Answer:
There are 775 - 91 + 1 = 685 integers.
In the given range, the smallest multiple of 14 is 98, and the largest multiple of 14 is 770. ((770-98)/14) + 1 = 49 multiples of 14.
So the probability of choosing a multiple of 14 from this range is 49/685.
for security purposes a jewelry company prints a hidden watermark on the logo of its official documents. the watermark is a chord located 0.7 centimeter from the center of a circular ring that has a radius measuring 2.5 centimeters. what is the length of the chord?
The chord length is approximately 1.397 centimeters where 0.7 centimeters is the separation from the center of the circle to the chord.
We can use the properties of circles to find the angle formed by the chord at the center of the circle to evaluate the length of the chord.
0.7 centimeters is the separation from the center of the circle to the chord. This remove is additionally the stature of the isosceles triangle shaped by the chord and the two radii of the circle.
Let θ be the angle between the chord and the center of the circle. You can use trigonometry to find θ.
sin(θ/2) = 0.7/2.5
[tex]θ/2 = sin⁻¹(0.7/2.5)[/tex]
θ/2 = 0.2793
θ=2×0.2793
θ ≈ 0.5586 radians
Now that we know θ, we can use the formula for the chord length of a circle.
chord length = 2 × radius × sin(θ/2)
Chord Length = 2 × 2.5 × sin(0.2793)
String length ≈ 1.397 cm
Therefore, the chord length is approximately 1.397 centimeters.
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Not all systems of equations have solutions. Determine which systems below have solutions and which ones don’t.
There is no solution to this system of equations. (option B).
What is equation?
An equation is a mathematical statement which is made by two expressions connected by an equal sign. For example, 3x – 8 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 8.
There is no solution to the given graph of two linear equations or system of linear equations.
From the given graph it is clear that graph of the given two equations shows two lines that are parallel to each other. They don't meet or intersect each other at any point.
Since no point is on both lines, there is no ordered pair that makes both equations true.
Hence, there is no solution to this system of equations.
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DUE FRIDAY PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!!
The equation of the circle passing through (6,1) and having a centre at (2,-3) is (x - 2)² + (y + 3)² = 32.
Explain the term centre
A centre is a point or location that is at the middle or heart of something. It can refer to the physical centre of an object or the conceptual centre of an idea or system. Centres can be used as reference points for measurements, calculations, or decision-making processes.
According to the given information
Here we can use the distance formula:
√((x - 2)² + (y + 3)²) = r
We also know that the circle passes through the point (6, 1). Substituting these coordinates into the equation above, we get:
√((6 - 2)² + (1 + 3)²) = r
√(16 + 16) = r
r = 4√(2)
Now we can use the centre and radius to write the equation of the circle in standard form:
(x - 2)² + (y + 3)² = (4√(2))²
(x - 2)² + (y + 3)² = 32
Therefore, the equation of the circle passing through (6,1) and having a centre at (2,-3) is (x - 2)² + (y + 3)² = 32.
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Taner wants to run a total of 6 kilometers between last week and this week. How far does Taner need to run this week to reach his goal?
Taner will only need to run 3 km this week to complete his 6 km running goal.
Describe the fractional number in detail:If we require a definition, we may start by saying that fractional numbers are numbers that symbolize one or possibly more portions of a unit that has been subdivided into equal parts.
To determine the fractional numbers, two whole numbers (including fraction terms) are separated by a horizontal line (the fraction line). The denominator just below line must be different from zero, whereas the numerator well above line may be any whole number.Given that, Taner's overall running goal is 6 km (including last week and this week)
So,
Taner's 2-week goal is 6 kilometres.
Now,
Taner's goal for the week is 3 kilometres = (6/2).
As the Taner completed 3 km of running last week. Taner can achieve his objective this week by running just 3 miles.
