The correct option is: A
Statement I is the cause and statement II is the effects.
Since the Government has imported large quantities of sugar as per trade agreement with other countries, the prices of sugar in the domestic market have fallen sharply in the recent months.
The reason behind this statement is:
An increase in supply always leads to a decrease in price.
Supply : Supply is a fundamental economic concept that describes the total amount of a particular good or service available to consumers. Supply can refer to the quantity available at a particular price or the quantity available across the price range displayed on the chart. It is closely related to the demand for goods or services at a particular price. All else being equal, when prices rise, producer supply increases as all firms try to maximize their profits.
Increase in Supply:
If the demand does not change, there is an inverse relationship between the supply and price of goods and services. When the supply of goods and services increases at the same demand, prices tend to fall resulting in lower equilibrium prices and higher equilibrium quantities of goods and services. When the supply of goods and services decreases for the same demand, prices tend to rise towards higher equilibrium prices and smaller quantities of goods and services.
Since the supply of sugar increases as government has over imported, the price of sugar decreases in domestic market.
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Here is a picture of the Mostar Bridge in Bosnia.The diagram shows one side of the bridge find the area of the bridge (yellow part). show your work.
The area of the bridge(yellow part) is 297.9 m².
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
From the given diagram the area of the bridge is the total area of the larger rectangle - the area of a semicircle - the area of the smaller rectangle.
We know the area of a rectangle is (length×width) and the area of a semicircle is (1/2)πr².
∴ The area of the bridge is = {(34×20) - (24×6.5) - (1/2)π(12)²} m².
= {680 - 156 - 226.1} m².
= 297.9 m².
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Angle M has a measure of 47°. What is the measure of angle PNL? 43° 47° 86° 94°
As angle M has a measure of 47°, then the measure of angle PNL is 43°
To find: the measure of ∠ PNL .
To proof
As given
∠ M = 47°
In ΔLMN
If the two sides of a triangle are equal and you use the property, the diagonals are also equal.
As given MN = LN
∠ M =∠ L = 47°
and ∠ MPN = 90 °
∠ MPN + ∠ NPL = 180° (Linear pair)
∠ NPL = 180° - 90°
∠ NPL = 90°
Now by using the angle sum property of a triangles.
in Δ NPL
∠NPL +∠PNL + ∠NLP = 180°
90 + 47 + ∠PNL = 180
137+ ∠PNL = 180
∠PNL = 180 - 137
∠PNL = 43 °
Therefor the Measure of angle PNL is 43°.
Hence proved
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Zachary bought 3 cartons of x eggs. He used 6 to make a cake. He then used the remaining eggs equally to make 2 pies. Draw a bar model to show how many eggs were used in each pie.
Answer:
Step-by-step explanation:
Richard and Elizabeth both bought a used car on the same day. Richard's used car
has 3,896 miles on it already, and he drives 238 miles per month. Elizabeth's car has
5,345 miles on it already, and she drives 187 miles per month. After how many
months will each car have the same number of miles on it?
Part 1:
What two equations represent this system of equations?
Part 2:
How many months will it take for both Richard and Elizabeth's cars to have the same
number of miles?
1. The two equations that represent this system of equations include
3896 - 238m
5345 - 187m
2. The months that it will it take for both Richard and Elizabeth's cars to have the same number of miles will be 28.4 months.
How to illustrate the equations that represents the information?Given that Richard's used car has 3,896 miles on it already, and he drives 238 miles per month. The equation will be:
3896 - 238m
Elizabeth's car has 5,345 miles on it already, and she drives 187 miles per month. The equation will be:
5345 - 187m
where m = number of months
The months that it take for both Richard and Elizabeth's cars to have the same number of miles will be:
3896 - 238m = 5345 - 187m
Collect like terms
51m = 1449
m = 1449 / 51
m = 28.4 months
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Let p be the probability that, in the process of repeatedly flipping a fair coin, one will encounter a run of 5 heads before one encounters a run of 2 tails. Given that p can be written in the form m/n where m and n are relatively prime positive integers, find m+n.
The value of m+n is 37.
Probability is a measure of the likelihood that an event will occur or the likelihood that something will happen. The range for probability varies from 0 to 1.
Let A signify the flipping of the head, and let B signify the flipping of the tail. The event ends when we get 5 heads or 2 tails while flipping.
