The center of mass of the thin plate of density delta = 6 bounded by the lines y = x and x = 0 and the parabola is located at (x, y) = (4/15, 1/15).
To find the center of mass of a thin plate,
Calculate the moments and products of inertia with respect to the x and y axes,
And then use them to find the coordinates of the center of mass.
First, determine the limits of integration.
Since the plate is bounded by the lines y=x and x=0 and the parabola y=20-x² in the first quadrant,
Integrate over the following limits.
0 ≤ x ≤ 4, and
x ≤ y ≤ 20 - x²
The mass of the plate can be found by integrating the density delta = 6 over the plate.
m = ∫∫over R δ dA
= ∫∫over R 6 dA
where R is the region bounded by the given curves.
m =[tex]\int_{0}^{4}[/tex] ∫x²⁰⁻ˣ² 6 dy dx
Simplifying the limits, we get,
m = ∫0⁴ 6x(20-x²) dx
Evaluating this integral gives,
m = 960
Next, find the moments and products of inertia.
The moments of inertia are given by,
Ix = ∫∫over R y² δ dA, and
Iy = ∫∫over R x² δ dA
The product of inertia is given by,
Ixy = ∫∫ over R xy δ dA
Substituting the given density delta = 6 and integrating over the region R, we get,
Ix = [tex]\int_{0}^{4}[/tex] ∫x²⁰⁻ˣ² y² 6 dy dx
= 64/3
Iy = [tex]\int_{0}^{4}[/tex] ∫x²⁰⁻ˣ² x² 6 dy dx
= 512/15
Ixy = [tex]\int_{0}^{4}[/tex] ∫x²⁰⁻ˣ² xy 6 dy dx
= 64/3
Using these moments and products of inertia,
The coordinates of the center of mass (X, Y) can be found using the following formulas.
X = Iy / m, and
Y= Iy / m
Substituting the values we have calculated, we get,
X = (512/15) / 960
= 4/15
Y = (64/3) / 960
= 1/15
Therefore, the center of mass of the thin plate is located at (x, y) = (4/15, 1/15).
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Use the figure shown below to complete the sentence? The area of the figure is blank square units
Can you pls help? This is geometry
Answer:
(x-3)^2+(y-2)^2=16
Step-by-step explanation:
The equation of a circle in standard form is (x-h)^2+(y-k)^2=r^2
So, the center is (3,2), so you have to input the opposite value.
(x-3)^2+(y-2)^2=4^2
simplify:
(x-3)^2+(y-2)^2=16
How much would a retailer pay for 30 dozen work gloves if the wholesaler's
list price is $62 a dozen, less 28% ?
The retailer would pay $1,339.20 for 30 dozen work gloves.
One dozen is equal to 12, so 30 dozen would be equal to 360 gloves.
The wholesaler's list price for one dozen gloves is $62.
The discount given by the wholesaler is 28%
The retailer pays 100% - 28% = 72% of the list price.
The price the retailer pays for one dozen gloves is:
$62 x 0.72 = $44.64
Therefore, the price the retailer pays for 30 dozen gloves is:
$44.64 x 30 = $1,339.20
So the retailer would pay $1,339.20 for 30 dozen work gloves.
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50 POINTS PLEASE HELP
A cone is shown below.
Which 2-dimensional shape results from slicing a cross section horizontally and parallel to the base.
A. rectangle
B. trapezoid
C. square
D. rhombus
E. ellipse
F. circle
Step-by-step explanation:
I don't know if so what we do this question but I kind of wish I can be with triangle don't ever stop and never ever disturb you
Solids $A$ and $B$ are similar. Use the given information and scale factor $k$ from solid $A$ to solid $B$ to find the volume of solid $B$ to the nearest thousandth. Cylinder $A$ has a volume of $112\pi$ cubic meters and $k=$ $\frac{1}{4}$. The volume of solid $B$ is about
cubic meters
The volume of solid B is about 7π cubic meters, which is approximately 21.99 cubic meters when rounded to the nearest thousandth.
The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. Since solids A and B are similar, they have the same shape, but different sizes.
Let V₁ be the volume of solid A, and V₂ be the volume of solid B. The scale factor k from solid A to solid B is 1/4, which means that the dimensions of solid B are 1/4 of the dimensions of solid A.
