Answer:
a) 18 in x 18 in x 18 in
b) [tex]S = 1944\ in2[/tex]
Step-by-step explanation:
a) Let's call 's' the side of the square base and 'h' the height of the solid.
The surface area is given by the equation:
[tex]S = 2s^2 + 4sh[/tex]
The volume of the solid is given by the equation:
[tex]V = s^2h = 5832[/tex]
From the volume equation, we have that:
[tex]h = 5832/s^2[/tex]
Then, using this value of h in the surface area equation, we have:
[tex]S = 2s^2 + 4s(5832/s^2)[/tex]
[tex]S = 2s^2 + 23328/s[/tex]
To find the side length that gives the minimum surface area, we can find where the derivative of S in relation to s is zero:
[tex]dS/ds = 4s - 23328/s^2 = 0[/tex]
[tex]4s = 23328/s^2[/tex]
[tex]4s^3 = 23328[/tex]
[tex]s^3 = 23328/4 = 5832[/tex]
[tex]s = 18\ inches[/tex]
The height of the solid is:
[tex]h = 5832/(18)^2 = 18\ inches[/tex]
b) The minimum surface area is:
[tex]S = 2(18)^2 + 4(18)(18)[/tex]
[tex]S = 1944\ in2[/tex]
What is 9+9+9 help me
Answer:
The answer is 27
Step-by-step explanation:
9+9+9=27
9*3=27
9+9=18+9=27
Answer:
27
Step-by-step explanation:
9+9=18
18+9=27
This can also be expressed as 9*3=27
Use cylindrical coordinates. Find the volume of the solid that lies within both the cylinder x2 y2
Answer:
hello your question is incomplete here is the complete question
Use cylindrical coordinates Find the volume of the solid that lies within both the cylinder x^2 + y^2=16 and the sphere x^2 + y^2 + Z^2= 81
Answer : [tex]\frac{4 \pi }{3} [729 - 65\sqrt{65} ][/tex]
Step-by-step explanation:
The given data
cylinder = x^2 + y^2 = 16
sphere = x^2 + y^2 +z^2 = 81
from the given data the solid is symmetric around the xy plane hence we will calculate half the solid volume above the plane then multiply the sesult by 2
Note : we are restricting our attention to the cylinder x^2 + y^2 = 16 and also finding the volume inside the sphere which gives bound on the z-coordinate as well
the r parameter goes from 0 to 4
ATTACHED IS THE REMAINING PART OF THE SOLUTION
showing the integration
In the figure below, what is the value of xº?
Answer:
[tex] \boxed{\sf x \degree = 62 \degree} [/tex]
Step-by-step explanation:
An exterior angle of a triangle is equal to the sum of the opposite interior angles.
[tex] \sf \implies x \degree + 38 \degree = 100 \degree \\ \\ \sf \implies x \degree + (38 \degree - 38 \degree) = 100 \degree - 38 \degree \\ \\ \sf \implies x \degree = 100 \degree - 38 \degree \\ \\ \sf \implies x \degree = 62 \degree[/tex]
In the given figure, the value of x is 62°.
What is angle ?An angle is the formed when two straight lines meet at one point, it is denoted by θ.
The given angles are,
x°, 38° and 100°.
To find the value of angle x, use exterior angle property.
According to exterior angle property,
The sum of two interior angles is equal to exterior angle.
Since, 100° is the exterior angle of x and 38.
x + 38 = 100
x = 100 - 38
x = 62.
The required value of angle x is 62°.
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Help me pls pls pls
Answer:
The Inequality for the amount of lift tickets she can buy:
a) x < 5
Therefore, to be able to have more than $420 to spend on snowboarding equipment, Helena must buy less than 5 tickets.
Step-by-step explanation:
We are told in the attached diagram that:
Helena has saved $595 to buy snowboarding equipment.
Lift tickets costs $35 per lift
She wants to have MORE THAN $420 left to spend.
Find the inequality, that represents the number of lift tickets she can buy
Step 1
Amount she can spend on lift tickets is calculated as:
Amount saved - Amount intended to spend on snowboarding
= $595 - $420
= $175
Step 2
Since the price of one lift ticket = $35
Let x represent the number of lift tickets Helena can buy.
