the $20, so we will call that amount x. x is a letter used as a variable to represent an unknown amount.
She had x dollars in her account before depositing the $20.
After she deposited the $20, she now has x plus 20, or x + 20.
We are told her account now has $85, so x + 20 must equal 85.
That allows us to write an equation which we can then solve to find the amount of money she had in the account before depositing the $20.
x + 20 = 85
Subtract 20 from both sides.
x + 20 - 20 = 85 - 20
x + 0 = 65
x = 65
Since the variable x represents the amount of money in the account before depositing the $20 birthday money, we can now answer the question.
Mary had $65.
you can use varibales in real life problems by using them to describe the constants
find the inverse function f -1 (x) for the given function f (x) plz don't write a random answer to get points this is the fourth time I have posted this I need actual help
The FunWorld Obstacle Course is scored by awarding 10 points for every activity that is passed and by deducting 5 points for every activity that is failed. Bob passed 4 activities and failed 3 activities. Tom passed 7 activities and failed 4 activities. Who got a higher score?
Bob passed 4 activities, so 4 x 10 = 40 points. He failed 3, so 3 x 5 = 15
Total points = 40-15 = 25 points.
Tom passed 7, so 7 x 10 = 70 points. He failed 4, so 4 x 5 = 20
Total points = 70-20 = 50 points.
Tom got a higher score.
Suppose the function, g(x), is used to model the height ,y, of a soccer ball, x seconds after the ball is kicked up in the air. The ball starts on the ground and travels in a parabolic shape as it reaches a maximum height and then returns to the ground. Suppose further that the ball reaches its maximum height of 15 feet in 2.2 seconds. What would be an appropriate domain for g(x)?
the ball reaches its maximum height of 15 feet in 2.2 seconds
The ball starts on the ground and travels in a parabolic shape as it reaches a maximum height and then returns to the ground
The ball starts on the ground at 0 seconds so the ball starts at x=0 seconds
the ball reaches its maximum height of 15 feet in 2.2 seconds
So it takes 2.2 second to reach the maximum height
It will take another 2.2 seconds to reach the ground
The time the ball in the air is 2.2 + 2.2 = 4.4
The ball will reach the ground in 4.4 seconds
So the domain for g(x) is {0,4.4}
Answer:
0 ≤ x ≤ 4.4
Step-by-step explanation:
Approximate 221 ( square root) to the nearest hundredths.
A. 14.28
B. 15.52
C. 14.86
D. 12.89
can y’all help please . i don’t know how to do this .
what is the common denominator for 30, 24, 18, and 12?
I believe it is 360 sorry if i am wrong i truely sorry
Which is a correct verbal expression for 9+ n?
Nine plus a unknown number equals unknown.
Answer:
The sum of 9 and a number.
Step-by-step explanation:
Sum = Add.
9 = 9
Number = n
Hope this helps :-)
A new sidewalk will be 4 feet wide 200 feet long and filled to a depth of 3 inches (0.25 foot) with concrete. How many cubic yards of concrete are needed?
The number of cubic yards of concrete that are needed to fill the sidewalk is 7.40741 cubic yards
Volume of a cuboidv = lwh
where
l = length
w = width
h = height
Therefore,
l = 200 ft
w = 4 feet
h = 0.25 feet
v = 200 × 4 × 0.25
v = 200 ft³
In yards the concrete will fill the following volume:
7.40741 yard³learn more on cuboid here:https://brainly.com/question/849398?referrer=searchResults
To find the volume of concrete needed for the sidewalk, multiply the length, width, and depth of the sidewalk. Convert the volume from cubic feet to cubic yards by dividing by 27.
Explanation:To find the volume of concrete needed, we need to multiply the length, width, and depth of the sidewalk. The length is given as 200 feet, the width is 4 feet, and the depth is 0.25 foot. Multiplying these values together gives us the volume in cubic feet. To convert this to cubic yards, we divide the volume in cubic feet by 27 (since there are 27 cubic feet in a cubic yard).
The volume of the sidewalk in cubic feet is 4 ft * 200 ft * 0.25 ft = 200 cubic feet. Dividing this by 27, we get the volume in cubic yards: 200 cubic feet / 27 = 7.41 cubic yards. Therefore, approximately 7.41 cubic yards of concrete are needed for the sidewalk.
Tell whether the angles are adjacent or vertical. Then find the value of X
for #5: you put the equations equal to each other then combine like terms & you’ll get x=41 & the angles are vertical.
for #6: you add the equations together to equal 180 bc that is the measure of a straight line. once you do so, you combine like terms & x should equal 14. & the angles are adjacent.