We can find the radius and height of solid B by multiplying the radius and height of solid A by 1/4. Therefore, we have:
V₂ = π(r/4)²(h/4) = (π/16)rh²
We are given that V₁ = 112π cubic meters, so we can solve for rh²:
112π = πr²h
rh² = 112
Substituting into the formula for V₂, we get:
V₂ = (π/16)rh² = (π/16)(112) = 7π
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Help please
I don't know ️
Please help me
Answer:
3×4-8=b
Step-by-step explanation:
The total number of batteries fatima has is :
3×4= 12
She has 12 batteries but she gave her brother 8
12-8=4
And batteries represent b
So the equation is
3×4-8=b
HELP PLEASE IF U DO I QILL GIVE 40 POINTS !!!!
Answer: c
Step-by-step explanation:
ginny and carter are learning about probability and their teacher hands them a bag with 18 red marbles and 10 green marbles. ginny draws 2 red marbles and keeps them on her desk. carter wants to draw green marbles on his turn. how did the probability of drawing a green marble change from when ginny drew her marbles to when carter will draw?
The probability of drawing a green marble for Carter increased from 0.357 to 0.385 after Ginny drew her two red marbles.
The probability of drawing a green marble for Carter did change after Ginny drew her two red marbles. This is because the total number of marbles left in the bag has decreased, which affects the probability of drawing a green marble.
Before Ginny drew her marbles, the probability of drawing a green marble for Carter was
P(Carter draws green) = 10/(18+10)
= 10/28
Divide the numbers
= 0.357
After Ginny drew her two red marbles, there are now 16 red marbles and 10 green marbles left in the bag. So the probability of drawing a green marble for Carter on his turn is
P(Carter draws green) = 10/(16+10) = 10/26 = 0.385
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What is the unit price for a piece of cheese if 1. 24 pounds costs $11. 25
The unit price for a piece of cheese is $0.11 per pound.
To find the unit price, we need to divide the total cost by the total weight. In this case, we have 1.24 pounds of cheese that costs $11.25.
So, we can set up a proportion
1.24 pounds / $11.25 = x pounds / $1
To solve for x, we can cross-multiply
1.24 pounds * $1 = $11.25 * x pounds
1.24 = $11.25 * x
x = 1.24 / $11.25
x = 0.11
So, the unit price is $0.11 per pound.
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Question 1-1
The table shows values of y relative to values of x in a proportional relationship. What is the constant of proportionality for this relationship?
X Y
6 24
8 32
10 40
12 48
Answer:
y = 4x
Step-by-step explanation:
To find the constant of proportionality, we need to calculate the ratio of y to x for any two corresponding values in the table.
Let's choose the first set of values: x = 6, y = 24.
y/x = 24/6 = 4
So the constant of proportionality is 4.
We can check this for the other sets of values as well:
- for x = 8, y = 32: y/x = 32/8 = 4
- for x = 10, y = 40: y/x = 40/10 = 4
- for x = 12, y = 48: y/x = 48/12 = 4
In each case, the ratio of y to x is equal to 4, so the constant of proportionality is indeed 4. Therefore, the relationship between x and y is:
y = 4x
Answer:10 40
Step-by-step explanation:
ADD: (Give answer in simplest form)
6 2/7+7 1/2
How can you model an expression such as a − b?
What are the solutions to the equation 9x2 = 36?
Answer: x = 2 and x = -2.
Step-by-step explanation:
The solutions to the equation 9x^2 = 36 can be found by first dividing both sides by 9, giving x^2 = 4. Then, taking the square root of both sides gives x = ±2. Therefore, the solutions are x = 2 and x = -2.
Answer:
Step-by-step explanation:
9x^2 = 36 | :9
x^2 = 4
x=+-2
Express the number 77 ten in base two
The binary representation of the number 77 ten is 1001101 two . This can be found by repeatedly dividing 77 by 2 and writing down the remainders in reverse order.
What is binary representation?Binary representation is a system of representing numbers using only two digits, usually 0 and 1. It is used extensively in digital electronics and computer programming.
What is remainder?The remainder is the amount left over after dividing one number by another. It represents the part of the dividend that could not be evenly divided by the divisor.
According to the given information:
To convert the number 77 ten to base two, we need to find the binary representation of this number.
One way to do this is to repeatedly divide the number by 2 and keep track of the remainders. We continue dividing until the quotient is 0. Then, we read the remainders in reverse order to get the binary representation.