Number of lift tickets she can buy = $175/ $35
= 5
The Inequality for the amount of lift tickets she can buy
x < 5
Therefore, to be able to have more than $420 to spend on snowboarding equipment, Helena must buy less than 5 tickets.
Find the lengths of the remaining sides of the triangle. a = 18 a is 60 degrees b is 30 degrees b = c =
Answer:
b= 10.39
c = 20.79
Step-by-step explanation:
a = 60 °
b = 30°
c= 180-(60+30)
c = 180-(90)
c = 90°
Length facing angle a = 18
Let's look for length facing angle b
b/sinb = a/sin a
b/sin 30 = 18/sin 60
b =( 18 * sin30)/sin 60
b = (18*0.5)/0.8660
b = 9/0.8660
b= 10.39
Let's look for c
c/sin c = a/sin a
c/sin 90 = 18/sin 60
c = (18 * sin 90)/sin 60
c =18/0.8660
c = 20.79
Pleaseeeee help, I need this now...
Answer:
7/16.
Step-by-step explanation:
The first triangle has no shading.
The second triangle has 1/4 shaded.
The third has 3/9.
The fourth has 6/16.
Based on this pattern, we can assume that the number of small triangles in each triangle are going to be squared of numbers, since the first had 1, the second 4, the third 9, the fourth 16. So, the 8th triangle would have 8^2 small triangles, or 64 triangles in total.
The first triangle has no shaded triangles. The second has 1. The third has 3. The fourth has 6. If you study the pattern, the second triangle has 1 more than the previous, the third has 2 more, the fourth has three more. And so, the fifth triangle would have 6 + 4 = 10 triangles, the sixth would have 10 + 5 = 15 triangles, the seventh would have 15 + 6 = 21 triangles, and the eighth would have 21 + 7 = 28 shaded triangles.
So, the fraction of shaded triangles would be 28 / 64 = 14 / 32 = 7 / 16.
Hope this helps!
Ruth has a beaker containing a solution of 800 mL of acid and 200 mL of water. She thinks the solution is a little strong, so she drains 100 mL from the beaker, adds 100 mL of water, and stirs the solution. Ruth thinks the solution is still too strong, so again she drains 100 mL from the beaker, and adds 100 mL of water. How many mL of water are now in the beaker?
Answer:
350 mL of water
Step-by-step explanation:
Well she starts with 200mL of water and there is 800 mL of acid of water.
She drains 100 mL of acid and adds 100 mL of water so there is 300 mL of water.
And she stirs meaning the compounds have mixed.
Then she drains 100 mL and she they are mixed she drains half of acid and half of water so she has 250 mL of water.
The she adds 100 mL of water so now there’s 350 mL of water left.
The unconditional probability of event A is 1/2. The unconditional probability of event B is 1/3. Say whether each of the following is true or false, and explain why.
(a) If A and B are independent, the chance that they both happen must be 1/2 x 1/3 = 1/6.
(b) If A and B are independent, the chance that at least one of them happens is 1/2 + 1/3 = 5/6.
(c) A and B cannot be both independent and mutually exclusive. The case is not possible.
Identify the vertex of the function. PLEASE HELP!!!
Answer:
Step-by-step explanation:
y-|x|+3
y=|x|+3
vertex=(0,3)
y=|x-4|-7
vertex(4,-7)
HELP ASAP PLEASE!!!! SHOW WORK D = child’s dosage in milligrams a = age of the child M = adult dosage in milligrams The child weighs 55 lbs. Convert the child’s weight in pounds (lbs.) to kilograms (kg).
Answer:
24.95 kg
Step-by-step explanation:
one pound =0.45356 kg
55 lbs=55*45356 =24.95 kg
Is the selection below a permutation, a combination, or neither? Explain your reasoning. Upper A group of 5 senators is chosen to be part of a special committee.
Answer:
Combination, but keep in mind that if the committee had two open positions, say President and Secretary, it would be a permutation
Step-by-step explanation:
The first thing to keep in mind is the difference between combination and permutation.
The main difference is that in the combinations the order does not matter, whereas in the permutations the order does matter.
Combination example:
Choose 7 people for a project.
