Melissa made pancakes using a circle mold. The circumference of the mold is 25.12cm. which measurement would be the correct diameter for this same circle?

Answer:

Step-by-step explanation:

\(\dag\bf\:P(x_1,y_1)=(3,0)\)

\(\dag\bf\:Q(x_2,y_2)=(-1,3)\)

\(\dag\bf\:R(x_3,y_3)=(11,6)\)

❅ Distance between P and Q :

\(\sf\:PQ=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

\(\sf\:PQ=\sqrt{(-1-3)^2+(3-0)^2}\)

\(\sf\:PQ=\sqrt{(-4)^2+(3)^2}\)

\(\sf\:PQ=\sqrt{16+9}\)

\(\sf\:PQ=\sqrt{25}\)

\(\bf\:PQ=5\:unit\)

❅ Distance between Q and R :

\(\sf\:QR=\sqrt{(x_3-x_2)^2+(y_3-y_2)^2}\)

\(\sf\:QR=\sqrt{(11-(-1))^2+(6-3)^2}\)

\(\sf\:QR=\sqrt{(12)^2+(3)^2}\)

\(\sf\:QR=\sqrt{144+9}\)

\(\sf\:QR=\sqrt{153}\)

\(\bf\:QR=12.37\:unit\)

❅ Distance between P and R :

\(\sf\:PR=\sqrt{(x_1-x_3)^2+(y_1-y_3)^2}\)

\(\sf\:PR=\sqrt{(3-11)^2+(0-6)^2}\)

\(\sf\:PR=\sqrt{(-8)^2+(-6)^2}\)

\(\sf\:PR=\sqrt{64+36}\)

\(\sf\:PR=\sqrt{100}\)

\(\bf\:PR=10\:unit\)

◈ Perimeter of Triangle :

➝ perimeter = PQ + QR + PR

➝ perimeter = 5 + 12.37 + 10

➝ Perimeter = 27.37 unit

Answer:

Nominal decisions can be broken into two distinct categories: dichotomous decisions and polychotomous decisions.

4 centimeters per second is approximately equal to 0.0893 miles per hour.

To convert 4 centimeters per second to miles per hour, we'll follow these steps:

Convert centimeters to miles.

Convert seconds to hours.

Convert centimeters to miles.

To convert centimeters to miles, we need to perform the following conversions:

1 mile = 160,934 centimeters.

Therefore, to convert 4 centimeters to miles, we divide by the conversion factor:

4 centimeters / 160,934 centimeters = 0.0000248558 miles.

Convert seconds to hours.

To convert seconds to hours, we use the following conversion:

1 hour = 3,600 seconds.

Therefore, to convert 1 second to hours, we divide by the conversion factor:

1 second / 3,600 seconds = 0.000277778 hours.

Now, we can calculate the conversion from centimeters per second to miles per hour by dividing the distance in miles by the time in hours:

0.0000248558 miles / 0.000277778 hours = 0.089288624 miles per hour.

Therefore, 4 centimeters per second is approximately equal to 0.0893 miles per hour.

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The missing quantity is 100 books in the double number line.

A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other. Proportions are represented by the symbols "::" or "=".

Let the missing quantity be x in the double number line.

According to the given condition, we can write the proportion would be as:

40 books : 2 boxes = x books : 5 boxes

⇒ 40 / 2 = x / 5

Apply the cross-multiplication operation,

⇒ 40 × 5 = 2x

⇒ 2x = 200

⇒ x = 200/2

⇒ x = 100

Therefore, the missing quantity is 100 books in the double number line.

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Answer:

\(H^{-1}(x)=\dfrac{\ln\left(x+\frac{4}{9}\right)}{\ln \left(\frac{2}{3}\right)}\)

Step-by-step explanation:

Given function:

\(H(x)=\left(\dfrac{2}{3}\right)^x-\dfrac{4}{9}\)

The domain of the given function is unrestricted:  (-∞, ∞).