Here's how the calculation works:
77 divided by 2 is 38 with a remainder of 1. Write down the remainder (1).38 divided by 2 is 19 with a remainder of 0. Write down the remainder (0).19 divided by 2 is 9 with a remainder of 1. Write down the remainder (1).9 divided by 2 is 4 with a remainder of 1. Write down the remainder (1).4 divided by 2 is 2 with a remainder of 0. Write down the remainder (0).2 divided by 2 is 1 with a remainder of 0. Write down the remainder (0).1 divided by 2 is 0 with a remainder of 1. Write down the remainder (1).Reading the remainders in reverse order gives us 1001101, which is the binary representation of 77 ten. Therefore, 77 ten = 1001101 two .
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In the picture below Pac-Man, from the video game PAC-MAN, is shown eating ghosts. In the pictare his mouth is open 60° and the radius of the circle is 13 mm, What is the area of the Pac-Man, to the nearest tenth mm"?
The solution of Circle and angle problem is the area of the Pac-Man, to the nearest tenth mm" is 131.8 mm²
what is circle and angle ?A circle is a geometric shape that is defined as the set of all points in a plane that are equidistant from a fixed point called the center.
An angle is a measure of the amount of turn between two lines that share a common endpoint, called the vertex of the angle.
According to given informationTo find the area of the Pac-Man, we need to find the area of the sector that represents its mouth and subtract the area of the triangle formed by the two radii and the chord of the sector.
First, we need to find the length of the arc that represents the mouth of Pac-Man. The formula for the length of an arc is:
L = (θ/360) x 2πr
Where L is the length of the arc, θ is the central angle in degrees, r is the radius of the circle, and π is approximately 3.14.
Plugging in the values we have:
L = (60/360) x 2π(13)
L = 4.29 mm
Next, we can find the area of the sector that represents the mouth of Pac-Man. The formula for the area of a sector is:
A = (θ/360) x πr²
Where A is the area of the sector, θ is the central angle in degrees, and r is the radius of the circle.
Plugging in the values we have:
A = (60/360) x π(13)²
A = 141.37 mm^2
Finally, we need to find the area of the triangle formed by the two radii and the chord of the sector. We can use the formula for the area of a triangle:
A = (1/2) x base x height
The base of the triangle is the chord of the sector, which is equal to twice the radius multiplied by sin(θ/2):
base = 2r x sin(θ/2)
base = 2(13) x sin(30)
base = 13 mm
The height of the triangle is equal to half the length of the chord times cos(θ/2):
height = (1/2) x (L/2) x cos(θ/2)
height = (1/2) x (4.29/2) x cos(30)
height = 1.47 mm
Plugging in the values we have:
A = (1/2) x 13 x 1.47
A = 9.53 mm²
Therefore, the area of the Pac-Man (sector minus triangle) is approximately:
A = 141.37 - 9.53
A = 131.84 mm²
Rounded to the nearest tenth, the area of the Pac-Man is 131.8 mm²
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please please please please please please please please help me out
The predicted length for a catfish with weight of 48 pounds is given as follows:
45 inches.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.Two points on the graph of the linear function are given as follows:
(20, 3) and (30, 21).
When x increases by 10, y increases by 18, hence the slope m is given as follows:
m = 18/10
m = 1.8.
Hence:
y = 1.8x + b.
When x = 20, y = 3, hence the intercept b is given as follows:
3 = 1.8(20) + b
b = 3 - 36
b = -33.
Hence the equation is:
y = 1.8x - 33.
The predicted length for a catfish with weight of 48 pounds is obtained as x when y = 48, hence:
48 = 1.8x - 33
x = 81/1.8
x = 45 inches.
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What is the probability that this person works at the Rhyl site?
First time seeing this type of question
Answer:
1/200×60/360=1/6÷200
1
Find the side lengths for the triangle with the following
measurements.
If your answer is not an integer round it to the nearest
hundredth.
side c = 50 and angle B = 21 degrees
side a =
side b=
The value of side a and b for the given triangle is 46.68 units and 17.92 units.
What is law of sines?A triangle's angles and side lengths are related by the law of sines, a trigonometric identity. It asserts that the ratio of the sine of one angle to the length of the side opposite that angle is constant for all three angles for any triangle with sides a, b, and c and opposing angles a, b, and c:
If a/sin(A) = b/sin(B) = c/sin(C), then
As long as at least one angle and its matching side length are known, this can be used to solve for unknown angles or side lengths in a triangle.
For the given triangle we have:
cos B = a / c
Thus, substituting the values we have:
cos 21 = a / 50
a = 46.68 units.