Example of permutation:
Choose 5 men for each specific role in a soccer team.
Therefore, "group of 5 senators is chosen to be part of a special committee" is a combination, but keep in mind that if the committee had two open positions, say President and Secretary, it would be a permutation.
The difference of m2 + n2 and m + n is
whats the square root of 145
Answer:
the square root is approximately 12.04
12.0415945788
Hope This Helps
find the equation of the circle
Step-by-step explanation:
Let's say the coordinates of Q are (h, k).
The slope of PQ is perpendicular to the tangent line.
(k − 2) / (h − 2) = -⅓
3(k − 2) = -(h − 2)
3(k − 2) = 2 − h
Solving for h:
h = 2 − 3(k − 2)
h = 2 − 3k + 6
h = 8 − 3k
(2, 2) is a point on the circle, so:
(2 − h)² + (2 − k)² = r²
Substituting:
9 (k − 2)² + (2 − k)² = r²
10 (k − 2)² = r²
The equation of the circle is:
(x − 8 + 3k)² + (y − k)² = 10 (k − 2)²
Without more information, there are an infinite number of possible solutions. For example, if k = 1, the equation of the circle is:
(x − 5)² + (y − 1)² = 10
what is 11/8-3/4 step by step
Answer:
5/8
Step-by-step explanation:
1 + 3/8 - 3/4 =
1 + (1 × 3)/(1 × 8) - (2 × 3)/(2 × 4) =
1 + 3/8 - 6/8 =
1 + (3 - 6)/8 =
1 - 3/8
- 3/8 already reduced to the lowest terms.
The numerator and the denominator have no common prime factors.
Their prime factorization:
3 is a prime number;
8 = 23
1 - 3/8 =
(1 × 8)/8 - 3/8 =
(1 × 8 - 3)/8 =
5/8
Hope this helpes
be sure to give brainliest
ABC and ADC are triangles. The area of triangle ADC is 52m^2
Given that,
ABC and ADC are triangles.
The area of ΔADC is 52 m².
Suppose , AD is the median.
According to figure,
We need to find the area of ΔABC
Using theorem of triangle
[tex]\bigtriangleup ADB +\bigtriangleup ADC=\bigtriangleup ABC[/tex]
Here, Δ ADB = Δ ADC
So, [tex]2 \bigtriangleup ADC=\bigtriangleup ABC[/tex]
Put the value of Δ ADC
[tex]\bigtriangleup ABC =2\times52[/tex]
[tex]\bigtriangleup ABC = 104\ m^2[/tex]
Hence, The area of ΔABC is 104 m².
find domain and range using interval notation
Hey there! :)
Answer:
D: [8, 12].
R: [-10, -6].
Step-by-step explanation:
Notice that the endpoints of the graph are closed circles. This means that square brackets will be used:
The graphed equation is from x = 8 to x = 12. Therefore, the domain of the function is:
D: [8, 12].
The range goes from y = -10 to -6. Therefore:
R: [-10, -6].
Answer:
D: [8 , 12]
R: [-10 , -6]
Step-by-step explanation:
Well for this parabola domain and rage are acttually limited because of the solid dots you see on the graph.
So first things first, what is range? Well range is the amount of y values on a line or anything in a graph.
And what’s domain? Domain is the amount of x values on a line or whatnot.
So let’s do domain first.
On the parabola the first x value is 8 and the last is 12 so we have to write this in interval notation which is [8 , 12].
Now for range the lowest y value is -10 and the highest is -6 so in interval notation it is [-10 , -6].
Triangle G Y K is shown. Angle G K Y is a right angle. Angle K G Y is 60 degrees and angle G Y K is 30 degrees. The length of G K is 27.Given right triangle GYK, what is the value of tan(G)?
Answer:
Sqrt 3
Step-by-step explanation:
The value of tan(G) is √3
What is right triangle?
Right triangle is defined as a triangle which one angle is a right angle or two sides are perpendicular.