Then, the outcomes are given by AAAAA, BAAAAA, BB, ABB, AABB, AAABB, AAAABB. The probability of getting a head is 1/2 and a tail is 1/2. The probability of the possible outcomes is 1/32, 1/64, 1/4, 1/8, 1/16, 1/32, and 1/64.
The outcomes with five heads are AAAAA and BAAAAA. The sum of the probabilities of getting 5 heads is,
[tex]\begin{aligned}\frac{1}{32}+\frac{1}{64}&=\frac{2+1}{64}\\&=\frac{3}{64}\end{aligned}[/tex]
And, the sum of all the outcomes is, [tex]\begin{aligned}\frac{1}{32 }+ \frac{1}{64}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}&=\frac{2+1+16+8+4+2+1}{64}\\&=\frac{34}{64}\end{aligned}[/tex]
Let p is the probability that a run of 5 heads will occur before a run of 2 tails. The desired probability p is,
[tex]\begin{aligned}p&=\frac{\text{number of event}}{\text{total outcome}}\\&=\frac{\frac{3}{64}}{\frac{34}{64}}\\&=\frac{3}{34}\end{aligned}[/tex]
Given, p is of the form m/n. So, m is 3 and n is 34. Then, m+n=3+34=37.
The answer is 37.
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please help me!!! this is due tomorrow
Answer:
Below
Step-by-step explanation:
Multiply L number and Bottom number ...then add the R number to get the top number
? = 100 - (3*24) = 28
The change in temperature after y minutes for a chemical in a lab can be represented by the expression −4(y − 3). Which other expression can be used to represent the change?
Other expression can be used to represent the change in temperature after y minutes is -4y + 12.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
The distributive property is a( b + c) = ab + ac.
Given expression that represents the change in temperature after y minutes for a chemical in a lab can be represented by the expression −4(y − 3).
Given expression is
-4(y - 3)
Applying distributive property:
= -4 × y - (-4)×3
= -4y + 12
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the regression equation is Y = 29.29 -0.88X, the sample size is 25, and the standard error of the slope is 0.22.
The test statistic for the test of whether the slope is of zero is given as follows:
t = -20.
How to calculate the test statistic?The equation that gives the test statistic is given as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which the parameters are defined as follows:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The value tested of the slope is of:
[tex]\mu = 0[/tex]
The regression line in this problem is of y = 29.29 - 0.88x, hence the mean slope is of:
[tex]\overline{x} = -0.88[/tex]
The standard error and the sample size are given as follows:
s = 0.22, n = 25.
Then the test statistic is calculated as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{-0.88 - 0}{\frac{0.22}{\sqrt{25}}}[/tex]
t = -20.
Missing InformationThe problem asks for the test statistic regarding whether the slope assumes a value of zero or different of zero.
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△JKL∼△STU Which statements are true? more than one are right? ∠K≅∠T
JK≅ST
KL/TU=JK/ST
JL=SU
m∠J=m∠S
∠K≅∠T , KL/TU=JK/ST and m∠J=m∠S are true .
Given: △JKL∼△STU
When two triangles are similar , then their corresponding sides are proportional and Corresponding angles of one triangle is equal to corresponding angles of another Triangle.
The two Triangles can be similar by following Similarity axiom
1. AA
2. S A S
3. S S S
The Options are
→∠K≅∠T( True) Corresponding angles are equal.
→JK≅ST (False)
→KL/TU=JK/ST (True) Because sides are proportional.
→JL=SU (False)
→m∠J=m∠S (True) Corresponding angles are equal.
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customers is equally likely to report a food allergy, what is the probability that at least one customer will report a food allergy?
The probability that at least one client will have a food allergy is 0.6323 and the percentage of customers who will have a food allergy is 0.08.
What is probability?
The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not.
As given in the question,
The percentage of customers who will have a food allergy is 0.08
At Ying Ying's bakery,
121 people place orders on a single day.
We can utilize the binomial distribution if we believe that each of the 12 clients has an equal probability of reporting a food allergy.
Formula for Binomial probability distribution:
P(X=x)=ⁿCₓ pˣ (1-p)ⁿ⁻ˣ
Here, P(x) = probability of getting success in x trials, n= sample size ,p = represents the probability that each event will succeed.
As given, we have
n = 12
p=0.08
Let x is the client will have a food allergy.