Now, sin B = b/50
Sin 21 = b / 50
b = 17.92 units.
Hence, the value of side a and b for the given triangles is 46.68 units and 17.92 units.
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The complete question is:
A random sample of 100 people was taken. Eighty-five of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 80%.
(1). The test statistic is
0.80
0.05
1.25
2.00
By z-test the test static is 1.25.
What is z-test?
It is a statistical test to determine whether two population means are different at the time when the variances are known and the sample size is large. Also it is a hypothesis test in which the z-statistic maintains a normal distribution.
A random sample of 100 people was taken. Eighty-five of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 80%.
So from the given information we have,
sample size (n)= 100
sample proportion ( p₁) = 0.85 [ 85 of the people in the sample favored candidate A]
So, the null hypothesis ,
H₀ : p = 0.80
The alternative hypothesis ,
Hₐ : p > 0.80
Now the test static can be determined by the formula of z-test
[tex]z= \frac{p_{1} - p }{\sqrt{\frac{p(1-p)}{n} } }[/tex]
[tex]z= \frac{0.85 - 0.80 }{\sqrt{\frac{0.80(1-0.80)}{100} } }[/tex]
[tex]z= \frac{0.05}{\sqrt{\frac{0.16}{100} } }[/tex]
z = (0.05× 10)/0.4
z= 1.25
Hence , by z-test the test static is 1.25.
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Mr. Saltanovitz built a square picture frame as
a gift for his wife. He measured the diagonals
of the frame to be 10 inches. But when she
opened the picture frame, she asked him
what size pictire would fit inside. Mr.
Saltanovitz quickly did some math in his head
and told her the dimensions.
What were the dimensions of the picture
frame (what is the length and width of the
frame)? Round to the nearest tenth of an
inch. Show the work you used to find the
dimensions.
The length and width of the square picture frame are both approximately 7.08 inches. The dimensions of the picture that would fit inside the frame are approximately 6.5 inches.
The diagonal of a square:In a square, the diagonal is a line segment that connects opposite corners of the square. Since a square has four congruent sides, we can use the Pythagorean theorem to find the length of the diagonal "d" in terms of the length "s" of the sides. The formula used is given by
=> d² = s² + s²
Here we have
The diagonal of the frame is 10 inches
Let's assume that the length and width of the square picture frame are both "x" inches.
Then, using the Pythagorean theorem, we can express the length of the diagonal (d) of the square picture frame in terms of "x":
=> d² = x² + x²
Simplifying this equation, we get:
=> d² = 2x²
We know that the length of the diagonal is 10 inches, so we can write:
=> 100 = 2x²
Solving for "x", we get:
=> x² = 50
=> x = 5√2
=> x = 7.071 inches
Therefore,
The length and width of the square picture frame are both approximately 7.08 inches.
To find the dimensions of the picture that would fit inside the frame, we can simply subtract a margin of, say, 0.5 inches from each dimension to allow for the picture to fit comfortably within the frame.
So, the dimensions of the picture that would fit inside the frame are approximately 6.5 inches by 6.5 inches.
Therefore,
The length and width of the square picture frame are both approximately 7.08 inches. The dimensions of the picture that would fit inside the frame are approximately 6.5 inches.
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5000 mL = how many liters?
5
Step-by-step explanation:
1000 ml= 1L
Answer: 5 liters
Step-by-step explanation:
We will use the knowledge of 1 liter being equal to 1,000 mL. Since we are trying to change 5,000 mL into liters, we will use dimensional analysis. We want to end up with liters, so we will put 1 liter over 1,000 mL so the mL units cancel out, since [tex]\frac{mL}{mL}[/tex] = 1.
[tex]\displaystyle (\frac{5,000\;mL}{1}) (\frac{1 \;liter}{1,000\;mL} )=5\;liters[/tex]
50 POINTS
The average speed of a baseball line drive is 82 miles per hour. Josiah practiced a new technique to improve his hitting speed. His coach recorded the speed of 45 random hits during practice and found that his average speed using the new technique was 83.2 miles per hour, with a standard deviation of 4.6 miles per hour.
Part A: State the correct hypotheses if Josiah is trying to prove the new technique is an improvement over the old technique. (2 points)
Part B: Identify the correct test and check the appropriate conditions. (4 points)
Part C: Carry out the test and determine if there is sufficient evidence at the 0.01 level that Josiah's technique has improved his drive speed.
On solving the provided question, we can say that As a result, we lack sufficient data at the hypothesis 0.01 level to declare that Josiah's new strategy has increased his driving speed.