As aˣ > 0, the range of the given function is restricted:  (-⁴/₉, ∞).

The inverse of a function is its reflection in the line y = x.

To find the inverse of a function, replace x with y:

\(\implies x=\left(\dfrac{2}{3}\right)^y-\dfrac{4}{9}\)

Rearrange the equation to make y the subject.

Add 4/9 to both sides:

\(\implies x+\dfrac{4}{9}=\left(\dfrac{2}{3}\right)^y-\dfrac{4}{9}+\dfrac{4}{9}\)

\(\implies x+\dfrac{4}{9}=\left(\dfrac{2}{3}\right)^y\)

Take natural logs of both sides:

\(\implies \ln\left(x+\dfrac{4}{9}\right)=\ln \left(\dfrac{2}{3}\right)^y\)

\(\textsf{Apply the power law}: \quad \ln x^n=n \ln x\)

\(\implies \ln\left(x+\dfrac{4}{9}\right)=y\ln \left(\dfrac{2}{3}\right)\)

Divide both sides by ln(2/3):

\(\implies y=\dfrac{\ln\left(x+\frac{4}{9}\right)}{\ln \left(\frac{2}{3}\right)}\)

Replace y with H⁻¹(x):

\(\implies H^{-1}(x)=\dfrac{\ln\left(x+\frac{4}{9}\right)}{\ln \left(\frac{2}{3}\right)}\)

The range of the original function is the domain of the inverse of the function.

Therefore, the domain of the inverse function is  (-⁴/₉, ∞).

The required inverse function of the given function is given as H⁻¹(x) = log[x + 4/9] / log[2/3].

Given that,
A function H(x) = (2/3)ˣ - 4/9, the inverse of the given function is to be determined.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
H(x) = y
y = (2/3)ˣ - 4/9
y + 4/9 = (2/3)ˣ
log[y + 4/9] = x log[2/3]
Now. invert x and y
log[x + 4/9] = ylog[2/3]
y = log[x + 4/9] / log[2/3]
Now, put y = H⁻¹[x]
H⁻¹(x) = log[x + 4/9] / log[2/3]

Thus, the required inverse function of the given function is given as H⁻¹(x) = log[x + 4/9] / log[2/3].

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If A=(-8,9) and B=(4,4), using the formula for distance between two points, we get:

Therefore, the distance between A and B is 13 units

Formula for distance between two points:

Answer:

equation of the circle J with center K(-7,3) and radius 6 is=

x^2+y^2+14x-6y+22=0

Step by step explanation:

Equation of circle with given centre (h,k) and radius r is

(x-h)^2+(y-k)^2=r^2

Given centre are K(-7,3) and radius 6.

So equation of Circle=

(x- -7)^2+(y-3)^2=6^2

x^2+14x+49+y^2-6y+9=36

x^2+y^2+14x-6y+22=0 answer

Answer:

(x + 7)² + ( y − 3)² = 36

Step-by-step explanation:

The equation of a circle with center (h, k) and radius r is                                (x − h)² + (y − k)² = r².

Define h, k and r using the given values. So, h= −7, k = 3, and r = 6.

Substitute the values into the equation of a circle.

(x − (−7))² + (y −3)²= 62

Simplify.

(x + 7)² + (y − 3)²= 36

Therefore, the equation of the circle J with center K (−7, 3) and radius 6 is (x + 7)² + (y − 3)²= 36.