In ΔGYK
∠GYK = 90°
∠KGY = 60°
∠GYK = 30°
side GK = 27
Let side KY = x
tan(Y) = tan30° = GK/KY
1/√3 = 27/x
x = 27√3
So side KY = 27√3
tan(G) = KY/KG
tan(G) = 27√3/27
tan(G) = √3
Hence, the value of tan(G) is √3
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Apply the product rules to determine the sign of each expression
Answer:
Step-by-step explanation:
1). [tex](\frac{-4}{9})\times (\frac{7}{4})=(-1)(\frac{4}{9})(\frac{7}{4} )[/tex]
[tex]=-\frac{7}{9}[/tex] [Negative]
2). [tex](-2\frac{3}{4})(-1\frac{1}{5})=(-1)(2\frac{3}{4})(-1)(1\frac{1}{5})[/tex]
[tex]=(-1)^2(2\frac{3}{4})(1\frac{1}{5})[/tex]
[tex]=(2\frac{3}{4})(1\frac{1}{5})[/tex] [Positive]
3). (3)(-3)(-3)(-3)(-3) = 3.(-1).3.(-1).3.(-1).3(-1).(3)
= (-1)⁴(3)⁵
= (3)⁵ [Positive]
4). [tex](-\frac{1}{6})(-2)(-\frac{3}{5})(-9)[/tex] = [tex](-1)(\frac{1}{6})(-1)(2)(-1)(\frac{3}{5})(-1)(9)[/tex]
= [tex](-1)^4(\frac{1}{6})(2)(\frac{3}{5})(9)[/tex]
= [tex](\frac{1}{6})(2)(\frac{3}{5})(9)[/tex] [Positive]
5). [tex](-\frac{4}{7})(-\frac{3}{5})(-9)=(-1)(\frac{4}{7})(-1)(\frac{3}{5})(-1)(9)[/tex]
[tex]=(-1)^3(\frac{4}{7})(\frac{3}{5})(9)[/tex]
[tex]=-(\frac{4}{7})(\frac{3}{5})(9)[/tex] [Negative]
6). [tex](-\frac{10}{7})(\frac{8}{3})=(-1)(\frac{10}{7})(\frac{8}{3})[/tex]
[tex]=-(\frac{10}{7})(\frac{8}{3})[/tex] [Negative]
Two cylindrical cans of beef stew sell for the same price. One can has a diameter of 8 inches and a height of 4 inches. The other has a diameter of 6 inches and a height of 7 inches. Which can contains more stew & is , therefore ,a better buy?
Answer:
Can 1 will contain more stew
Step-by-step explanation:
Can -1diameter= 8
radius=d/2=4
height=4
therefore volume= [tex]\pi[/tex] r2 h= 201.06
Can-2Diameter= 6
radius=d/2=3
height= 7
therefore volume= [tex]\pi[/tex] r2 h= 197.92
The cylindrical can that contains more stew is the first can which has a diameter of 8 inches and a height of 4 inches.
What is the volume of a right circular cylinder?Suppose that the radius of considered right circular cylinder be 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.
The more volume of a can is, the more stew it can store.
For first can:
Height = 4 inches, diameter of base = 8 inches.Since radius = diameter/2, so radius of base = 8/2 = 4 inches.
Thus, volume of first can: [tex]V = \pi (4)^2 (4) = 64\pi \: \rm unit^3[/tex]
For second can:
Height = 7 inches, diameter of base = 6 inches.Since radius = diameter/2, so radius of base = 6/2 = 3 inches.
Thus, volume of first can: [tex]V = \pi (3)^2 (7) = 63\pi \: \rm unit^3[/tex]
Thus, as π > 0, so first can can contain more stew.
Thus, the cylindrical can that contains more stew is the first can which has a diameter of 8 inches and a height of 4 inches.
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Bry blew 91 bubbles. Ken blew 7 bubbles
How many times as many bubbles did Bry blow
Answer:
13 times
Step-by-step explanation:
You divide 91 and 7 to get your answer as the answer is asking for times.
Answer:
the answer is 13
Step-by-step explanation:
91/7=13
70/7=10 and 21/7=3
Let the predictor variable x represent heights of males and let response variable y represent weights of males. A sample of 153 heights and weights results in s Subscript eequals16.75064 cm. Using the regression found from the data, a height of 185 cm is used to find that the predicted weight is 91.4 kg and the 95% prediction interval is (58.2 kg comma 124.6 kg ). Write a statement that interprets that prediction interval. What is the major advantage of using a prediction interval instead of simply using the predicted weight of 91.4 kg? Why is the terminology of prediction interval used instead of confidence interval?
