The coordinate of T ' will be;
⇒ T ' = (- 31, - 23)
What is Coordinates?A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
This is a Dilation with a scale factor of 4 (D4).
Now,
Since, The Center of Dilation of this transformation is at the center. But the transformation is given by a scale factor of 4 and adding to (-3,1) as;
⇒ T ' = 4 (- 7, - 6) + (-3, 1)
= (- 28, - 24) + (-3, 1)
= (- 31, - 23)
Thus, The coordinate of T ' = (- 31, - 23)
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Question A zoo sells 43 adult tickets and 80 child tickets in one day. Each adult ticket costs $20 and each child ticket costs $13.
The total amount of ticket sales on this day is $1900.
What is meant by an algebra?Math has several different subfields, including algebra. Algebra, a common thread that runs through nearly all of mathematics, is the study of mathematical symbols and the rules for using them in formulas.
Elementary algebra is crucial for all mathematical applications since it deals with the manipulation of variables, which are frequently represented by Roman letters, as though they were numbers. The study of algebraic structures such as groups, rings, and fields is known as abstract algebra, mostly in education (the term is no more in common use outside educational context). In contemporary presentations of geometry, linear algebra—which deals with linear equations and linear mappings—is used.
Given,
Number of adult tickets sold by zoo=43
And number of child tickets sold by zoo=80
Also given that,
The cost of each adult ticket=$20
And the cost of each child ticket=$13
20 x 43 = 860
80 x 13 = 1040
860 + 1040 = 1900
Therefore, the total amount of ticket sales on this day is $1900
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The complete question is:
"Question A zoo sells 43 adult tickets and 80 child tickets in one day. Each adult ticket costs $20 and each child ticket costs $13.
What is the total amount of ticket sales on this day?
Enter your answer in the box.
$="
Assume that all variables are implicit functions of time t. Find the indicated rate. x^2 + 5y^2 + 2y = 75; dx/dt = 14 when x = 6 and y = -3: find dy/dt
The answer to the given question, assuming that all variables are implicit functions of time t, the indicated rate x^2 + 5y^2 + 2y = 75; dx/dt = 14 when x = 6 and y = -3 is dy/dt = 6.
What is implicit function?An implicit function is a function which is defined by an implicit equation, written in terms of both dependent and independent variables. While an explicit function is a function which is represented in terms of an independent variable.
In this case, we have equation:
x^2 + 5y^2 + 2y = 75
We use the chain rule to bridge it:
2x(dx/dt) + 10y(dy/dt) + 2(dy/dt) = 0
Since x = 6; y = -3; and dx/dt = 14, then:
2x(dx/dt) + 10y(dy/dt) + 2(dy/dt) = 0
2*6*14 + 10*(-3)*(dy/dt) + 2*(dy/dt) = 0
168 + (-30)(dy/dt) + 2(dy/dt) = 0
168 - 28(dy/dt) = 0
28(dy/dt) = 168
dy/dt = 6
Hence, the indicated rate x^2 + 5y^2 + 2y = 75; dx/dt = 14 when x = 6 and y = -3 is dy/dt = 6.
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use cylindrical coordinates. evaluate x2 dv, e where e is the solid that lies within the cylinder x2 y2
The value of the expression on evaluation is 96π / 5.
Here we have to find the value of the expression.
∫∫∫x² dV
E is indeed the solid that exists inside the cylinder x² + y² = 4 above the surface z =0.
E's precession through into xy-plane is x² + y² ≤4 where r≤2 with Ф[0, 2π].
∫∫∫ x² dV = ∫[tex]\int\limits^2\pi _0 {} \, \int\limits^2_0{} \, \int\limits^3r_0[/tex] r² cos² Фrd dФ
= [tex]\int\limits^2\pi _0 {} \, \int\limits^2_0 \int\limits^3r_z=0 {} \,[/tex]r³ cos²Ф dz dr dФ
= [tex]\int\limits^2\pi _0 {} \, \int\limits^2_0 {} \,[/tex] 3[tex]r^{4}[/tex]cos²Ф dr dФ
= 3 [tex]\int\limits^2\pi _0 {} \,[/tex] 1/2 [tex]2^{5}[/tex]/ 5 ( 1 + cos² Ф )dr dФ
= 48 / 5 [( Ф + 1/2 sin 2Ф)[tex]]^{2\pi } _{0}[/tex]
= 96π / 5
Therefore the value of the expression is 96π/5.