The distance covered is 36 km and the original rate is 4 km/hr

From the question, we have the following parameters that can be used in our computation:

Let speed be y and distance be x

The equation of time is

time = x/y

So, we have the following equations

x/(y + 1/2) = x/y - 1

x/(y - 1) = x/y + 3

So, we have

x/y - x/(y + 1/2) = 1

x/(y - 1) - x/y = 3

When solved graphically, we have

x = 36 and y = 4

This means that

The distance covered is 36 km and the speed is 4 km/hr

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The number of workers in all, in the company, given the percentage that are men and the number who are not, is 3, 600 workers

The percentage of workers who are men is 85 % which means that the percentage who aren't men is :

= 100 % - 85 %

= 15 %

The number of workers in the company is therefore :

= Number of workers who aren't men / Percentage who aren't men

= 540 / 15 %

= 3, 600 workers

Another way to find the number of workers is:

x = 85%x + 540

x - 0.85x = 540

0.15x = 540

x = 540 / 0.15

x = 3, 600 workers

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Answer:

Shoprite

Step-by-step explanation:

At giant each case of water is 4.33 You can figure this out by dividing the overall cost of 12.99 by 3 and that gives you the cost of one case of water. At Shoprite you get 4 cases for 12.00 again you divide the overall cost of 12.00 by 4 and that gives you 3.00 so you get a better deal at shoprite there fore shoprite is the better place to shop for water

Answer:

Octagon

Step-by-step explanation:

A polygon refers to a two-dimensional closed shape consists of straight sides.

Perimeter of a polygon = 24 inches

Length of each side of the polygon = 3 inches

Number of sides of a polygon = Perimeter of a polygon ÷ Length of each side of the polygon = \(\frac{24}{3} =8\)

An octagon is a polygon consisting of 8 sides of same dimension.

So,

Name of polygon is octagon.

The statement is true.

When the block is in equilibrium, each spring is stretched an additional ∆x. This implies that the forces from the two springs are balanced, and the block is not experiencing any net force in the equilibrium position.

When the block is set into oscillation with amplitude a, it will pass through its equilibrium point during the oscillation. At the equilibrium point, the displacement of the block is zero, and it changes direction. At this point, the block has its maximum speed v, as it is accelerating towards the equilibrium position.

The speed of the block decreases as it moves away from the equilibrium position, reaches zero at the maximum displacement (amplitude), and then starts accelerating towards the equilibrium point again. Therefore, when the block passes through its equilibrium point, it has its maximum speed v.

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The matrix A  eigenvalues and eigenvectors are as follows:

Eigenvalue λ1 = 1 with eigenvector v1 = [1, -1]

Eigenvalue λ2 = 6 with eigenvector v2 = [4, 1]

Using the equation  (A - λI)v = 0, where is an eigenvalue of A, I am the 2x2 identity matrix, and v is the associated eigenvector, we can determine the eigenvalues and eigenvectors of the matrix A = [[5, 4], [1, 2]].

First, we calculate the (A - λI) matrix's determinant:

det(A - λI) = |5-λ 4| = (5-λ)(2-λ) - 4 = λ^2 - 7λ + 6

|1 2-λ|

We obtain the characteristic equation by setting the determinant to zero:

λ^2 - 7λ + 6 = 0

We obtain two eigenvalues after solving for  λ :

λ = 1 and λ = 6

Next, For each eigenvalue, we identify the appropriate eigenvectors:

For λ = 1, We solve the system of linear equations represented by the equation(A - λI)v = 0:

4v1 + 4v2 = 0

v1 + v2 = 0

The second equation is evidently as straightforward as v1 = -v2. When we enter this into the initial equation, we get:

4v2 - 4v2 = 0

Thus, the eigenvector for λ = 1 is v = [1, -1].

For λ = 6, We solve the system of linear equations represented by the equation(A - λI)v = 0:

-v1 + 4v2 = 0

-v1 + 4v2 = 0

v1 - 4v2 = 0

It is evident that the first equation is just v1 = 4v2. When we enter this into the second equation, we get:

4v2 - 4v2 = 0

Thus, the eigenvector for λ = 6 is v = [4, 1].

Therefore, The matrix A  eigenvalues and eigenvectors are as follows:

Eigenvalue λ1 = 1 with eigenvector v1 = [1, -1]

Eigenvalue λ2 = 6 with eigenvector v2 = [4, 1]

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AnswerAnswer:

1. no

2. no

4. no

6. yes, none of the numbers repeat

8. yes, none of the numbers repeat

Step-by-step explanation:

It has been a while since I did this so  not exaI'm not exactly sure about the rest of them.

