A pet shop said that there are 24% of black cats and 16% wereorange. Assume that they're correct and a large sample of cats arerandomly selected.a.) What is the probability that two cats selected f

A radius and diameter are parts of a circle. Thus the reasons required in the question are given as;

i. A tangent is always perpendicular to the radius of a circle because they are always at a right angle.

ii. A line that is drawn from the end of a diameter of a circle to its circumference form a right angle because they are always perpendicular.

A circle is a figure that is bounded by a curved line which is called its circumference. Some of its parts are radius, diameter, chord, sector, etc.

Thus the reasons required in the question are given as;

i. A tangent is always perpendicular to the radius of a circle because they are always at a right angle.

ii. A line that is drawn from the end of a diameter of a circle to its circumference form a right angle because they are always perpendicular.

For further clarifications on parts of a circle, visit: https://brainly.com/question/15618723

#SPJ1

The correct statements of Polynomials are 40m⁶ - 4 = 4(10m⁶ - 1), 15m³ - 6m = 3m(5m² - 2), 6m² + 18m = 6m²(m + 3). so, the correct answer is A), B) and C).

The factorizations step by step:

40m⁶ - 4 = 4(10m⁶ - 1)

To factor out the common factor of 4, we can use the distributive property:

40m⁶ - 4 = 4 * 10m⁶ - 4 * 1

= 4(10m⁶ - 1)

Therefore, the statement is true.

15m³ - 6m = 3m(5m² - 2)

To factor out the common factor of 3m, we can use the distributive property:

15m³ - 6m = 3m * 5m² - 3m * 2

= 3m(5m² - 2)

Therefore, the statement is true.

6m² + 18m = 6m²(m + 3)

To factor out the common factor of 6m², we can use the distributive property:

6m² + 18m = 6m² * 1 + 6m² * 3

= 6m²(1 + 3)

= 6m²(m + 3)

Therefore, the statement is true.

32m⁴ + 12m³ = 4m³(8m + 3)

This statement is not true, as the factorization should be 4m³(8m² + 3).

To factor out the common factor of 4m³, we can use the distributive property:

32m⁴ + 12m³ = 4m³ * 8m² + 4m³ * 3

= 4m³(8m² + 3)

Therefore, the corrected statement is 32m⁴ + 12m³ = 4m³(8m² + 3). so, the correct options are A), B) and C).

To know more about Common Factors:

https://brainly.com/question/29167102

#SPJ4

Answer:

244,140,634

Step-by-step explanation:

Answer:

439 foot

Step-by-step explanation:

x/205=x+150/275

275x=205x+30750

70x=30750

x=439 foot

Answer:

Slope=3/2

Y-intercept=3

Step-by-step explanation:

Step-by-step explanation:

Applying Pythagoras theorem ,

\({24}^{2} = {11}^{2} + {x}^{2} \\ 576 = {121} + {x}^{2} \\ {x}^{2} = 576 - 121 \\ {x}^{2} = 455 \\ x = \sqrt{455} \\ x = 21.33\)

To determine which of the given sets is a subspace of ℝ³, check if they satisfy the 3 properties of a subspace: closure under addition, closure under scalar multiplication, and containing the zero vector.

In summary, the only set that is a subspace of ℝ³ is W = {(a, b, 1): a and b are real numbers}.

To learn more about subspace visit:

brainly.com/question/13390612

#SPJ11

The class() function will return the class or data type of the object a.

To use the accessor $ to extract the state abbreviations and assign them to an object a, we need to know the specific context or data structure involved. The $ accessor is commonly used in programming languages like R and jQuery to access specific elements or properties within an object or data frame.

Assuming we have an object or data frame containing state abbreviations, we can use the $ accessor in R as follows:

a <- object$state_abbreviations

Here, "object" refers to the name of the object or data frame containing the state abbreviations, and "state_abbreviations" represents the specific column or property that holds the state abbreviations.

Regarding the class of the object a, we can determine it by using the class() function in R:

class(a)

The class() function will return the class or data type of the object a.

Learn more about function here:

https://brainly.com/question/11624077

#SPJ11

Points a,b and c satisfied the Pythagoras theorem. Thus, the triangle abc is a right angled triangle.

Every triangle has inner angles that add up to 180 degrees. A right angle and a right triangle are both formed when one of their internal angles is 90 degrees.

Given coordinates :

a(5,2) , b(2,-3) and c(-8,3).