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y=3-x 3y+x=5 solve by substitution method
Answer:
x = 2
y = 1
Step-by-step explanation:
3y + x = 5 y = 3 - x
3(3 - x) + x = 5
9 - 3x + x = 5
9 - 2x = 5
-2x = -4
x = 2
Now put 2 in for x and solve for y
3y + x = 5
3y + 2 = 5
3y = 3
y = 1
Let's Check
1 = 3 - 2
1 = 1
So, x = 2 and y = 1 is the correct answer.
Emily predicted her car payment to be $250 each month. Her actual car payment is $275 each month. By what percent was Emily’s prediction off?
Answer:
10%
Step-by-step explanation:
Question 13(Multiple Choice Worth 2 points)
(Making Predictions MC)
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the number of cookies the college will need?
The college will have about 480 students who prefer cookies.
The college will have about 640 students who prefer cookies.
The college will have about 1,280 students who prefer cookies.
The college will have about 1,440 students who prefer cookies.
The claim that makes the most accurate statement regarding how many cookies the institution will require There will be 480 pupils who favour cookies at the college.
Explain about the percentages:Decimals or fractions can also be used to represent percentages. Divide a percentage by 100 to turn it into a fraction.
If the sample of 225 students was truly random and not just selected from a certain group, we may calculate percentages depending on it.
For this computation, see the worksheet that is provided. Pie was favoured by 16% of the 225 students, as can be seen. These percentages can be employed to forecast the number of students in each category if they are reflective of the 4000-student overall student population. 640 students make up 16% of 4000.As a result, "There will be roughly 640 pie-loving pupils at the college."
Thus, the claim that makes the most accurate forecast regarding how many cookies the institution will require There will be 480 pupils who favour cookies at the college.
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can yall help me on this i have been stuck on it for a long time
The least common multiple of two or more numbers is the smallest number that is a multiple of each of the given numbers. For example, the LCM of 2 and 3 is 6, because 6 is the smallest number that is a multiple of both 2 and 3.
For this problem, the number of packs bought is the least common multiple of 10 and 12, which is obtained by factoring them into prime numbers as follows:
10 - 12|2
5 - 6|2
5 - 3|3
5- 1|5
1 - 1
Hence:
lcm(10, 12) = 2² x 3 x 5 = 60.
Hence:
The number of packs of buns is given as follows: 6, as 60/10 = 6.The number of hot dogs is given as follows: 5, as 60/12 = 5.More can be learned about the least common multiple at https://brainly.com/question/10749076
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The sum of the interior angles of a regular polygon is 1080°.
a. ) Classify the polygon by the number of sides.
b. ) What is the measure of one interior angle of the
polygon?
c. ) What is the measure of one exterior angle of the
polygon?
a) The polygon has 8 sides and is called an octagon.
b) The measure of each interior angle of the octagon measures 135 degrees.
c) The measure of each exterior angle of the octagon measures 45 degrees.
a. To classify the polygon by the number of sides, we can use the formula for the sum of the interior angles of a polygon:
Sum of interior angles = (n - 2) x 180 degrees
where n is the number of sides of the polygon.
In this case, we are given that the sum of the interior angles is 1080 degrees. So we can set up an equation as follows:
(n - 2) x 180 = 1080
Simplifying this equation, we get:
n - 2 = 6
n = 8
b. To find the measure of one interior angle of the polygon, we can use the formula for the measure of each interior angle of a regular polygon:
Measure of each interior angle = (n - 2) * 180 degrees / n
Substituting n = 8 into this formula, we get:
Measure of each interior angle = (8 - 2) * 180 degrees / 8
= 135 degrees
c. To find the measure of one exterior angle of the polygon, we can use the fact that the sum of the interior and exterior angles of a polygon is 180 degrees. Therefore, the measure of each exterior angle of a regular polygon is:
Measure of each exterior angle = 360 degrees / n
Substituting n = 8 into this formula, we get:
Measure of each exterior angle = 360 degrees / 8
= 45 degrees
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Bonsoir j'arrive pas à faire c'est deux exo sur la proportionnalité merci de l'aide bonne soirée.
Exercice 2, Pour faire un mélange de café, on utilise 150 kg d'arabica et 80 kg de robusta. Pour obtenir 805 kg de mélange de même composition.