Answer:

An arc of a circumference or of a circle mostly is a portion of the circumference. The length of an arc for all intents and purposes is simply the length of this portion of the circumference in a definitely major way. The circumference itself can particularly be considered an arc that goes around the circle in a fairly major way.

Answer : value of x and y in the matrix equation is:

x = -3

y = +4, -4

Step-by-step explanation :

The matrix expression is:

\(\left[\begin{array}{ccc}x+4\\y^2+1\end{array}\right]+\left[\begin{array}{ccc}-9x\\-17\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]\)

First we have to add left hand side matrix.

\(\left[\begin{array}{ccc}(x+4)+(-9x)\\(y^2+1)+(-17)\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]\)

Now we have to add left hand side terms.

\(\left[\begin{array}{ccc}x+4-9x\\y^2+1-17\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]\)

\(\left[\begin{array}{ccc}4-8x\\y^2-16\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]\)

Now we have to equating left hand side matrix to right hand matrix, we get:

\(\Rightarrow 4-8x=28\text{ and }y^2-16=0\\\\\Rightarrow 8x=4-28\text{ and }y^2=16\\\\\Rightarrow x=-3\text{ and }y=\pm 4\)

Therefore, the value of x and y in the matrix equation is -3 and +4, -4 respectively.

Answer:

D is wrong. The correct answer choice is C ( x=-3 and y= +4, -4)

Step-by-step explanation:

Math unit test review

The probability that a class of 50 has an average score that is less than 77 is approximately 11.90%.

To solve this problem, we need to use the central limit theorem, which states that the distribution of sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
In this case, we have a population of marks on a biology final test that is normally distributed with a mean of 78 and a standard deviation of 6. We want to know the probability that a class of 50 has an average score that is less than 77.
Using the central limit theorem, we can calculate the standard error of the mean as follows:
standard error of the mean = standard deviation / square root of sample size
standard error of the mean = 6 / √50
standard error of the mean = 0.8485
Next, we need to calculate the z-score for a sample mean of 77:
z-score = (sample mean - population mean) / standard error of the mean
z-score = (77 - 78) / 0.8485
z-score = -1.18
We can use a standard normal distribution table or calculator to find the probability associated with a z-score of -1.18. The probability of a sample mean less than 77 is approximately 0.1190 or 11.90%.
Therefore, the probability that a class of 50 has an average score that is less than 77 is approximately 11.90%.

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Answer:

-1/2

Step-by-step explanation:

If you go to any point on the line, you count down 1 point, and over to the right by 2 points to get back to the line. That is what makes the slope -1/2.

Answer:

The slope of the line is \( - \frac{1}{2} \)

Step-by-step explanation:

☆Remember: \(slope = \frac{rise}{run} \)

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We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

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If car weighs "1650-kg" and truck weighs "3-tons", then weight of car as percentage of weight of truck is 55%.

In order to express the weight of car as a percentage of weight of truck, we need to convert the weights to the same unit of measurement.

We know that,

⇒ Weight of the car = 1650 kg,

⇒ Weight of the truck = 3 tons,

Since 1 ton is equal to 1000 kg, we convert the weight of truck from "ton" to "Kg" by multiplying it by 1000,

So, Weight of truck in kg = 3×1000,

Weight of truck in kg = 3000 kg,

So, Percentage = (Weight of car)/(Weight of truck) × 100,

Substituting the values,

⇒ Percentage = (1650/3000) × 100,

⇒ Percentage = 0.55 × 100,

⇒ Percentage = 55%

Therefore, the weight of the car is 55% of the weight of the truck.

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Answer:

-6/7

Step-by-step explanation:

since both fractions have a common denominator (bottom part of fraction) you would end up subtracting 4-10 which would give you a -6. the denominator stays 7 so you end up with -6/7

Given:

The equation is

\(y=21.2x\)

Where, y is earnings for working in dollars and cents and x is the number of working hours.

