A dog weighs 80 pounds more than a cat. Their combined weight equals 120 pounds. What is the dog’s weight?

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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The graph of the point of intersection is given below.

The point of intersection.

(5/√17, 20/√17) and (-5/√17, 20/√17)

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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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

Answer: 193

Step-by-step explanation:

(12 x 16) + 9/9 = 192 + 1 = 193

Assuming second term is 9/(3²)?

Answer:

Step-by-step explanation:

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.

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:

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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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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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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∠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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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.

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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Answer:

-------------------------------------

Given sequence:

We observe that it has a linear increase and common difference of terms is 5:

So d = 5, a₁ = - 1, find the nth term:

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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The solution of the logarithm equation are as follows:

a. l = 100000

b. l = 1000000

Any equation in the variable x that contains a logarithm is called a logarithmic equation.

Let's solve the logarithm equation as follows:

a.

50  = 10 log₁₀ l

Using logarithm law,

50  = 10 log₁₀ l

50  = log₁₀ l¹⁰

10⁵⁰ = l¹⁰

multiply both sides of the exponents by 1 / 10

Hence,

l = 10⁵

Hence, the value of  l = 100000

b.

60 = 10 log₁₀ I

Using logarithm rule,

60 = 10 log₁₀ I

60 = log₁₀ l¹⁰

10⁶⁰ = l¹⁰

multiply both sides of the exponents by 1 / 10

l = 10⁶

Hence, the value of  l = 1000000

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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

Cadastral 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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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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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.

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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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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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

Therefore the result of adding the system of equations  2x + y = 4  ,

6=3x-y is 5x =10

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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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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If you want to invest $20,000 in a no-load mutual fund with a 6.5% yield then 1300 we earn each year.

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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This is one way of writing a quadratic function:

[tex]f(x)= a(x-h)^2+k[/tex]

We'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.

[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.

[tex]f(x) = -6(x+5)^2 - 1[/tex]

[tex]f(x) = -6(x+5)^2 - 1[/tex]

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?

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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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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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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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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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.

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.

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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The area of the bridge(yellow part) is 297.9 m².

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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