Following that, the probability that at least one client will have a food allergy will be:
P(x≥1) = 1 - P(x<1)
= 1 - P(x=0)
= 1 - ¹²C₀(0.08)⁰(1 - 0.08)¹²⁻⁰
= 1 - (1)(0.12)¹²
= 1 - 0.3677
= 0.6323
Hence , the probability that at least one client will have a food allergy will be 0.6323 when the percentage of customers who will have a food allergy is 0.08.
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Complete Question
When a customer places an order at Ying Ying's bakery, there is an 8\%8%8, percent probability that the customer will report a food allergy. One day, 121212 customers place orders at Ying Ying's bakery.
Assuming that each of the 121212 customers is equally likely to report a food allergy, what is the probability that at least one customer will report a food allergy?
what is the result of adding the system of equations 2x y 43x y 6x 10x y 25x 10
Therefore the result of adding the system of equations 2x + y = 4 ,
6=3x-y is 5x =10
Describe equation:Equations are statements in mathematics containing the equals (=) sign flanked on either side by two algebraic expressions. The relationship between the expressions printed on the left and right sides is shown to be equal in this way. In all mathematical equations, LHS = RHS is used. You can solve equations to find the value of an unknown variable that stands in for an unknown quantity. If a sentence lacks a "equal to" sign, it is not considered an equation. It will be considered to be a phrase.
Here,
Given:
we have to solve the system of equations given. .Each equation is added together to remove the variable Y.
2x + y = 4
+
3x - y = 6
________
=> 5x =10
Therefore the result of adding the system of equations 2x + y = 4 ,
6=3x-y is 5x =10
The value of x :
x =10 / 5 = 2
⇒ x=2
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In 2010, the U.S. Congress passed the Tax Relief, Unemployment Insurance Reauthorization, and Job Creation Act of 2010. The act reduced the self-employment tax rate from 15.3% to 13.3%. Estimate the reduction in self-employment tax for an individual whose taxable earnings totaled $50,319.
Answer:A topic sentence is used to bring
to a paragraph.
Step-by-step explanation:
A topic sentence is used to bring
to a paragraph.
Find the point in the first quadrant where the line y = 4 x intersects a circle of radius 5 centered at the origin.
The graph of the point of intersection is given below.
The point of intersection.
(5/√17, 20/√17) and (-5/√17, 20/√17)
What is a circle?A circle is a two-dimensional figure with a radius and circumference of
2πr.
The equation of a circle is x² + y² = r²
We have,
The equation of a circle
x² + y² = r²
r = 5
x² + y² = 25 ______(1)
The line.
y = 4x _____(2)
Now,
The line intersects the circle.
The point of intersection.
x² + (4x)² = 25
x² + 16x² = 25
17x² = 25
x = √(25/17)
x = ± 5/√17
x = 5/√17 and x = -5/√17
Now,
At x = 5/√17,
y = 4 x 5/√17
y = 20/√17
At x = -5/√17,
y = 4 x 5/√17
y = 20/√17
Thus,
The point of intersection.
(5/√17, 20/√17) and (-5/√17, 20/√17)
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Find the length of side AC in the right triangle ABC with sides AC = 13 cm, BC = 5 cm and
The length of AB is equal to 12cm
How to find the length of a triangle?
If leg an is the missing side, change the equation such that an is on one side and compute the square root of that number: a = √(c² - b²)
Leg b = √(c² - a²) if leg b is unknown.
The equation is c = √(a² + b²) for the hypotenuse c that is absent.
What is the side length of a triangle?According to the law of the sides of a triangle, the lengths of any two of the triangle's sides added together are always more than the length of the third side. The triangle inequality theorem is another name for this condition. This indicates that a triangle with the dimensions 3, 4, and 9 is impossible because 3 + 4 =7 < 9.
a = √(c² - b²)
a=?,b=5,c=13
a=√169-25
a=12cm
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model cutting and sewing finishing packaging and shipping profit/glove regular model 1 1/2 1/8 $5 catcher's model 3/2 1/3 1/4 $8
The inequality of each model cutting, sewing finishing packaging and shipping profit
The maximum value = 5x + 8y
1R + 3/2 C ≤ 900
1/2 R + 1/3 C ≤ 300
1/8 R + 1/4 C ≤ 100
R, C ≥ 0
Consider x be the number of regular model of gloves to be produced
y be the catcher’s model of gloves to be produced
The maximum value = 5x + 8y
Then the inequality will be
The inequality of Cutting and Sewing
1R + 3/2 C ≤ 900
The inequality of Finishing
1/2 R + 1/3 C ≤ 300
The inequality of Packaging and Shipping
1/8 R + 1/4 C ≤ 100
R, C ≥ 0
Therefore, the inequality of each model cutting, sewing finishing packaging and shipping profit has been found
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A few stores have windows with one solid wall and two glass sides forming a triangular display space called ____________windows
A few establishments have what are known as Corner windows, which are triangle display spaces with one solid wall and two glass sides.