Quelle quantité doit-on utiliser de chaque qualité de café ?
Exercice 3, Pour faire une boisson à la framboise, André met 4 volumes de sirop pour 7 d'eau et Béatrice met 5 volumes de sirop pour 9 d'eau.
Quelle est la boisson la plus sucrée?
l'exercice 3 est la boisson d'Andres. Je suis désolé si cela ne ressemble pas vraiment à un français parfait, je parle anglais et j'utilise Translate. passe une bonne journée!
A rock brought back from the moon contained 1/8 of the radioactive substance that was present when the rock was formed. If the half-life of this substance is 1.5 billion years, how old in the moon rock?
PLS anser quick
Answer:
4.5 billion years
Step-by-step explanation:
Answer: We can use the formula for radioactive decay:
N = N0 * (1/2)^(t/T)
where N is the current amount of the radioactive substance, N0 is the original amount, t is the time that has passed, T is the half-life.
Let's assume that the original amount of the substance in the rock was 8 units. If the current amount is 1 unit, then:
1 = 8 * (1/2)^(t/1.5 billion)
Taking the natural logarithm of both sides, we get:
ln(1) = ln(8) - (t/1.5 billion)*ln(2)
Simplifying:
0 = ln(8) - (t/1.5 billion)*ln(2)
t/1.5 billion = ln(8)/ln(2)
t = 1.5 billion * (ln(8)/ln(2))
t ≈ 3.91 billion years
Therefore, the moon rock is about 3.91 billion years old.
Step-by-step explanation:
7) suppose that the temperatures of healthy humans are approximately normally distributed with a mean of 98.6 degrees and a standard deviation of 0.8 degrees. if 130 healthy people are selected at random, the probability that the average temperature for these people is 98.25 degrees or higher is closest to
Answer: To solve this problem, we need to use the central limit theorem to find the distribution of the sample means. The central limit theorem states that if we take random samples of size n from a population with a mean μ and a standard deviation σ, the distribution of the sample means approaches a normal distribution with a mean of μ and a standard deviation of σ/√n, as n gets larger.
In this case, we have a population of healthy humans with a mean temperature of μ = 98.6 degrees and a standard deviation of σ = 0.8 degrees. We want to find the probability that the average temperature for a sample of 130 healthy people is 98.25 degrees or higher. The sample size is large enough to use the normal distribution to approximate the distribution of the sample means.
The z-score corresponding to a sample mean of 98.25 degrees is:
z = (98.25 - 98.6) / (0.8 / sqrt(130)) = -1.91
Using a standard normal distribution table or calculator, we can find the probability that a standard normal random variable is greater than -1.91:
P(Z > -1.91) = 0.9719
Therefore, the probability that the average temperature for a sample of 130 healthy people is 98.25 degrees or higher is approximately 0.9719 or 97.19%.
Step-by-step explanation:
Justine takes a sheet of paper and makes a diagonal cut from one corner to the opposite corner, making two triangles. The cut she makes is 5 inches long and the width of the paper is 3 inches. What is the paper's length? inches
The whole number 330 is divisible by 2, 3, 5, 6, 10, and 11.
TrueFalse
Answer: True
Step-by-step explanation:
Answer:
Step-by-step explanation:
330/2 = 165
330/3 = 110
330/5 = 66
330/6 = 55
330/10 = 33
330/11 = 30
the answer is true
can you help me with numbers 4 and 5 please, this has to be in by tomorrow
Answer:
4. The smaller angle is 35°.
5. AngleCAB = 40°
AngleDAC = 50°
Step-by-step explanation:
4) The 3 angles shown all together add up to 180°.
3x+10 + 90° + 2x+5 = 180°
combine like terms.
5x + 105 = 180
subtract 105
5x = 75
divide by 5
x = 15
One of the angles is 3x+10 and the other is 2x+5.
2x+5 is the smaller angle. If x=15, then 2x+5
= 2(15) + 5
= 30 + 5
= 35
The smaller angle is 35°.
5) The two angles in this question add up to 90°.