Find the distance between the points using the distance formula:

d = √[(x2 - x1)² + (y2 - y1)²]

ab = √[(2 - 5)² + (- 3 - 2)²]

ab = √[(-3)² + (- 5)²]

ab = √[9 + 25]

ab = √34

ab² = 34

bc = √[(2 + 8)² + (- 3 - 3)²]

bc  = √[(10)² + (- 6)²]

bc  = √[100 + 36]

bc  = √136

bc²  = 136

ac = √[(-8 - 5)² + (3 - 2)²]

ac = √[(-13)² + (1)²]

ac = √[169 + 1]

ac = √170

ac² = 170

Now,

(ac)² = (bc)² + (ab)²

170 = 136 + 24

170 = 170

This, points a,b and c satisfied the Pythagoras theorem. Thus, the triangle abc is a right angled triangle.

know more about the right angled triangle

https://brainly.com/question/64787

#SPJ1

This linear relationship is also known as Beer's Law

The main purpose of creating the Beer's Law plot with the concentration of the Allura Red dye on the x-axis and absorbance on the y-axis is to show the linear relationship between the concentration of the Allura Red dye and its absorbance.

This linear relationship is also known as Beer's Law.

Learn more about Beer's Law

brainly.com/question/30723190

#SPJ11

Step-by-step explanation:

Para hacer las porciones para 32 personas, multiplique cada cantidad de ingrediente por 4 ya que la receta proporciona 8 porciones y 8 * 4 = 32

Papa seca = \(\frac{1}{2} *4\)

                     = 2 papas secas

Cerdo = \(\frac{1}{2} *4\)

       = 2 kg de carne de cerdo

Cebollas = 1 * 4

            = 4 cebollas grandes

Aji panca = 3 * 4

               = 12 cucharadas de aji panca

Ajo molido = \(1\frac{1}{2} *4\)

                       = \(\frac{3}{2} *4\)

                       = 6 cucharadas de ajo molido

Sal = 1 * 4

      = 4 cucharadas de sal

The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

Learn more about equation at

https://brainly.com/question/12998758

#SPJ11

To compare numerical measurements of body condition (Cond) between two different age groups using SPSS outputs, you can follow these steps:

Import your data into SPSS and make sure the variable for age group is coded appropriately (e.g., 1 for Group 1, 2 for Group 2).

Run a descriptive statistics analysis for the variable "cond" separately for each age group.

This will provide you with the mean and standard deviation for each group.

To compare the means between the two groups, you can use an independent samples t-test.

Go to Analyze > Compare Means > Independent Samples T-Test.

Select "cond" as the Test Variable and "age group" as the Grouping Variable.

Click OK to run the analysis.

The output will provide you with the t-value, degrees of freedom, and p-value.

The t-value indicates the magnitude of the difference between the means,

while the p-value tells you if the difference is statistically significant.

If the p-value is less than your chosen significance level (e.g., 0.05),

you can conclude that there is a significant difference in body condition between the two age groups.

Remember to interpret the results in the context of your study and consider any limitations or potential confounding factors.

To know more about measurements visit:

https://brainly.com/question/28913275

#SPJ11

To find a nonzero solution to a system of homogeneous equations, the corresponding matrix must be singular, meaning it has no inverse and its determinant is zero, allowing for the existence of eigenvectors corresponding to the eigenvalue λ = 0.

When we have a system of homogeneous equations, it means that all the equations in the system have a right-hand side of zero. Such a system can be written as Ax = 0, where A is the coefficient matrix and x is the column vector of variables.

To find a nonzero solution, we need to find a value of x such that Ax = 0, but x ≠ 0.

If A is a singular matrix, it means that it has no inverse, and its determinant is zero. This implies that the rows of A are linearly dependent, which in turn means that the columns of A are also linearly dependent. In other words, some of the columns of A can be expressed as linear combinations of the others.

When we multiply a singular matrix A by any nonzero vector x, we get a linear combination of its columns that equals zero, since the columns of A are linearly dependent.

Therefore, we can always find a nonzero vector x that satisfies Ax = 0. This nonzero vector x is called an eigenvector corresponding to the eigenvalue λ = 0, which is the only eigenvalue of a singular matrix.

Hence, finding a nonzero solution to a system of homogeneous equations requires that the matrix corresponding to this system is singular because only singular matrices have eigenvectors corresponding to the eigenvalue λ = 0, which are the solutions to the homogeneous equation Ax = 0.