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based on the survey data and calculated expected values, what is the value of the chi-square (\chi^2) test statistic, using the following formula? \chi^{2}
The value of chi-square statistic is;
In the contingency table, "O" stands for the observed value, "E" for the predicted value, and "I" for the "ith" position.
Given,
Chi- Square test;-
A statistical technique called the chi-square test is used to compare actual outcomes with predictions. The goal of this test is to establish whether a discrepancy between observed and expected data is the result of chance or a correlation between the variables you are researching.
We have to find the value of chi- square statistic;
The chi-squared statistic is a single figure that indicates the degree to which the counts you saw deviate from the counts you would anticipate if there were no association at all in the population. If I is the "ith" position in the contingency table, "O" is the observed value, "E" is the anticipated value, and "O" is the observed value.
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←+++
-5 -4 -3 -2
5
4+
3
2+
1+
-2
-3
Y
-5
1 2 3 4 5
Find the inequality represented by the graph.
Answer:
i don't know?please tell me in breif i didn't understand?
the coordinates of the midpoint of a line segment PQ(1, - 2). the coordinates of p are (-3, 2). find the coordinates of Q
The coordinates of the midpoint of a line segment PQ(1, - 2). the coordinates of p are (-3, 2). the coordinates of Q is (4, -4).
In mathematics, how do you find coordinates?You do the reverse to determine a point's coordinates in a coordinate system. Start at the point, then move up or down a vertical line until you reach the x-axis. Your x-coordinate is shown there. Then repeat the process while tracing a horizontal line to determine the y-coordinate.
What kind of example are coordinates?a group of values that exhibit precise positioning On graphs, it is typically represented by a pair of numbers: the first number indicates the length along, while the second number indicates the length up or down. The point (12,5), for instance, is 12 units down and 5 units up.
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6 suppose a die is tossed 1000 times, and the following frequencies are obtained for the number of pips up when the die comes to a rest. x1 x2 x3 x4 x5 x6 163 178 142 150 183 184 using the chi-squared goodness of fit test, assess whether we have evidence that this is not a symmetrical die. record the standardized residuals
We have evidence that this is not a symmetrical die the standardized residuals is 9.5699.
Given that,
The following frequencies are found for the number of pips up when the die comes to rest, assuming a die is tossed 1000 times. Find out if there is proof that this die is not symmetrical using the chi-squared goodness of fit test. The standardized residuals should be noted.
x₁ x₂ x₃ x₄ x₅ x₆
163 178 142 150 183 184
We know that,
observed expected Op-Ep (Op-Ep)²/Ep
x₁ 163 166.7 -3.7 0.082
x₂ 178 166.7 11.3 0.7659
x₃ 142 166.7 -24.7 3.6598
x₄ 150 166.7 -16.7 1.673
x₅ 183 166.7 16.3 1.5938
x₆ 184 166.7 17.3 1.7954
-----------
9.5699
Expected = 1/nΣXa=1/6(1000)=166.7
Therefore, We have evidence that this is not a symmetrical die the standardized residuals is 9.5699.
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Anyone please help in this part!
Answer:
x= 40 degree
y = 80 degree
Step-by-step explanation:
where is z?
Of the 1500 trains leaving a train station one day, 1290 left within 5 minutes
Of the scheduled time. What percentage of the trains left within 5 minutes
of the scheduled time?
Answer:
55
Step-by-step explanation:
a and b are in direct proportion. the equation of proportionality is a=8b. work out the value of a when b=4.
The required value of 'a' in the equation of proportionality is 32.
What is direct proportion?
Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value.
It is symbolised by the proportional sign ∝.