7x-16 + 6x+2 = 90°
combine like terms
13x - 14 = 90
add 14
13x = 104
divide by 13
x = 8
Angle CAB = 7x - 16
= 7(8) - 16
= 56 - 16
= 40
AngleCAB = 40°
AngleDAC = 6x + 2
= 6(8) + 2
= 48 + 2
= 50
We also could have just subtracted to find angleDAC 90 - 40 = 50.
AngleDAC = 50°
City Hospital reported 49 deaths in June. There were 489 discharges. Eight of those deaths occurred within 48 hours of admission. What is the gross death rate?
The gross death rate is 8.38%.
What is a Rate?
A rate is a measure of the frequency of an event or occurrence in relation to a specific population or time period. Rates are often expressed in terms of units per time or per population, such as cases per 100,000 people or births per year.
The gross death rate is the number of deaths in a given time period divided by the total population or, in this case, the total number of discharges.
To calculate the gross death rate for City Hospital in June, we need to subtract the eight deaths that occurred within 48 hours of admission from the total number of deaths:
Total deaths = 49 - 8 = 41
Then, we divide the total number of deaths (41) by the total number of discharges (489) and multiply by 100 to get the rate per 100 discharges:
Gross death rate = (41 ÷ 489) x 100 = 8.38%
Therefore, the gross death rate for City Hospital in June is 8.38%.
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five birds were perched on a branch could half of the fly away why or why not
Cassie starts college in the fall and has decided to live in an apartment. Her monthly living ex- penses are as follows: Rent with utilities: $800 Hydro: $40 Phone/internet/TV: $129 Groceries: $300 (a) If she attends school for 18 months, what will be her total living expenses?
What value of x makes this equation true?
A. x = −48
B. x = 1
C .x =1/2
D. x = 8
The value of x that makes the equation true is 8
What is linear equation?A linear equation is a type of equation that the highest power of it's variable is 1. Example of linear equation include, x+2 =y, x+7/2 =15.
The graph of a linear equation is a straight line and it is represented in form of y = mx+b. Where m is the slope and b is the y intercept.
Solving x-7 = (3/4)x -5
collecting like terms
x-(3/4)x = 7-5
x/4 = 2
x = 8
therefore the value of x that will make the equation x-7 = (3/4)x -5 true is 8.
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Given the triangle ABC, if angle A is 9 º, side a is 44 m, and side b is 46 m, find angle C. Please round to one decimal
The angle of C is 161.4°.
Law of Sine:Law of sines defines the ratio of sides of a triangle and their respective sine angles are equivalent to each other. The other names of the law of sines are sine law, sine rule and sine formula.
We have :
In the Triangle ABC,
Angle A is 9 º
Side of a is 44 m,
and side of b is 46 m
To find the angle of C
Now, use the law of sines to find angle B:
b/sin B = a/sin A
Plug all the values in above formula :
=> 46/Sin B = 44/Sin 9°
=> 46 × Sin9°/ 44 = Sin B
Sin B = 0.164
[tex]B = Sin^-^10.164[/tex]
B = 9.555
Now, By angle sum of property of a triangle,
The sum of three angles of a triangle is 180°
So, Let's apply angle sum property to find angle C
=> ∠ A + ∠ B + ∠C = 180°
Put the value of B = 9.555 and angle A = 9°
=> 9° + 9.555 + ∠C = 180°
18.555 +∠C = 180°
∠C = 180°- 18.555
∠C = 161.4°
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Please help!! I missed yesterday…
a.
the value of s that yields the coordinate (2, 0) is 2.
b.
the value of s that yields the coordinate (9, 1) is estimated 9.055.
How do we calculate?we use the distance formula between the origin and point P on the path:
d(P) = √ (x^2 + y^2) = s
For the coordinate (2, 0), we have x = 2 and y = 0. So, we can plug these values into the distance formula and solve for s:
d(P) = √(x^2 + y^2)
= √t(2^2 + 0^2) = 2
For the coordinate (9, 1), we have x = 9 and y = 1. So, we can plug these values into the distance formula and solve for s:
d(P) = √t(x^2 + y^2)
= √t(9^2 + 1^2)
= √(82)
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3. A box contains 36 books and some toys. The ratio of the number of books to the number of toys is 4 : 5.