Answer:
Check Explanation
Step-by-step explanation:
- Write a statement that interprets that prediction interval.
The prediction interval (58.2 kg, 124.6 kg) represents the range of values that the true predicted weight for a height of 185 cm using the regression obtained from the data can actually, possibly take on to a certain level of confidence.
- What is the major advantage of using a prediction interval instead of simply using the predicted weight of 91.4 kg?
The prediction interval is better to use instead of just using a predicted weight because in computing the prediction interval, we consider all the factors, biases and significant factors that can introduce uncertainties into the regression used to just find the predicted weight.
So, the prediction interval is more encompassing and has a better chance of containing the true weight that corresponds to the height 185 cm because it incorporates so many things thay can go wrong with the regression into its computation unlike the predicted weight.
- Why is the terminology of prediction interval used instead of confidence interval?
This is because the interval is obtained from the regression results, used in predicting weights, given height.
Confidence interval is used for numerical distributions to estimate the interval of range of values where the true population mean can be found with a certain level of confidence.
Hope this Helps!!!
Interval values describes a range of values in which the the true or actual value will likely reside based on a certain level of Confidence.
1.)
Tbe prediction interval describes a range of values which will contain the actual value based on a certain level of confidence.
2.)
The prediction interval gives an interval estimate rather than a point estimate, which increases the probability of obtaining a true value.
3.)
The prediction interval is used instead of confidence interval, because it is concerned with prediction using a linear model while confidence interval is associated with estimating the population mean from a sample.
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I do not know what to do i need help plz
Answer:
savings per weekAlyssa saves more money per week than Sarah doesSarah: (0, 8); Alyssa: (0, 0)Step-by-step explanation:
A "rate of change" is usually referring to ...
"something" per "something else"
The "per" signifies division, as in a fraction, so this can also be written ...
"something" / "something else"
When the "something else" is one of it (1 week, for example), the rate is called a "unit rate."
When you're dealing with a graph, the "rate of change" usually refers to the slope of the line or curve on the graph. That is why it is computed as ...
rate of change = (vertical change)/(horizontal change)
So, you can find what the "something" is by looking at the chart label and the vertical axis label. You can find what the "something else" is by looking at the horizontal axis label.
__
1. The rates of change in this problem represent ...
total savings $ per week
__
2. Alyssa's higher rate of change means Alyssa's savings per week are higher than Sarah's.
__
3. The "initial value" is the value of the curve or line where the number on the horizontal axis is zero (0). It is usually, but not always, at the left side of the graph. It is also often called the "y-intercept", because it it the value where the curve intercepts the vertical (y) axis. Here, you're asked for an ordered pair, so you want the (x, y) values at that point. We've already said the x-value is zero.
Sarah's initial value: (0, 8)
Alyssa's initial value: (0, 0)
Samples of aluminum-alloy channels were tested for stiffness. the following frequency distribution was obtained. The distribution is assumed to be normal.stiffness frequency2480 232440 352400 402360 332320 21a) What is the approximate mean of the population from which the sample were taken?b) What is the approximate standard deviation of the population from which the samples were taken?c) What is the approximate probability that stiffness would be less than 2350 for any given channel section?
Answer:
The answer is explained below
Step-by-step explanation:
stiffness frequency
2480 23
2440 35
2400 40
2360 33
2320 21
a) The mean for the population is calculated using the formula:
[tex]mean (\mu)=\frac{\Sigma f_ix_i}{\Sigma f_i} \\=\frac{x_1f_1+x_2f_2+.\ .\ .+x_nf_n}{x_1+x_2+.\ .\ . +x_n} \\=\frac{(2480*23)+(2440*35)+(2400*40)+(2360*33)+(2320*21)}{23+35+40+33+21} =\frac{365040}{152}=2401.6[/tex]
b) The standard deviation is given by:
[tex]\sigma=\sqrt{ \frac{\Sigma f_i(x_i-\mu)^2}{\Sigma f_1} } \\=\sqrt{ \frac{f_1(x_1-\mu)^2+f_2(x_2-\mu)^2+.\ .\ .+f_n(x_n-\mu)^2}{f_1+f_2+.\ .\ .+f_n} } \\=\sqrt{ \frac{23(2480-2401.6)^2+35(2440-2401.6)^2+40(2400-2401.6)^2+33(2360-2401.6)^2+21(2320-2401.6)^2}{23+35+40+33+21 }}\\=\sqrt{\frac{390021.12}{152} }= 50.7[/tex]
c) We have to find the z score for x = 2350. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma}=\frac{2350-2401.6}{50.7}=-1.02[/tex]
From the z table:
The probability that stiffness would be less than 2350 for any given channel section = P(x < 2350) = P(z < -1.02) = 0.1539 = 15.39%
Find the inverse of the function f(x)=4+ \sqrt{x-2}
Answer:
y = (x - 4)² + 2 , x ≥ 4.