Given fill-in-the-blank;
A few stores have windows with one solid wall and two glass sides forming a triangular display space called ______ windows.
The solution for the above statement is Corner windows.
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solve the following expression
(12 × 4²) + 9/3²
Answer: 193
Step-by-step explanation:
(12 x 16) + 9/9 = 192 + 1 = 193
Assuming second term is 9/(3²)?
Scores on an IQ test are normally distributed. A sample of 18 IQ scores had standard deviation s=8.
(a) Construct a confidence interval for the population standard deviation . Round the answers to at least two decimal places.
(b) The developer of the test claims that the population standard deviation is 3. Does this confidence interval contradict this claim? Explain.
a) The 95% confidence interval for the population standard deviation is given as follows: (5.25, 10.49).
b) Since the interval does not contain 3, yes, it contradicts the claim of the developer.
What is the confidence interval for the standard deviation?The bounds of the confidence interval for the variance are given as follows:
[tex]\frac{(n - 1)s^2}{\chi^{2}_{\frac{\alpha}{2}}} \leq \sigma \leq \frac{(n - 1)s^2}{\chi^{2}_{1 - \frac{\alpha}{2}}}[/tex]
The parameters are given as follows:
n is the sample size.s is the sample standard deviation.[tex]\chi^2[/tex] represents the critical values.The critical values of the chi-square distribution with a confidence level of 95% and 18 - 1 = 17 df are given as follows:
7.5641 and 30.191.
Hence the lower bound of the interval for the variance is given as follows:
17 x 7²/30.191 = 27.59.
The upper bound of the interval is of:
17 x 7²/7.5641 = 110.13.
The standard deviation is the square root of the variance, hence the bounds are given as follows:
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Suppose that the scatterplot of log x and log y shows a strong positive correlation close to 1. Which of the following is true?
a. The variables x and y also have a correlation close to 1 b. A scatterplot of the variables log x andy shows a strong nonlinear pattern c. The residual plot of the variables and y shows a random pattern d. A scatterplot of the variables x andy shows a strong nonlinear pattern e. A residual plot of the variables log x and log y shows a nonrandom pattern
The correct options are;
a. The variables x and y also have a correlation close to 1 .
b. A scatterplot of the variables log x and y shows a strong nonlinear pattern .
The correlation is a measurement of a dependence between 2 variables. If the logarithm of the correlation function shows a linear tendency, it because the correlation between x and y shows a exponential tendency.
This mean that x and y are non linear correlated, but them are correlated.
For this type of data is used a non linear correlation technique know it as logarithm correlation.
Option c is incorrect because random patterns have a correlation value close to 0, which is not the case.
So ,
The correct options are;
a. The variables x and y also have a correlation close to 1
b. A scatterplot of the variables log x andy shows a strong nonlinear pattern
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what numbers do you need to determine the surface area of a right cone?; what numbers must you know to find the surface area and volume of a sphere?; find the volume of the sphere with a great circle of radius 7 cm.; given a regular pentagon with radius 5, and each side of length 6, find the area of the pentagon.
1) To determine the surface area of a right cone, we must know the radius of the circular base and height of the cone.
2) To determine the surface area and volume of a sphere, we must know the radius of the sphere.
3) The volume of the sphere with a great circle of radius 7 cm is 1436.75 cubic centimeters
4) The area of a regular pentagon with radius 5, and each side of length 6 is 45 square units
To determine the surface area of a right cone:
The formula for the surface area of a right cone is,
A = πr[r + √(h² + r²)]
this means, to determine the surface area of a right cone, we must know the radius of the circular base and height of the cone.
To find the surface area and volume of a sphere:
The formula for the surface area of sphere is,
A = 4πr²
and the formula for the volume of sphere is,
V = 4/3 πr³
This means, to determine the surface area and volume of a sphere, we must know the radius of the sphere.