For instance, if x and y are two quantities or variables that are intimately linked to one another, we can say x & y. The ratio of x and y becomes equal to a constant when the proportionality sign is removed, for example, x/y = C, where C is a constant.
Given, a = 8b
When b = 4 then
So, a = 8*4 = 32
Hence, the required value of 'a' in the equation of proportionality is 32.
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If X is a metric space, and fn:X→R (n∈N) is a sequence of functions, then fn converges pointwise to f if for every x∈X one has limn→[infinity]fn(x)=f(x).
|f(x) − f n(x)| = lim m→∞
|f m(x) − f n(x)| ≤ ϵ /2< ϵ
Converges Uniformly
A sequence of functions f n(x); n = 1, 2, 3,…. Is said to be uniformly convergent to f for a set E of values of x, if for each ε > 0, a positive integer N exists such that |f n(x) – f(x)| < ε for n ≥ N and x ∈ E.
A sequence (f n) of functions f n : A → R is uniformly Cauchy
on A if for every ϵ > 0 there exists N ∈ N such that
m, n > N implies that |f m(x) − f n(x)| < ϵ for all x ∈ A.
The key part of the following proof is the argument to show that a pointwise
convergent, uniformly Cauchy sequence converges uniformly.
A sequence (f n) of functions f n : A → R converges uniformly on
A if and only if it is uniformly Cauchy on A.
Suppose that ( f n) converges uniformly to f on A. Then, given ϵ > 0, there
exists N ∈ N such that
|f n(x) − f(x)| < ϵ/2
for all x ∈ A if n > N.
It follows that if m, n > N then
|f m(x) − f n(x)| ≤ |f m(x) − f(x)| + |f(x) − f n(x)| < ϵ for all x ∈ A,
which shows that (f n) is uniformly Cauchy.
Conversely, suppose that (f n) is uniformly Cauchy. Then for each x ∈ A, the
real sequence (f n(x)) is Cauchy, so it converges by the completeness of R. We
define f : A → R by
f(x) = limn→∞
f n(x),
and then f n → f pointwise.
To prove that f n → f uniformly, let ϵ > 0. Since (f n) is uniformly Cauchy,
can choose N ∈ N (depending only on ϵ) such that
|f m(x) − f n(x)| < ϵ /2
for all x ∈ A if m, n > N.
Let n > N and x ∈ A. Then for every m > N we have
|f n(x) − f(x)| ≤ |f n(x) − f m(x)| + |f m(x) − f(x)| < ϵ /2 + |f m(x) − f(x)|.
Since f m(x) → f(x) as m → ∞, we can choose m > N (depending on x, but it
doesn’t matter since m doesn’t appear in the final result) such that
|f m(x) − f(x)| < ϵ/2.
It follows that if n > N, then
|f n(x) − f(x)| < ϵ for all x ∈ A,
Then proves that f n → f uniformly
Alternatively, we can take the limit as m → ∞ in the Cauchy condition to get
for all x ∈ A and n > N that
|f(x) − f n(x)| = lim m→∞
|f m(x) − f n(x)| ≤ ϵ /2< ϵ
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The distance s that an object falls varies directly with the square of the time, t , of the fall. If an object falls 16 feet in one second, how long will it take for it to fall 112 feet?
After 3 seconds will it take for it to fall 112 feet.
What is distance?
Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.
Given:
The distance s that an object falls varies directly with the square of the time, t , of the fall.
⇒ D = KT^2
Where D is the distance
T is the time
K is the proportionality constant
As an object falls 16 feet in one second.
⇒ D = 16, T = 1
⇒ 16 = K(1)^2
16 = K
Therefore, the equation becomes
D = 16T^2
To find the how long will it take for it to fall 112 feet.
Here D = 112 feet
Plug D = 112 in the above equation.
112 = 16T^2
7 = T^2
T = √7
T = 2.65
T ≈ 3
Hence after 3 seconds will it take for it to fall 112 feet.
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HELP!!!!!! 40 POINTS!!!!