Step-by-step explanation:
Finding the inverse of
f(x) = 4 + √(x - 2)
Begin by swapping the x and y variables in the equation:
x = 4 + √(y - 2)
Subtract 4 from both sides:
x - 4 = √(y - 2)
Square both sides:
(x - 4)² = y - 2
Add 2 to both sides to get your equation:
y = (x - 4)² + 2
However, the domain restriction also needs to be included since the question involves finding the inverse of a square root function. In this case, the domain restriction would be x ≥ 4.
Previous 20 Two groups leave on different flights from the same airport. Group A flies 200 miles due south, then turns 68° toward west and flies 75 miles. Group B flies 75 miles due north, then turns 51° toward east and flies 200 miles. Which group is farther from the airport?
Answer:
Group B is farther from the airport.
Step-by-step explanation:
To find the distance of each group to the airport we can use the law of cosines in the triangle created with the two movements done and the resulting total distance.
Law of cosines:
[tex]c^2 = a^2 + b^2 - 2ab*cos(angle)[/tex]
For group A, we have the sides of 200 miles and 75 miles, and the angle between the sides is (180-68) = 112°, so the third side of the triangle is:
[tex]c^2 = 200^2 + 75^2 -2*200*75*cos(112)[/tex]
[tex]c^2 = 56863.198[/tex]
[tex]c = 238.46\ miles[/tex]
For group B, we also have the sides of 200 miles and 75 miles, and the angle between the sides is (180-51) = 129°, so the third side of the triangle is:
[tex]c^2 = 200^2 + 75^2 -2*200*75*cos(129)[/tex]
[tex]c^2 = 64504.612[/tex]
[tex]c = 253.98\ miles[/tex]
The distance from group B to the airport is bigger, so group B is farther from the airport.
Sue has $1.80 in dimes and nickels. If she has 9 more dimes than nickels, How many of dimes and nickels does she have?
Answer:
15 dimes6 nickelsStep-by-step explanation:
Let d represent the number of dimes. Then d-9 is the number of nickels. The total value (in cents) is ...
10d +5(d-9) = 180
15d -45 = 180 . . . . . simplify
d -3 = 12 . . . . . . . . . .divide by 15
d = 15
15 -9 = 6 = number of nickels
Sue has 15 dimes and 6 nickels.
Answer:
15 dimes, 6 nickels
Step-by-step explanation:
D = # of dimes, and N = # of nickels
10D + 5N = 180
D = N + 9
Substitute:
10 (N + 9) + 5N = 180
10N + 90 + 5N = 180
15N = 90
N = 6
D = 15
Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 17. Use the empirical rule to determine the following. (a) What percentage of people has an IQ score between 66 and 134? (b) What percentage of people has an IQ score less than 83 or greater than 117? (c) What percentage of people has an IQ score greater than 117? (a) 95% (Type an integer or a decimal.) (b) (Type an integer or a decimal.)
Answer:
(a) 95% of people have an IQ score between 66 and 134.
(b) 32% of people have an IQ score of less than 83 or greater than 117.
(c) 16% of people have an IQ score greater than 117.
Step-by-step explanation:
We are given that scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 17.