After some toys are given away, the ratio of the number of books to the number of toys becomes 12:11. Find:
(1) the initial number of toys in the box,
(2) the number of toys that are given away.
Answer:
4512Step-by-step explanation:
Given 36 books in a box with toys such that the books : toys ratio is 4 : 5, you want the initial number of toys and the number given away if the ratio becomes 12 : 11.
RatiosThe number of books remains constant at 36. We can rewrite the ratios so that each shows the correct number of books:
ratios are books : toys
before: 4 : 5 = 36 : 45 . . . . . . . multiply by 9
after: 12 : 11 = 36 : 33 . . . . . . . . multiply by 3
1. Initial ToysBased on the above, we see the initial number of toys is 45.
2. Given awayThe final number of toys is 33, so the number given away is ...
45 -33 = 12
12 toys were given away.
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x2 − 12x + 49 = 22.
Which equation has the same solution(s) as the given equation?
M. (x − 6)2 = 9
P. (x − 7)2 = 22
R. (x + 7)2 = 4.7
S. (x − 12)2 = −27
By quadratic formula the equation that has the same solution(s) as X² − 12x + 49 = 22 is M. (x − 6)² = 9 since it has solutions x=3 and x=9 which are also solutions to X² − 12x + 49 = 22
quadratic formula defined?The quadratic equation ax² + bx + c = 0 can be resolved using the quadratic formula.
that uses the constants (a, b, c) and the numerical coefficients.
When factoring cannot be utilized to solve the quadratic expressions, this approach of solving a quadratic equation is typically used.
x = √(b² - 4ac) / (-b √(b²) / (2a)
We must solve each of the preceding equations to determine which one has the same solution(s) as X²- 12x + 49 = 22 in order to determine which equation has the same solution(s) as X²- 12x + 49 = 22.
Let's start by figuring out X²- 12x + 49 = 22:
X² − 12x + 49 = 22
X² − 12x + 27 = 0
The quadratic formula can then be used to find the value of x:
x = √(b² - 4ac) / (-b√(b²) / (2a)
where a=1; b=-12; and c=27.
x = (-(-12) ±√((-12)² - 4(1)(27))) / (2(1))
x = (12 ±√(144 - 108)) / 2
x = (12 √(36))/ 2
x = (12 6) / 2
x = 6,3
So x = 6,3 is the answer to the equation X²- 12x + 49 = 22.
Let's now resolve each of the provided equations:
M. (x − 6)² = 9 (x -6)² -9=0
(x-6+3)(x-6-3)=0
(x-3)(x-9)=0, where x=3 or x=9
P. (x − 7)² = 22 (x-7)²-22=0
(x-7+√(22))=0
(x=7+√(22))
or (x=7-√(22))
R. (x + 7)² = 4.7 (x+7)²-4.7=0
(x+7+√(4.7))(x+7-√(4.7))=0
No effective remedies
S. (x − 12)²= −27 (x-12)²+27=0
No effective remedies
Therefore, the equation that has the same solution(s) as X² − 12x + 49 = 22 is M. (x − 6)² = 9
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8 Find in degrees. 17 [?] degrees Round to the nearest hundredth.
Answer:
Θ ≈ 28.07°
Step-by-step explanation:
using the sine ratio in the right triangle
sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{8}{17}[/tex] , then
Θ = [tex]sin^{-1}[/tex] ( [tex]\frac{8}{17}[/tex] ) ≈ 28.07° ( to the nearest hundredth )
A particle moves along the y-axis so that at time t≥0 its position is given by y(t)=t3−6t2+9t. Over the time interval 0
Therefore, the maximum displacement of the particle is 4 units, and it occurs at time t = 1.
To find the maximum displacement, we need to first determine the particle's velocity and acceleration.