Knowing that correlation coefficients have values between -1 and 1 and that the closer the value is to -1 or 1, the stronger the correlation -- which of the following correlation coefficients would represent the strongest correlation?
A. -0.5
B. 0.02
C. -0.97
D. 0.87
The strongest correlation is represented by -0.97. It can be find out using knowledge of correlation coefficients.
What is the correlation coefficient between 1 and -1?
The formula returns a value between 1 and -1 :
where 1 indicates a strong positive relationship and -1 indicates a strong negative relationship.
According to the rule of correlation coefficients , the strongest correlation is considered when the value is closet to either (+1) or (-1).
So, in given options -0.97 is closet to (-1).
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what angle is half of its supplement; the measure of one angle is 15 less than half the measurement of its supplement; complement angle; complementary angles add up to; what are supplementary angles; two angles that add up to 90
So one angle is of measurement 130 degree and the other angle is of measurement 50 degree.
What are angles?When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.
When two lines meet at a point, an angle is created.
An "angle" is the measurement of the "pening" between these two rays. It is symbolized by the character. The circularity or rotation of an angle is often measured in degrees and radians.
Angles are a common occurrence in daily life.
Angles are used by engineers and architects to create highways, structures, and sports venues.
According to our question-
One angle's measurement is 15 less than its supplement's measurement.
Let's say that the supplement angle is measured in degrees.
So the measurement of the other angle is
And the sum of the measurement of supplementary angles is 180.
Multiplying both sides by 2
Therefore, one angle is 130 degrees in length and the other is 50 degrees.
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Can someone please help me with C? I am not sure how to solve or which theorem to use.
There is no time within the interval 0≤t≤2, at which the amount of money raised is 10.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
Given the amount of money raised during a competing fund-raising campaign is modeled by the function M defined by M(t)=240(2t−1)(2t+36), where M(t) is measured in United States dollars and t is the time in days, to get the time t if the money raised is 10 dollars,
Then will substitute M = 10 into the modeled function and calculate the value of t.
M(t)=240(2t−1)(2t+36)
10=240(2t−1)(2t+36)
1 = 24(2t−1)(2t+36)
open the parenthesis;
1 = 24(4t²+72t-2t-36)
1 = 96t²+1680t-864
96t²+1680t-865 = 0
On factorizing, t = 2 is not a factor of the expression.
Thus there is not a time within the interval 0≤t≤2,
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f(x) = ax^3 + bx^2 + cx + d In the polynomial above, a, b, c, and d are constants. If f(–5) = 3, which of the following must be true about f(x)? A x – 3 is a factor of f(x). B The remainder when f(x) is divided by x + 5 is 3. C x + 2 is a factor of f(x). D x + 5 is a factor of f(x).
The remainder when f(x) is divided by x + 5 is 3.
What is an Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
we discovered that the polynomial equation is the equation that results from equating a polynomial function to zero. A linear equation results from equating a function to zero if it is a linear polynomial. We get a quadratic equation if the function is a quadratic polynomial.
f(x) = ax^3 + bx^2 + cx + d
In the polynomial above, a, b, c, and d are constants and f(-5)=3.
- 5 is the root of the given polynomial when remainder is 3 so we get the one factor of the given polynomial and that is,
x-(-5)=(x+5)
That is if f(-5)=3 it means that the remainder when f(x) is
divided by (x-(-5))=x+5 is 3
Hence, The remainder when f(x) is divided by x + 5 is 3
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Graph the line whose y intercept is -9 and whose x intercept is 7
The graph of the linear equation y = 9/7x - 9 is attached below
Graph of a Linear EquationA linear graph is the graphical representation of a straight line. It showcases a linear equation in two variables and shows the linear association between two quantities. A linear function often have a straight line with a slope and y-intercept.
To solve this, we can simply write an equation of the linear equation which is often given as
y = mx + c
m = slopec = y-interceptLet's substitute the values and find the equation;
y = 9/7x - 9
Kindly find the attached image below;
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which of the following are binomials
A polynomial with two terms is called a binomial. For instance, the binomials x 2 x -2 x2 and x 6 x -6 x6 both exist.