For a sphere with radius r = 7 cm the volume would be,
V = 4/3 * π * 7³
V = 1436.75 cubic centimeters
Now we need to find the area of a regular pentagon with radius 5, and each side of length 6.
The formula for the area of a regular pentagon is:
A = 1/2 × P × a
where 'p' is the perimeter of the pentagon and 'a' is the apothem of a pentagon.
The perimeter of the pentagon is:
P = 5 * side lengths
P = 5 * 6
P = 30 units
We know that an apothem of a regular polygon is a radius of the inscribed circle.
From given dimensions, a = 5 units
so, the area of a regular pentagon would be,
A = 1/2 × 30 × 5
A = 45 square units
Therefore, the area of a regular pentagon is 45 square units
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If you want to invest $20,000 in a no-load mutual fund with a 6.5% yield, how much will you earn each year?
If you want to invest $20,000 in a no-load mutual fund with a 6.5% yield then 1300 we earn each year.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
The amount to invest is $20,000
Twenty thousand is the investment
and 6.5% is the yield.
We need to find how much we earn in each year.
Convert 6.5% to decimal
6.5/100=0.065
Multiply 0.065 with the 20000
0.65×20000
1300
Hence, we earn 1300 each year as an interest.
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A conical-shaped reservoir has a depth of 20 feet and a radius of 10 feet. Water is leaking out so that the surface is falling at the rate of 1/2ft/hr. Find the rate, in cubic feet per hour at which water is draining when the water is 8 feet deep. V=1/3πr2h
The rate at which water is draining when the water is 8 feet deep is calculated to be 2.54 ft³/ h
The vertex angle of the conical-shaped reservoir can be given as follows;
tan θ = R/H
Here R represents the radius and H illustrates the depth
so here we can say that the vertex angle will remain constant; therefore;
r/y = R/H
r/8 = 10/20
r = (10/20) × 8
r = 4
now for the volume, we can say;
V=1/3πr^2h
also, we can say;
r = y/2
Therefore here we will have;
V = 1/3π(y/2)^2y = 1/12 πy³
now for volume flow rate, we can determine as follows;
Q = dV/dt = 3/12πy²(dy/dt)
Q = 1/4 πy²v
Substituting the values as follows;
Q = 1/4 π(8)²(1/2)ft³/h
Q = 2.54 ft³/ h
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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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The vertex form of the quadratic function f(x) = -6x² - 60x - 151 is
f(x)= a(x - h)² + k.
What is the value of a?
What is the value of h?
What is the value of k?
This is one way of writing a quadratic function:
[tex]f(x)= a(x-h)^2+k[/tex]
(h,k) = vertexa = vertical stretchSolving the QuestionWe're given:
[tex]f(x) = -6x^2 - 60x - 151[/tex]
To write a quadratic function in vertex form, we must complete the square.
⇒ Put parentheses around the first two terms containing x and x²:
[tex]f(x) = (-6x^2 - 60x) - 151[/tex]
⇒ Factor out -6 (keeping the x's in the parentheses):
[tex]f(x) = -6(x^2+10x) - 151[/tex]
⇒ To complete the square, add, inside the parentheses, the square of half the coefficient of x.
⇒ In this case, the coefficient of x is 10.⇒ Half of this value is 5.⇒ The square of 5 is 25.⇒ Add this inside the parentheses:[tex]f(x) = -6(x^2+10x+25) - 151[/tex]
⇒ Now, we cannot randomly introduce a new value into a function. To balance the +25, subtract -6(25) outside the parentheses:
[tex]f(x) = -6(x^2+10x+25) - 151-(-6*25)\\f(x) = -6(x^2+10x+25) - 151-(-150)\\f(x) = -6(x^2+10x+25) - 151+150\\f(x) = -6(x^2+10x+25) - 1[/tex]
⇒ Finally, complete the square.
Remember: [tex](a+b)^2=a^2+2ab+b^2[/tex]In this case, a is x, and b is 5:[tex]f(x) = -6(x+5)^2 - 1[/tex]
Answer[tex]f(x) = -6(x+5)^2 - 1[/tex]
a = -6h = -5h = -1Usain 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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Find the angle θ , in radians, in the given right triangle. The length of the side adjacent to θ is 16 and the length of the side opposite θ is 10. A right triangle with height 10 opposite from angle theta and base 16 adjacent to angle theta. 10 16 Round your answer to the nearest hundredth
Angle θ is equal to 0.56 radian.