The velocity of the particle is given by the derivative of its position function:
[tex]v(t) = y'(t) = 3t^2 - 12t + 9[/tex]
The acceleration of the particle is given by the derivative of its velocity function: a(t) = v'(t) = 6t - 12
Now, to find the maximum displacement, we need to find the time at which the particle comes to rest.
This occurs when its velocity is zero:
[tex]3t^2 - 12t + 9 = 0[/tex]
Simplifying this equation, we get:
[tex]t^2 - 4t + 3 = 0[/tex]
This quadratic equation factors as:
(t - 1)(t - 3) = 0
So the particle comes to rest at t = 1 or t = 3.
Next, we need to determine whether the particle is at a maximum or minimum at each of these times.
To do this, we look at the sign of the acceleration:
When t = 1, a(1) = 6(1) - 12 = -6, which is negative.
Therefore, the particle is at a maximum at t = 1.
When t = 3, a(3) = 6(3) - 12 = 6, which is positive.
Therefore, the particle is at a minimum at t = 3.
Finally, we need to find the displacement of the particle at each of these times:
[tex]y(1) = 1^3 - 6(1)^2 + 9(1) = 4[/tex]
[tex]y(3) = 3^3 - 6(3)^2 + 9(3) = 0.[/tex]
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Write five other iterated integrals that are equal to the given iterated integral. Integral^1_0 Integral^1_y Integral^y_0 f(x, y, z)dz dx dy Integral^1_0 Integral^1_y Integral^z_0 f(x, y, z) dx dz dy Evaluate the triple integral using only geometric interpretation and symmetry. integral integral integral_c (4 + 5x^2yz^2) dV, wher C is the cylindrical region x^2 + y^2 lessthanorequalto 4, -2 lessthanorequalto z lessthanorequalto 2
The value of the triple integral is 1920pi/3.
Here are five other iterated integrals that are equal to the given iterated integral:
[tex]\Integral^2_0 \Integral^y_0 \Integral^1_0 f(x, y, z) dx dy dz[/tex]
[tex]\Integral^2_0 \Integral^z_0 \Integral^1_z f(x, y, z) dx dz dy[/tex]
[tex]\Integral^1_0 \Integral^y_0 \Integral^1_z f(x, y, z) dx dz dy[/tex]
[tex]\Integral^1_0 \Integral^z_0 \Integral^1_y f(x, y, z) dx dy dz[/tex]
[tex]\Integral^z_0 \Integral^1_0 \Integral^y_z f(x, y, z) dx dy dz[/tex]
To evaluate the triple integral of[tex](4 + 5x^2yz^2) dV[/tex]over the cylindrical region [tex]x^2 + y^2[/tex] <= 4, -2 <= z <= 2, we can use geometric interpretation and symmetry.
Note that the integrand [tex](4 + 5x^2yz^2)[/tex] is an even function of x and y, and an odd function of z.
Therefore, the integral over the region where z is positive is equal in magnitude but opposite in sign to the integral over the region where z is negative.
Hence, we can evaluate the integral over the region 0 <= z <= 2, and then double the result.
The region of integration is a cylinder of radius 2 and height 4.
Since the integrand is not dependent on x and y, we can factor out[tex](4 + 5z^2)[/tex] from the integrand, and evaluate the remaining integral over the unit disc in the x-y plane.
Thus, the triple integral can be written as:
[tex]8 * \Integral^2_0 \Integral^2pi_0 \Integral^2_0 (4 + 5z^2) r^3 sin(\theta) dr d(\theta) dz[/tex]
Integrating with respect to r from 0 to 2 and with respect to [tex]\theta[/tex] from 0 to [tex]2\pi[/tex], we get:
[tex]8 * \Integral^2_0 \Integral^2pi_0 (4 + 5z^2) sin(\theta) d(\theta) dz[/tex]
Integrating with respect to theta from 0 to 2pi, we get:
[tex]16pi * \Integral^2_0 (4 + 5z^2) dz[/tex]
Integrating with respect to z from 0 to 2, we get:
16pi * (32/3 + 80) = 1920pi/3.