How do you identify binomials?A single-term expression is referred to as a monomial, a two-term expression as a binomial, and a three-term expression as a trinomial. An expression's name is just its number of terms if it has more than three terms.
What is difference between monomial and binomial?Monomials have one term, binomials have two, trinomials have three, and polynomials have one or more terms.
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Greenpoint had 224,710 residents at the time of its founding. Currently it is 20% smaller. What is the current population?-
Answer:
179,768
Step-by-step explanation:
Greenpoint had 224,710 residents at the time of its founding. Currently it is 20% smaller. What is the current population?
100% - 20% = current population is now 80%
80% = 0.8
0.8 * 224,710 = 179,768
what is the opposite of the interger on the number line
Opposite of an integer on the number line is the same integer with opposite sign
what is number line ?
The visual representation of numbers on a straight line is called a number line. On an endless line that extends on both sides, either horizontally or vertically, this line is used to compare numbers that are spaced at equal intervals. The numbers on a horizontal number line grow as we approach towards the right side and drop as we move towards the left.
The number line's opposite of the integer "a" is "-a"; hence, the opposite of the integer "-a" is "a" on the number line, but on the other side of 0.
For example,
The number line's opposite of the integer "4" is "-4"
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design and implement an application that reads in a set of values in the range of 1 to 100 (yes, you should error check for this) and then creates a chart showing how often the values appeared. the chart should look like the one below and should show how many values fell in the range of 1-10, 11-20, 21-30, and so on.
Sample Output: Code to copy: //Import the required package. import java.util.Scanner; //Define the class Main. class Main { //Start the execution of the main() method.
Code of Origin:Origin C is a programming language that is ANSI C compatible and also incorporates C++ and C# features. The majority of Origin objects can be accessed programmatically thanks to built-in C++ classes. The NAG C Library's extensive collection of numerical computational routines is also included.
C, a replacement for the programming language B, was initially created by Ritchie at Bell Labs between 1972 and 1973 to create utilities for Unix. It was used to re-implement the Unix operating system's kernel. C increasingly gained popularity in the 1980s.
import java.io.*;
import java.util.Scanner;
public class histogram
{
public static void main(java.lang.String[] args)
throws IOException
{
Scanner scan = new Scanner (System.in);
final int min = 1;
final int max = 10;
final int limit = 10;
int[] a = new int[max];
for (int b = 0; b < a.length; b++)
{
a[b] = 0;
}
System.out.println("Enter Number between 1 and 100: \n (Or press 0 to stop)");
int number = scan.nextInt();
while (number >= min && number <= (limit*max) && number != 0)
{
a[(number-1)/limit] = a[(number - 1 ) / limit] + 1;
System.out.print("Please enter a value:");
number = scan.nextInt();
}
System.out.println("\n__Histogram__");
for (int y = 0; y < a.length; y++)
{
System.out.print(" " + (y * limit + 1) + " - " + (y + 1) * limit + "\t");
return;
}
for (int z = 0; z < a[b]; z++)
{
System.out.print("*");
}
System.out.println(0);
}
}
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both the t-test for dependent means and t-test for independent means, the formula for estimating the population variance from the sample involves taking the sum of squared deviations and dividing it
The formula for estimating the population variance from the sample requires calculating the sum of squared deviations and dividing it by the number of observations. This is true for both the t-test for dependent means and the t-test for independent means.
This formula is referred to as the "variance sum of squares"or the t-test for dependent means, the formula is:
Where:
x1 = observation 1
x2 = observation 2
N = number of observations
For the t-test for independent means, the formula is:
Sample Variance = [(Σx12)/N + (Σx22)/N]/2
Where:
x1 = observation 1
x2 = observation 2
N = number of observation
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In the video, it was remarked that for small values of the equation of motion for the pendulum, 9 sin 0 = 0 is similar to the linear spring equation. If we take two nonzero terms of the L series for sin into account, the model is even more spring-like, but this time to a non-linear spring. From this perspective, which of the following kind of spring is the pendulum most like?