Find the value of r so that the line through (1,4) and (-5,r) has a slope of 1/3
Final answer:
To determine the value of r for the line to have a slope of 1/3, the slope formula is applied and solved to find that r must be 2.
Explanation:
To find the value of r so that the line through the points (1,4) and (-5,r) has a slope of 1/3, we use the formula for the slope (m) of a line given two points (x1, y1) and (x2, y2): m = (y2 - y1) / (x2 - x1).
Step 1: Insert the known values into the slope formula
Slope (m) = 1/3, x1 = 1, y1 = 4, x2 = -5, y2 = r
1/3 = (r - 4) / (-5 - 1)
Step 2: Solve for r
1/3 = (r - 4) / (-6)
-2 = r - 4
r = 2
Therefore, the value of r is 2 for the line to have a slope of 1/3.
Write the equation of the line parallel to the given line and passing through the given point. y=−2x−1 through (4,3)
if the lines are parallel the slopes are the same so the slope is -2
the equation for a line given a point and a slope is
y-y1 = m(x-x1)
y-3= -2(x-4)
y-3 = -2x+8
y = -2x+11
Evaluate the square root
[tex]\sqrt{a}=b\iff b^2=a\ for\ a\geq0\ and\ b\geq0\\\\\sqrt{\dfrac{1}{144}}=\dfrac{\sqrt1}{\sqrt{144}}=\dfrac{1}{12}\\\\\\\sqrt1=1\ because\ 1^2=1\\\\\sqrt{144}=12\ because\ 12^2=144[/tex]
py+7=6y+qp, y, plus, 7, equals, 6, y, plus, q y=y=y, equals
Py +7 = 6y + qp
Solve the equation for y
To solve the equation for y we need to get y alone
Py +7 = 6y + qp
Subtract 6y from both sides
Py - 6y +7 = + qp
Subtract 7 from both sides
Py - 6y = + qp - 7
Now factor out y
(P - 6)y = qp - 7
Divide by P - 6 from both sides
[tex]y =\frac{qp - 7}{(P - 6)}[/tex]
Answer:
y= p−6 /q−7
Step-by-step explanation:
The strategy
Move all y-terms on one side of the equation, and move all constant terms to the other side of the equation.
Using the distributive property, group like terms together on both sides of the equation.
To isolate y, divide both sides by the coefficient of y.
Solving for y
py+7 = 6y+q
py+7 -6y = q
py-6y= q - 7
y(p-6) = q-7
When asked to factor the trinomial 4x^2+20x+25, a student gives the answer (2x-5)(2x-5). What is one thing wrong with this answer?
The minus signs should be plus signs
can you solve the equation 2/3(4x-5)=8 by using the division property of equality? explain
Answer:
Yes, you can use the division property of equality in this equation.
Step-by-step explanation:
This is because we have a variable (x) that is being MULTIPLIED (by 4). The opposite of multiplication is division. Since this is an equation that needs properties of equality to solve the variable, division would be a property of equality being used.
one integer is 5 more than another. their product is 50. Find the integers
What is the slope of this line?
The slope of this line is 1/4, because slope is rise/run. This line rises 1 for every 4 it runs. The slope is positive because the line is moving upward.
To enter a local fair, one must pay an entrance fee and pay for the number of ride tickets he/she wants. Admission to the fair is given by the equation f(x) = .50x + 10, where x represents the number of tickets purchased and f(x) represents the total price. How much does each ride ticket cost?
A) $10
B) $0.50
C) $10.50
D) Not enough information.
It is B because they show the X variable next to the .50 cents meaning that this can change depending on how many the rider buys in this Equation.
Answer:
no the answer is a $10. i took the usatestprep :)
Step-by-step explanation:
How many numbers between 1 and 100 (inclusive) are divisible by 9 or 4?
There are 11 numbers divisible by 9 between 1 and 100, and 25 numbers divisible by 4 between 1 and 100. So there are 11 + 25 = 36, so 36 numbers divisible by one or the other, but this also includes every number which is divisible by both 9 and 4 twice.
Answer:34
Step-by-step explanation:
I had the answer on khaun academy
34÷3536
with a remainder please
0.00961538461
I typed this for 20 characters
Round each decimal number to the nearest hundred 8.314
8.31 because it goes after the decimal tenth then hundreth the for is in the thousandths
The answer is 8.3 Hope this helps