What do you mean by inverse trignometry?
Inverse trigonometric functions are just the sine, cosine, tangent, cotangent, secant, and cosecant functions of the fundamental trigonometric functions. The terms arcus functions, antitrigonometric functions, and cyclometric functions are also used to describe them. To find the angle for any trigonometric ratio, apply these inverse trigonometric functions.
It is given that in right angle triangle, base of the triangle is 16 and height of the triangle is 10.
Now to find θ, from the given right angled triangle. Using the formula for tanθ
tanθ = P/B = 10/16 = 5/8
θ = [tex]tan^{-1}(5/8) = tan^{-1}(0.625) = 0.56[/tex] radian.
Therefore, angle θ is equal to 0.56 radian.
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help meeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeeeeeee
The estimate of the number of students studying abroad in 2003 is 169 and the estimate of the number of students studying abroad in 2018 is 433
a. Estimate the number of students studying abroad in 2003.
The function is given as:
y = 123(1.065)^x
Where x represents years from 1998 to 2013
2003 is 5 years from 1998.
This means that
x = 5
Substitute the known values in the above equation
y = 123(1.065)^5
Evaluate the exponent
y = 123 * 1.37008666342
Evaluate the product
y = 168.520659601
Approximate
y = 169
Hence, the estimate of the number of students studying abroad in 2003 is 169
b. Assuming this equation continues to be valid in the future, use this equation to predict the number of students studying abroad in 2018.
2018 is 20 years from 1998.
This means that
x = 20
Substitute the known values in the above equation
y = 123(1.065)^20
Evaluate the exponent
y = 123 * 3.52364506352
Evaluate the product
y = 433.408342813
Approximate
y = 433
Hence, the estimate of the number of students studying abroad in 2018 is 433
17. You probably know the Fibonacci numbers 1,1,2,3,5,8,⋯ , where f n+2 =f n+1 +f n and we number as f 1 =1,f 2 =1 . Try applying the Euclidean algorithm to a pair of consecutive Fibonacci numbers? As a function or formula of n , how long does it take?
Applying the Euclidean algorithm to a pair of consecutive Fibonacci numbers is GCD of that numbers .
Given :
You probably know the Fibonacci numbers 1 , 1 , 2 , 3 , 5 , 8 , ⋯ , where f n+2 = f n+1 + f n and we number as f 1 = 1,f 2 = 1 . Try applying the Euclidean algorithm to a pair of consecutive Fibonacci numbers .
Euclidean algorithm :
The Euclidean Algorithm is a technique for quickly finding the GCD of two integers .
GCD ( 1 , 2 )
2 = 1 * 2 + 0
GCD ( 1 , 0 )
hence GCD ( 1 , 2 ) is 1 .
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Here are the first four terms of a sequence. -1 4 9 14 Write an expression for the n th term of this sequence.
Answer:
The nth term is aₙ = 5n - 6-------------------------------------
Given sequence:
-1, 4, 9, 14, ...We observe that it has a linear increase and common difference of terms is 5:
4 - (-1) = 9 - 4 = 14 - 9 = 5So d = 5, a₁ = - 1, find the nth term:
aₙ = a₁ + (n - 1)daₙ = - 1 + (n - 1)*5 = - 1 + 5n - 5 = 5n - 6A prestigious university wants to estimate the average starting salary of its graduates. The alumni outreach department sends an email to the most recent address they have on file for every graduate. The email asks the graduates to participate in a survey about their employment history and starting salary.
What are some possible concerns?
Some graduates won't check their emails and therefore won't respond (non-response bias)
Graduates might claim they make more $ than they actually do (response bias)
The correct option is option C i.e., current students are not included in the sample for the survey.
Current students are not required to participate in this survey because its main objective is to learn about respondents' career histories and starting salaries .
Survey could mean:
Research into humans and statistics.
A statistical survey is a technique for gathering numerical data on constituents of a population.
Type of survey
Spatial measurement : measuring places and distances on Earth using the technique and science of surveyingPhotogrammetry, a method of collecting information using aerial photographs and satellite imageryCadastral surveyors provide paperwork, diagrams, plats, and maps to prove who owns the land.
Most of Western Canada is divided into one-square-mile pieces using the Dominion Land Survey technique for agricultural and other uses. Identifying and surveying land parcels in the United States using the Public Land Survey System.
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