O ideal linear spring
O hard spring O soft spring
Hard spring
What is Spring?
They swing back and forth around a stationary point. Classic examples of this type of vibrating motion are a simple pendulum and a mass on a spring. The use of motion detectors demonstrates that the vibrations of these items have a sinusoidal character, even if this is not obvious from plain viewing.
Let θ be A,
[tex]A''+(g/l)sinA=0\\sinA=A - (A^{3} /3!)+(A^{5} /5!)....\\[/tex]
taking first 2 terms,
[tex]A'' +(g/l)(A-A^{3}/3!)\\[/tex]
intergrating both sides,
[tex]A'+(g/l)(A^{2}/2 -A^{4}/24)=c[/tex]
integrating again,
[tex]A+(g/l)(A^{3} /6-A^{5}/120)=ct+c_{1}[/tex]
power is 5= non linear spring
Additionally, a larger degree indicates that the displacement over time diminishes more quickly.
Hence its a hard spring.
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After the amount due on a sale of $33,400, terms n/eom, is received from a customer, the seller consents to the return of the entire shipment for a cash refund. The cost of the merchandise returned is $20,040. a. What is the amount of the refund owed to the customer?
The total shipment amount of $ 33,066 must be paid back in order to receive a cash reimbursement for the $20,040 in goods that were returned.
what is amount ?When describing a singular noun that CANNOT be measured, you should use the word amount. – When discussing a singular, plural, or countable noun, the word number should be used. – Any single or plural noun that can be counted or measured should be referred to as having a certain quantity.
1/10 n (unclear) indicates that the consumer settled their debts within 10 days and was entitled to a 1% sales discount.
Therefore, the consumer should receive a refund equal to what they paid, which is 1% less than the total amount.
Using that as a basis, the calculation is,
Amount owed * (1-discount rate)
= $ 33,400 * ( 1 - 0.01)
= $ 33,066
$ 33,066 is is the sum that must be reimbursed.
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the tennis team is having a bake sale.Cookies sell for $1 each and cupcakes are $3 each .Of Dj spends $15 for 7 items,how many cupcakes did he buy?
Answer:
4 cupcakes
Step-by-step explanation:
Answer:
4
cupcakes
Step-by-step explanation:
This is because it says the cupcakes are 3$ each. if you buy 7 items for 15$
3x4=12.
Tell whether the table of values represents a linear, exponential, or quadratic function.
The table of values represents a quadratic function. And a quadratic function is y = x² / 10.
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function.
Linear functions have constant first differences.
Here, if a and b is the first and second term.
Then the first difference is b-a.
Quadratic functions have constant second differences.
Let the first differences are:
b-a = m, c-b = n
Then the second difference is n-m.
Exponential functions have a constant ratio.
The ratio of first term and second term is b/a.
Here, from the table;
y₂-y₁ = 0.4 - 0.9 = -0.5 = m₁
y₃-y₂ = 0.1 - 0.4 = -0.3 = m₂
y₄-y₃ = 0 - 0.1 = -0.1 = m₃
y₅-y₄ = 0.1 - 0 = 0.1 = m₄
y₆-y₅ = 0.4 - 0.1 = 0.3 = m₅
From the first differences, we have no idea about the function property.
So, the second differences:
m₂ - m₁ = -0.3 + 0.5 = 0.2
m₃ - m₂ = -0.1 + 0.3 = 0.2
m₄ - m₃ = 0.1 + 0.1 = 0.2
m₅ - m₄ = 0.3 - 0.1 = 0.2
Here, the second differences are constant 0.2.
And the common ratio is varying.
So, quadratic functions have constant second differences.
And the quadratic function is y = x² / 10.
Therefore, the given function is a quadratic function.
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Solve the problem.
How much money needs to be invested now to get $2000 after 4 years at 8%
compounded quarterly? Express your answer to the nearest dollar.
A) $584
B) $1457
C) $1848
D) $2746
Answer:
A) $584
Step-by-step explanation:
Compounded quarterly means it is compounded 4 times a year.