To know more about homogeneous equations refer here:

https://brainly.com/question/30504189#

#SPJ11

Total number of men and women wearing sunglasses = 290

According to the question,

Total number of men and women = 2000

half of the adults were women = 1/2 × 2000

Number of women = 1000

Number of men = (Total adults) - (Number of women )

Number of men = 2000 - 1000

= 1000

given,

20% of women were wearing sunglasses = 20/100 × 1000

= 200

9% of men were wearing sunglasses = 9/100 × 1000

= 90

Total number of adults wearing glasses = 200 + 90

= 290

In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is often denoted by the symbol "%" or simply as "percent" or "pct." For example, 35% is equivalent to the decimal 0.35, or the fraction.

To learn more about percentage from the given link

https://brainly.com/question/24304697

#SPJ4

The first and the second terms of the recursive sequence are given as follows:

a) u(1) = -25.

b) u(2) = -15623.

The definition of the recursive sequence is presented as follows:

u(n + 1) = u(n)³ + 2.

The initial term is needed to solve the sequence, hence it is given as follows:

u(0) = -3.

Thus the term with index 1 is given as follows:

u(1) = u(0)³ + 2.

u(1) = -3³ + 2

u(1) = -27 + 2

u(1) = -25.

Considering the term with index 1, the term with index 2 is obtained as follows:

u(2) = u(1)³ + 2

u(2) = (-25)³ + 2

u(2) = -15623.

And then the same rule is obtained if needed to obtain the 3th, 4th terms, and so on, considering the previous term and the definition.

More can be learned about recursive sequences at https://brainly.com/question/27868858

#SPJ1

Answer:

D

Step-by-step explanation:

So we want to find θ. We are already given the hypotenuse and the side length opposite to θ. Therefore, we can use the trig function sine to find θ.

Recall that:

\(\sin(\theta)=opp/hyp\)

Plug in 10.2 for the opposite side and 15 for the hypotenuse:

\(\sin(\theta)=10.2/15\)

Solve for θ. Use a calculator:

\(\theta=\sin^{-1}(10.2/15)\\\theta\approx42.8436\textdegree\)

The answer is D.

Answer:

Please see below for answers and explanation and attachments

Step-by-step explanation:

These models are best figured out using regression analysis which is a rather complicated computation but luckily there are calculators that can solve

1. The best way to approach this problem is to plot the values and see whether the model is a linear equation or a higher degree equation.

For all three cases it appears that the equations are not linear which would have suggested a model of the form y = mx + b where y = profit in $, x = hours, m is the slope (rate of increase in profit) and b a constant, the y-intercept

For example if you look at the data for the dog walker table, the increase in $ for every additional hour of service is not constant eliminating a linear model. For the first hour, the increase is $7, the second hour it is $11, the third it is $27

So i assumed a quadratic model of the form y = ax² + bx + c where y = profit in $ and x is the number of hours of service for all three businesses

There are plenty of online calculators out there which can rapidly compute the quadratic regression model parameters fitting the data and provide a level of goodness of fit of the equation through a statistic known as the correlation coefficient, r

I entered the data for all 3 rows and came up with the following results
In all the equations, y represents the profit in $ and x the hours

I have also attached screenshots of the computation results which should be self explanatory

Dog Walker

Equation:
y = 1.05357x² + 8.3964x - 6.7

Correlation Coefficient r:
0.9913546  (pretty high goodness of fit)

House Sitter
Equation:
\(y = 1.482x^2 + 1.396x + 9.3\)

Correlation Coefficient r:
0.99556069

Lawn Care
Equation:
y = -5.875x² + 30.582143x + 116.9

Coefficient of Correlation r:
0.9794537681  

The attached screenshots will provide all necessary info.

I hope that helps ya out :)

The name of the segment inside the large triangle is called the: 3. angle bisector.

The word "bisect" means to divide into two equal halves. Therefore, an angle bisector can be defined as a line segment that divides the an angle in a triangle into two parts that are of the same angle measure.

The image shows a triangle which has a segment that divides a vertex angle into equal parts. Thus, the segment can be named as an angle bisector.

A perpendicular bisector divides a segment into two equal halves at right angle, while a midsegment joins the middle points of two sides of a triangle. The median also, is a segment that joins a vertex of a triangle to the midpoint of the side that is opposite the angle.

Therefore, we can state that the name of the segment is: 3. angle bisector.

Learn more about the angle bisector on:

https://brainly.com/question/24334771

#SPJ1

The correct option that describes the number and type of solutions of the quadratic equation is: There are two unequal real solutions. The correct answer alternative is option a.