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You can measure the amount of overlap of 2 data sets by comparing the distance between the meadians of the IQR
The given statement "You can measure the amount of overlap of 2 data sets by comparing the distance between the medians of the IQR" is False. Because the distance between the medians can give some indication of how much overlap there is between two data sets, it is not the only factor to consider other factors are means or standard deviation.
The median is a measure of central tendency that divides the data into two halves. The interquartile range (IQR) is a measure of spread that gives the range of the middle 50% of the data.
Therefore, the distance between the medians of the IQR can give an idea of how much overlap there is between two data sets, but it is not the only measure to consider.
Other measures of overlap include comparing the means or standard deviations of the data sets, or using statistical tests such as a t-test or ANOVA to compare the groups. So, the given statement is False.
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--The given question is incomplete, the complete question is given
" You can measure the amount of overlap of 2 data sets by only comparing the distance between the medians of the IQR. True or False."--
Add or Subtract then complete the chart
The simplified form of the polynomial (4x² - 3x + 10) + (-9x² + 4x - 6) is -5x² + x + 4.
The constant term is the term without a variable, in this case, 4 is the constant term.
What is polynomial?
A polynomial is a mathematical expression that consists of variables and coefficients
To simplify the polynomial, we need to combine like terms. We have:
(4x² - 3x + 10) + (-9x² + 4x - 6)
= 4x² - 3x + 10 - 9x² + 4x - 6 (distributing the negative sign)
= (4x² - 9x²) + (-3x + 4x) + (10 - 6) (grouping like terms)
= -5x² + x + 4 (combining like terms)
Therefore, the simplified form of the polynomial (4x² - 3x + 10) + (-9x² + 4x - 6) is -5x² + x + 4.
In the polynomial -5x² + x + 4, the degree is 2, the leading coefficient is -5, and the constant term is 4.
The degree of a polynomial is the highest power of the variable in the polynomial, in this case, x² has the highest power of 2.
The leading coefficient is the coefficient of the term with the highest power of the variable, in this case, -5 is the coefficient of the x² term, so it is the leading coefficient.
The constant term is the term without a variable, in this case, 4 is the constant term.
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Please help and give explanations! 20 pts.
Answer:
N'(2, 3)
Step-by-step explanation:
my trick is counting how many spaces away it is from the axis it's being reflected over. So for this one N was at (2, -3) so I counted upwards 3 spaces from the 2 and i got to (2,3). i hope that makes sense the way i explained it.
hope this helps ;)
Answer:
see attached
Step-by-step explanation:
You want the image of point N(2, -3) after reflection in the y-axis, plotted on the graph.
ReflectionA line of reflection is the perpendicular bisector of the segment between a point and its image. That is, the image point is as far from the line as the original point, but on the opposite side of it.
The attached figure shows the location of image point N'(-2, -3).
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Additional comment
The coordinate transformation for reflection in the y-axis just changes the sign of the x-coordinate. That puts the image point as far to the left as the original is to the right:
(x, y) ⇒ (-x, y) . . . . . . reflection in the y-axis
standard error of an estimator is not affected by the multiple choice question. population standard deviation. sample size. population size
The term that is not affected the standard error of an estimator is population size, from the provide data in options. So, option (c) is right one.
The standard error is a statistical term that used to measured the accuracy that a sample distribution represents a population by using standard deviation. The standard error(SE) is very similar to standard deviation of a distribution. Both are used to measure the spread of distribution. Higher the value SE, the more spread out your data is. In statistical way, standard error is also called standard error of mean, SEM, it represents the deviation of sample mean deviates from the actual mean of a population.
It is calculated simply by dividing the standard deviation by the square root of the sample size. That is [tex]SE = \frac{σ }{\sqrt{n}}[/tex]
where , n --> sample size
σ --> population standard deviations
Now, from the above formula it is clearly seen that standard error term or an estimator affected by sample size (n) and population standard deviations ( σ). So, right choice for answer is population size.
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Complete question:
standard error of an estimator is not affected by the multiple choice question.
a) population standard deviation
b) sample size
c) population size