This means that the amount its compounded 16 times during this period.
to compound the money you must multiply it by 1+ the rate its being compounded so here it is .08.
work: (584 * 1.08)= 630.72
630.72 *1.08= 681.1
... repeat until done 16 times and $2000 is reached.
Usain Bolt masses 94 kg and runs at 10 m/s. How much kinetic energy does he have?
Usain’s brother, Insane Bolt, runs twice as fast and has the same mass. How much kinetic energy does he have?
If you double the mass of an object, how does this affect its kinetic energy?
You serve a volleyball with a mass of 2.1 kg. The ball leaves your hand with a speed of 30 m/s.
A car is traveling with a velocity of 40 m/s and has a mass of 1120 kg.
Determine the kinetic energy of a 1000-kg roller coaster car that is moving with a speed of 20.0 m/s.
Usain bolt with a mass of 94 kg and speed 10m/s has kinetic energy 4700j
What is kinetic energy and what is its formula?
The energy that an object has as a result of motion is known as kinetic energy. It is described as the amount of effort required to move a mass-determined body from rest to the indicated velocity. The formula of kinetic energy is [tex]\frac{1}{2}mv^2[/tex]
We are given that the mass of usain bolt is 94 kg and that he runs at a speed of 10m/s
That means the value of m and v are 94 kg and 10 m/s respectively
Substituting the values in the formula we get
Kinetic energy = [tex]\frac{1}{2}94*10^2[/tex]
Kinetic energy = [tex]47*100\\[/tex]
Kinetic energy = [tex]4700 j[/tex]
Hence the kinetic energy of Usain bolt is 4700 j
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ustify the last two steps of the proof.
Given: RS is congruent to UT and RT is congruent to US
Prove: triangle RST is congruent to triangle UTS
Proof:
1. RS is congruent to UT 1. Given
2. RT is congruent to US 2. Given
3. ST is congruent to TS 3. _______________
4. triangle RST is congruent to triangle UTS
4. ______________
The given two triangles are congruent by Side Side Side congruency.
As from the question we get to know that ΔRST and Δ UTS
and
RS = UT
RT = US
The proof for the above claim
RS = UT {given}
RT = US {given}
ST = TS {Common}
Therefore, we can say that by SSS theorem ΔRST and Δ UTS is congruent to each other.
ΔRST ≅ Δ UTS by SSS Theorem
If two geometric figures are identical in every way, they are said to be congruent.
For example, two squares having the same side-length are congruent.
Similarly, two circles with the same radius are congruent.
If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. If moved, they coincide with one other. ’ ≅’ is the congruence symbol.
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How many subjects are needed to estimate the mean number of books read the previous year within six books with 90% confidence?
This 90% confidence level requires subjects. (Round up to the nearest subject
Answer:
Step-by-step explanation:
To determine the number of subjects needed to estimate the mean number of books read the previous year within six books with 90% confidence, you would need to use a sample size calculation. There are several factors that can affect the sample size needed, including the desired level of confidence, the desired level of precision, the variability of the population being sampled, and the size of the population.
One way to calculate the sample size is to use a sample size calculator, which can be found online or in statistical software. These calculators typically ask for the desired level of confidence, the desired level of precision, and the estimated standard deviation of the population being sampled.
Alternatively, you can use a sample size formula to calculate the sample size. For example, the formula for calculating the sample size for a simple random sample with a known population standard deviation is:
n = (Z*sigma / E)^2
where n is the sample size, Z is the z-score corresponding to the desired level of confidence (e.g., for a 90% confidence level, Z would be 1.645), sigma is the population standard deviation, and E is the desired level of precision (e.g., 6 books in this case).
To use this formula, you would need to know the population standard deviation, which may require collecting data from a pilot study or using estimates based on similar populations.
It's important to note that sample size calculations are based on statistical assumptions, and the actual sample size needed may vary depending on the specific characteristics of the population being sampled. Additionally, sample size calculations are based on estimates, so the actual level of precision may differ from the desired level.