What is null hypothesis?A null hypothesis is a statistical hypothesis that states that a certain collection of observations has no statistical significance. Hypotheses are examined using sample data to determine their viability. It is also known as "zero" and is represented by the symbol H0. Researchers begin with the assumption that there is a relationship between the variables. The null hypothesis, on the other hand, asserts that there is no such link. Although the null hypothesis may not appear to be significant, it is an important component of research.
Part A: The following are the hypotheses for Josiah's test:
There is no statistically significant change in the average speed of Josiah's hits utilising the old and new techniques. In scientific notation: H0 = 1 - 2 = 0, where 1 represents the population mean speed of hits using the old approach and 2 represents the population mean speed of hits using the new technique.
Alternative hypothesis: There is a substantial difference in the average speed of Josiah's hits when employing the old and new techniques, with the new technique producing a faster average speed. In mathematical terms: Ha: 1 - 2 0.
Part B: We'll use a t-test because we're comparing two means and don't know the population standard deviation. We will assume that the sample sizes are big enough for the Central Limit Theorem to apply, and that the sample means have a normal distribution. We also suppose that the two samples are independent, which means that the speed of one strike is independent of the speed of the other.
Part C: To run the test, we must compute the test statistic and compare it to the critical value with 44 degrees of freedom (n1 + n2 - 2).
The test statistic is calculated as follows:
[tex]t = (x1 - x2 - 0) / (s / \sqrt(n1 + n2 - 2))[/tex]
where x1 represents the sample mean speed using the old approach, x2 represents the sample mean speed using the new technique, s represents the pooled standard deviation, and n1 and n2 represent the sample sizes.
When we plug in the values, we get:
[tex]t = (82 - 83.2 - 0) / (4.6 / \sqrt(45)) = -2.06[/tex]
At the 0.01 significance level, the critical value for a one-tailed t-test with 44 degrees of freedom is -2.681. We cannot reject the null hypothesis since our test statistic (-2.06) is bigger than the crucial threshold.
As a result, we lack sufficient data at the 0.01 level to declare that Josiah's new strategy has increased his driving speed.
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The perimeter of a triangle is 73 inches. If the second side is 5 inches longer than twice the first side, and the third is 4 inches less than twice the first side how long is each side?
Using the formula for the perimeter of a triangle, x + (2x+5) + (2x-4) = 73. Solving for x, so the first side is 18 inches, the second side is 41 inches, and the third side is 32 inches.
What is perimeter?Perimeter is the total distance around the outside of a closed two-dimensional shape, such as a polygon or a circle. It is found by adding the lengths of all the sides of the shape.
What is equation?An equation is a mathematical statement that shows the equality of two expressions or values, often with one or more variables that can be solved for.
According to the given information :
Let the first side of the triangle be x.
Then, the second side is 2x + 5, and the third side is 2x - 4, according to the given conditions.
The perimeter of the triangle is the sum of the lengths of its sides, so we can write:
x + (2x + 5) + (2x - 4) = 73
Simplifying the equation:
5x + 1 = 73
5x = 72
x = 14.4
Therefore, the first side of the triangle is 14.4 inches, the second side is 2(14.4) + 5 = 33.8 inches, and the third side is 2(14.4) - 4 = 24.8 inches.
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PLEASE HELPPP DUE SOONN
The line(s) or plane(s) that contain point N and appear to fit the description are as follows;
Line perpendicular to QR is NR.
Line parallel to QR is PN.
Line(s) skew to JN.
Plane parallel to plane LMQ is JNP.
All the pairs of angles have been identified below.
The values of x and y are shown below.
How to identify all pairs of angles?In this exercise, all of the various pairs of angles should be identified as follows;
Consecutive interior = ∠3 and ∠5.
Consecutive interior = ∠4 and ∠6.
Alternate interior = ∠3 and ∠6.
Alternate interior = ∠4 and ∠5.
Alternate exterior = ∠1 and ∠8.
Alternate exterior = ∠2 and ∠7.
Corresponding = ∠1 and ∠5.
Corresponding = ∠2 and ∠6.
Corresponding = ∠3 and ∠7.
Corresponding = ∠4 and ∠8.
Next, we would determine the values of x and y as follows;
x + 35 = 180 (sum of angles on a line)
x = 180 - 35
x = 145°
y = 35 (corresponding angles theorem).
y + 48 = 180
y = 180 - 48
y = 132°
5x - 17 = 48 (vertical angles theorem).