Let X = scores of an IQ test
SO, X ~ Normal([tex]\mu=100, \sigma^{2} = 17^{2}[/tex])
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
Now, the empirical rule states that;
68% of the data values lie within 1 standard deviation from the mean.95% of the data values lie within 2 standard deviations from the mean.99.7% of the data values lie within 3 standard deviations from the mean.(a) The percentage of people having an IQ score between 66 and 134 is given by;
z score for 66 = [tex]\frac{X-\mu}{\sigma}[/tex] = [tex]\frac{66-100}{17}[/tex] = -2
z score for 134 = [tex]\frac{X-\mu}{\sigma}[/tex] = [tex]\frac{134-100}{17}[/tex] = 2
This means that the percentage of people having an IQ score between 66 and 134 is 95%.
(b) Firstly, we have to find the percentage of people having an IQ score between 83 and 117;
z score for 83 = [tex]\frac{X-\mu}{\sigma}[/tex] = [tex]\frac{83-100}{17}[/tex] = -1
z score for 117 = [tex]\frac{X-\mu}{\sigma}[/tex] = [tex]\frac{117-100}{17}[/tex] = 1
This means that the percentage of people having an IQ score between 83 and 117 is 68%.
This means that the percentage of people having an IQ score of less than 83 or greater than 117 = 100% - 68% = 32%.
(c) In the above part, we find that there are 32% of the values that have an IQ score of less than 83 or greater than 117.
This means that half of this will be less than 83 and half of this will be greater than 117.
So, the percentage of people having an IQ score greater than 117 = [tex]\frac{32\%}{2}[/tex] = 16%.
Find the velocity. Please help. Thank you!
Answer:
His final velocity is 48.03 m/s
Step-by-step explanation:
Using SI units (m, kg, s)
a = 3.7
x0 = 25
x1 = 300
v0 = 16.5
Apply kinematics formula
v1^2 - v0^2 = 2a(x1-x0)
solve for v1
Final velocity
v1 = sqrt(2a(x1-x0)+v0^2)
= sqrt( 2(3.7)(300-25)+16.5^2) )
= 48.03 m/s
) Find the average rate of change of the area of a circle with respect to its radius r as r changes from (i) 2 to 3 (ii) 2 to 2.5 (iii) 2 to 2.1 (b) Find the instantaneous rate of change when r − 2. (c) Show that the rate of change of the area of a circle with respect to its radius (at any r) is equal to the circumference of the circle. Try to explain geometrically why this is true by drawing a circle whose radius is increased by an amount Dr. How can you approximate the resulting change in area DA if Dr is small?
Answer and Step-by-step explanation:
The rate of change of an area of a circle in respect to tis radius is given by:
ΔA / Δr = [tex]\frac{\pi(r_{1}^{2} - r_{2}^{2}) }{r_{1} - r_{2}}[/tex]
(i) 2 to 3:
ΔA / Δr = [tex]\frac{\pi(3^{2} - 2^{2}) }{3-2}[/tex] = 5π
(ii) 2 to 2.5
ΔA / Δr = [tex]\frac{\pi(2.5^{2} - 2^{2}) }{2.5-2}[/tex] = 4.5π
(iii) 2 to 2.1
ΔA / Δr = [tex]\frac{\pi(2.1^{2}-2^{2})}{2.1-2}[/tex] = 4.1π
Instantaneous rate of change is the change of a rate at a specific value. In this case, it wants at r = 2, so take the derivative of area and determine the area with the specific radius:
[tex]\frac{dA}{dr}[/tex] = π.r²
A'(r) = 2.π.r (1)
A'(2) = 4π
Note that expression (1) is the circumference of a circle, so it is shown that to determine the instantaneous rate of change of the are of a circle, is the circumference of any given radius.
The circles in the attachment shows a circle with radius r (light green) and a circle with radius r + Δr (darker green).
The rate of change between the two circles is the area shown by the arrow:
ΔA = π,[r² - (r+Δr)²]
ΔA = π.[r² - r² + 2rΔr + Δr²]
ΔA = π.(2rΔr + Δr²)
If Δr is too small, Δr² will be approximately zero, so
Δr²≈0
ΔA = π.(2rΔr)
The rate of change with respect to its radius will be:
ΔA / Δr = π.(2rΔr) / Δr
ΔA / Δr = 2.π.r
which is the circumference of a circle, so, this is the geometrical proof.