To find:

The rate of change.

Solution:

The slope intercept form of a linear function is

\(y=mx+b\)          ...(i)

Where, m is the slope and b is the y-intercept.

We have,

\(y=21.2x\)            ...(ii)

On comparing (i) and (ii), we get

\(m=21.2\)

Therefore, the rate of change is 21.2 dollar and cents per hour.

9514 1404 393

Answer:

  A.  Subtract 6 from the x value to get the y value.

Step-by-step explanation:

Sometimes, it works well to simply try the answers to see what works. Sometimes, it works better to use a point other than the first or second.

Using the last point (x, y) = (16, 10), we can try the rules:

  subtract 6 from x: 16 -6 = 10 . . . this rule works

  multiply by 1/2: 16×1/2 = 8, not 10 . . . doesn't work

  multiply by 1/4: 16×1/4 = 4, not 10 . . . doesn't work

  add 6 to x: 16 +6 = 22, not 10 . . . doesn't work

The only rule that works is ...

  Subtract 6 from the x value to get the y value.

_____

Additional comments

You cannot always assume the table represents a linear function. In this case, all of the answer choices are linear functions, so that is a reasonable assumption. The x-values all have the same difference: 4. The y-values also all have the same difference: 4. So the slope of the line is 4/4 = 1, which tells you right away that "multiply by 1/2" and "multiply by 1/4" will be wrong.

The x-values are all greater than the y-values, so "add 6 to the x value" will not be correct. Since the slope is 1, the difference between x and y will be a constant, easily found from any table entry.

  y = x + b . . . . equation of a line with a slope of 1

  2 = 8 + b . . . . using the first table entry

  -6 = b . . . . . . . subtract 8

Then ...

  y = x - 6

Answer:

summing up what the other person said,

its a, i also did this on edge 2021,

so i can confirm:).

Answer:

B trust me

Step-by-step explanation:

Answer:

There is a 9/10 probability that the marble will not be yellow.

Step-by-step explanation:

If there are a total of ten marbles, and there is one yellow marble, there is a

1 yellow marble / 10 total marbles chance of getting a yellow marble. Then subtract it from 10/10 to get the probability of NOT getting a yellow marble.

10/10 - 1/10 = 9/10.

Answer:

9/10

Step-by-step explanation:

I THINK I THINK I THINK

Answer:

-360

Step-by-step explanation:

I got it right

Answer:

vertex = (- 1, 0 )

Step-by-step explanation:

given a parabola in standard form

ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the vertex is

\(x_{vertex}\) = - \(\frac{b}{2a}\)

y = x² + 2x + 1 ← is in standard form

with a = 1 and b = 2 , then

\(x_{vertex}\) = - \(\frac{2}{2}\) = - 1

substitute x = - 1 into y for corresponding y- coordinate

y = (- 1)² + 2(- 1) + 1 = 1 - 2 + 1 = 0

vertex = (- 1, 0 )

The resultant matrix after elementary row operation is:

\(A = \left[\begin{array}{ccc}-12&20&8\\-24&3&-9\end{array}\right]\)

What is elementary row operation?

In mathematics, the elementary row operation is a method in which the two rows exchanged. In this, the rows are either multiplied, added or division. Sometimes, single row is multiplied by some constant.

According to the question, the given matrix A is written below:

\(A = \left[\begin{array}{ccc}-3&5&2\\8&-1&3\end{array}\right]\)

Now, performing elementary row operations represented by \(-3R_{2} +4R_{1}\)

The given matrix becomes after elementary row operations:

\(A = -3R_{2} + 4R_{1} = \left[\begin{array}{ccc}-12&20&8\\-24&3&-9\end{array}\right]\)

Hence, the resultant matrix after elementary row operation is::

\(A = \left[\begin{array}{ccc}-12&20&8\\-24&3&-9\end{array}\right]\)

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