5x = 65
x = 13°.
2x + 58 = 180 (sum of angles on a line)
2x = 238
x = 119°.
2y = 58 (corresponding angles theorem).
y = 29°.
5y - 21 = (180 - 116)
5y = 21 + 64
y = 85/5
y = 17
6x + 32 = 116
6x = 116 - 32
x = 84/6
x = 14
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A study is done on the population of a certain fish species in a lake. Suppose that the population size P (t) after t years is given by the following exponential function P(t)=510(0.72)^t
The population size of the fish species after 5 years is approximately 99.
What is the Population Size of the Species?The population size of the fish species after t years is given by the exponential function P(t)=510(0.72)^t. To find the population size, we simply need to substitute the given value of t in the equation.
For example, if we want to find the population size after 5 years, we substitute t=5 in the equation:
P(5) = 510(0.72)^5
P(5) = 510*0.1934917632
P(5) = 98.680799232
P(5) ≈ 99.
Therefore, the population size of the fish species after 5 years is approximately 99.
We can determine whether the population is growing or decaying by examining the value of the base of the exponential function, which is 0.72 in this case. Since the base is less than 1, we know that the exponential function represents exponential decay. This means that the population of the fish species in the lake is decreasing over time, and the rate of decrease is determined by the value of the base. In this case, the population is decreasing by a factor of 0.72 each year.
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if the diameter of a circle is 4x+12 then find the area?
please solve this question...this question is based on "multiplying binomials by binomials"
since the formula for the area of a circle squares the radius, the area of the larger circle is always 4 or 22 multiple the tiny square
Use your shapes to create a new shape with an area of 4 square units. Trace your shape.
We can construct a shape of area 4 square meters using the four shapes square, rectangle, triangle and parallelogram.
What are your knowledge of area ?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
The area of a plane figure is the area that its perimeter encloses. The amount of units in a figure determines its area. Area is measured in square units like cm² and m². Area of a shape is a two dimensional quantity.
Area of a square = side² (a²)
Area of a triangle = 1/2 × base length × height (1/2×b×h)
Area of a rectangle = length × breadth ( l×b )
Area of a parallelogram = base length × height ( b×h)
Consider the square of side 1 m
Area = 1 × 1 = 1 m²
Now consider the triangle of base length , b = 1/2 m and height, h = 2 m
∴ Area = 1/2×1/2×2 = 1/2 m²
Once more , area of the parallelogram of side 1 m and height 2 m is given by
Area = 1×2= 2 m²
For the rectangle of length 1/2 m and breadth 1 m
Area = l × b = 1/2 × 1 = 1/2 m²
∴ Total area = 1 + 1/2 + 2 + 1/2 = 4 square meter.
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If the height of this prism is 10 cm, what is the surface area
of the rectangular prism?
Surface Area = 2lw + 2lh + 2wh
5 cm
5 cm
Answer:
2(5)(5) + 4(5)(10) = 50 + 200 =
250 square centimeters
Suppose that a Normal model described student scores in a history class. Parker has a standardized score (z-score) of +2.5. This means that Parker
A. is 2.5 points above average for the class.
B. none of these
C. is 2.5 standard deviations above average for the class.
D. has a score that is 2.5 times the average for the class.
E. has a standard deviation of 2.5.
Parker's standardized score (z-score) of +2.5 means that he is 2.5 standard deviations above the average score for the class. C
Normal distribution, the mean (average) is represented by the letter μ and the standard deviation by σ.
The z-score is a measure of how many standard deviations a data point is away from the mean.
A positive z-score indicates that the data point is above the mean, while a negative z-score indicates that it is below the mean.
Parker's z-score of +2.5 tells us that his score is 2.5 standard deviations above the class average.
We don't know the exact values of μ and σ, but we can use the properties of the Normal distribution to make some general statements about Parker's score.
99% of the data in a Normal distribution falls within 3 standard deviations of the mean.
Since Parker's z-score is 2.5, we can estimate that his score is higher than about 99% of the scores in the class.
Parker is performing very well in the history class compared to his peers.
z-score is a standardized measure, which means that it can be used to compare scores from different distributions.
If we wanted to compare Parker's score to the scores of students in another class, we could convert both sets of scores to z-scores and compare them directly.
Parker's z-score of +2.5 means that he is performing exceptionally well in the history class, with a score that is 2.5 standard deviations above the class average.
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