The discriminant of a quadratic equation is the part of the equation under the square root in the quadratic formula, which is b² - 4ac. In the given equation, 2x² - 7x + 4 = 0, the values of a, b, and c are 2, -7, and 4, respectively.

To compute the discriminant, we plug in these values into the formula:

Discriminant = b² - 4ac
= (-7)² - 4(2)(4)
= 49 - 32
= 17

The discriminant is 17.

To determine the number and type of solutions of the quadratic equation, we look at the value of the discriminant. If the discriminant is greater than 0, there are two unequal real solutions. If the discriminant is equal to 0, there is one real solution. If the discriminant is less than 0, there are two imaginary solutions.

Since the discriminant in this case is 17, which is greater than 0, there are two unequal real solutions. Therefore, the correct answer is (a) There are two unequal real solutions.

To know more about  quadratic equation here:

https://brainly.com/question/30098550#

#SPJ11

Answer:I hope this helps.

Step-by-step explanation:

In determining whether a process is in statistical control, the R-chart should be analyzed first.

Given that, in determining whether a process is in statistical control, the _____ should be analyzed first.

A quality control technique called statistical process control uses statistical techniques to monitor and manage a process. This makes it possible to maintain an effective process that generates more products that meet specifications while using less trash.

When measuring small subgroups (n 10) from a process at regular intervals, an R-chart is a sort of control chart that is used to track the process variability (as the range). The value of a subgroup range is represented by each point on the chart.

Therefore, in determining whether a process is in statistical control, the R-chart should be analyzed first.

To learn more about statistical control visit:

https://brainly.com/question/17150305.

#SPJ4

The expression that does not represent "four more than one-third x" is 0X +4.

"Four more than one-third x" can be represented algebraically as 1/3x + 4. The expressions 11x + 3 and 01/x + 4 do not contain the term 4, so they cannot represent "four more than one-third x".

On the other hand, the expression 0X + 4 is equivalent to just 4, since any term with a coefficient of zero can be omitted. Therefore, 0X + 4 does not contain the term 1/3x, and thus it also does not represent "four more than one-third x".

For more questions like Expression click the link below:

https://brainly.com/question/14083225

#SPJ11

Answer:

d= Deondre's age

d + 3

c = the number of people in the class

1/2c

w = wildcat's score

a = away team's score

w = 2a + 7

c = cost of the sweater

s = the regular cost of the sweater

c = 1/2s

y = total in the bank

x = number of weeks

y = 75x + 300

y = altitude

x = number of minutes

y = 200x + 1000

Step-by-step explanation:

We need to pour 250 ml of liquid from container B to container A so they can be equal in volume.

To make container A and B equal in volume, we need to pour some liquid from container B into container A. Let's call the amount of liquid that we need to pour from container B to container A as "x" ml.

After pouring x ml of liquid from container B to container A, the total volume of liquid in container A will be (750 + x) ml, and the total volume of liquid in container B will be (1250 - x) ml.

Since we want the volumes of both containers to be equal, we can set up the equation:

750 + x = 1250 - x

Solving for x:

2x = 500

x = 250

Therefore, we need to pour 250 ml of liquid from container B to container A so they can be equal in volume.

To learn more about Equation

https://brainly.com/question/29657988

#SPJ4

To rotate a point around a vector in 3D, you can use the Rodrigues' rotation formula, which involves finding the cross product of the vector and the point, then adding it to the point multiplied by the cosine of the angle of rotation and adding the vector cross product multiplied by the sine of the angle of rotation.

To rotate a point around a vector in 3D, you can use the Rodrigues' rotation formula, which involves finding the cross product of the vector and the point, then adding it to the point multiplied by the cosine of the angle of rotation and adding the vector cross product multiplied by the sine of the angle of rotation.

The formula can be written as:

Rotated point = point * cos(angle) + (cross product of vector and point) * sin(angle) + vector * (dot product of vector and point) * (1 - cos(angle)) where point is the point to be rotated, vector is the vector around which to rotate the point, and angle is the angle of rotation in radians.

Rodrigues' rotation formula can be used to rotate a point around any axis in 3D space. The formula is derived from the rotation matrix formula and is an efficient way to rotate a point using only vector and scalar operations. The formula can also be used to rotate a set of points by applying the same rotation to each point.

To know more about Rodrigues rotation formula refer here:

https://brainly.com/question/32592897

#SPJ11