Find the area of a circle with a radius of 4 m two ways. First, find it using the formula for the area of a circle. Then, find it by breaking the circle into equal sectors and rearranging the sectors as a parallelogram. Show all calculations. Use π, instead of an approximation, in your answers. Round to the nearest tenth

From the given information provided, Susan's percentile rank in class is approximately 6.9%.

To find the percentile rank for Susan who is 5th in a class of 58 students, we need to use the following formula:

Percentile rank = (Number of students below Susan / Total number of students) x 100

Since Susan is the 5th student in the class, there are 4 students with higher ranks than her. Therefore, the number of students below Susan is 4.

Using the formula, we can calculate the percentile rank as:

Percentile rank = (4 / 58) x 100

Percentile rank = 6.9 (rounded to one decimal place)

Learn more about percentile here: brainly.com/question/28395856

#SPJ4

Answer:

Step-by-step explanation:

the coefficients of this quadratic are -1, 4 and 4, and so the discriminant b^2 - 4ac works out to 16 - 4(-1)(4), or 0.  Thus this graph has two real, equal roots which are the same point on the graph, the vertex, the maximum of the function.

Letting x = 0, we find that y is 4.  Thus, the y-intercept is (0, 4).  Plot this.

Using the formula x = -b / [2a], we find the axis of symmetry:

   x = -4 / [2*(-1)] = -4 / [-2] = +2

The axis of symmetry is the vertical line x = 2.  

At x = 2, y = -(2)^2 + 4(2) + 4, OR -4 + 8 + 4, or 0.

The vertex and maximum value are (2, 0).  The graph touches the x-axis in only one place.

Draw the axis of symmetry x = 2.  Plot the vertex (2, 0) and the y-intercept.  Reflect the y-intercept about the axis of symmetry to obtain a second point on the graph at the same y-value as (0, 4).

basically you would do length x width

5x and x

6 and 4

Use the slope formula below:

\( \large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }\)

The m-term represents the slope.

The formula is the changes of two y-points over the changes of two x-points. We are given two points. Substitute both points in the formula.

\( \large{m = \frac{9 - ( - 7)}{ - 2 - 4} } \\ \large{m = \frac{9 + 7}{ - 6} \longrightarrow \frac{16}{ - 6} } \\ \large{m = \frac{8}{ -3 } \longrightarrow - \frac{8}{3} }\)

Therefore the slope is -8/3

Answer

Hope this helps! Let me know if you have any doubts.

Answer:

y = -8 / 3x + 11/3

Step-by-step explanation:

Using the slope formula:

\(slope = y = \frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}\)

1. Select one point to be \((x_{1} ,y_{1} )\) and the other \((x_{2} ,y_{2} )\)

I chose (-2, 9) to be \((x_{1} ,y_{1} )\) and (4, -7) to be \((x_{2} ,y_{2} )\)

2. Plug the values into the formula:

\(y = \frac{-7-9}{4-(-2)} \\\\y= \frac{-16}{6} \\\\y = \frac{-8}{3}\)

3. Finding the c-value by plugging in one of the points into the equation

y = mx + c

9 = -8/3 (-2) + c

9 = 16/3 + c

c = 11/3

4. y = -8/3x + 11/3

Answer:

-6y+27

Step-by-step explanation:

-3*2y=-6y

-3*-9=27

because multiplying 2 negatives make a positive.

so,

-3(2y-9) = -6y+27

Answer:

x=4

Step-by-step explanation:

There

The addition law is particularly useful when calculating the probability of the union of two events. It allows us to determine the probability of either event A or event B occurring.

This law provides a straightforward method for calculating probabilities in situations where we want to know the likelihood of at least one of the events happening.

The addition law, also known as the sum rule, states that the probability of the union of two events A and B is given by the sum of their individual probabilities minus the probability of their intersection. Mathematically, this can be expressed as P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

When we are interested in computing the probability of the union of two events, the addition law allows us to combine the probabilities of the individual events to obtain the overall probability of at least one of them occurring. It is particularly helpful in situations where the events are not mutually exclusive, meaning that they can occur together or independently.

In contrast, when calculating the probability of the intersection of two events or dealing with conditional events, other rules such as the multiplication rule and conditional probability formulas are more appropriate.

To learn more about intersection click here:

brainly.com/question/12089275

#SPJ11

Answer:

I think it might be d because it is the only one with 4x and 10

A histogram is a univariate display of quantitative data that organizes data into bins and shows the frequency of observations within each bin.


A histogram is a graphical representation that displays the distribution of quantitative data. It consists of a series of contiguous bars, where each bar represents a specific range or bin of values, and the height of the bar corresponds to the frequency or count of observations falling within that range.

Histograms are commonly used to visualize the shape, central tendency, and spread of a dataset. By examining the heights of the bars, one can determine the frequency of values within each bin and identify patterns such as peaks or clusters. This makes histograms an effective tool for exploring the distribution and characteristics of a single variable in a dataset.

Learn more about Dataset here: brainly.com/question/24058780
#SPJ11

The standard deviation of the thickness of layer 1 = 15.81 x 10⁻⁵ m

                                                                       layer 2 = 20 x 10⁻⁵m

                                                                       layer 3 = 17.32 x 10⁻⁵ m

The variance of the thickness of the three layers is 25,40 and 30 in nanometers

Let v₁, v₂, v₃ be the variance of the three layers of thickness.

Then, the standard deviation of the thickness of these layers can be found using the formula

                             v = σ²

Let us re-write this equation in order to find the standard deviation,

                             σ = √v

where v is the variance and

          σ is the standard deviation

The standard deviation of layer 1 is

                          σ₁ = √v₁

                              = √(25 x 10⁻⁹)

                              = √(250 x 10⁻¹⁰)

                              = 15.81 x 10⁻⁵

The standard deviation of layer 2 is

                            σ₂ = √v₂

                                 = √(40 x 10⁻⁹)

                                 = √(400 x  10⁻¹⁰)

                                 = 20 x 10⁻⁵

The standard deviation of layer 3 is

                             σ₃ = √v₃

                                  = √(30 x  10⁻⁹)

                                  = √(300 x 10⁻¹⁰)

                                  = 17.32 x 10⁻⁵

Therefore, the standard deviation is 15.81 x 10⁻⁵m , 20 x 10⁻⁵ m, 17.32 x 10⁻⁵m

Learn more about the standard deviation in

https://brainly.com/question/13905583

#SPJ4

======================================================

Work Shown:

We use the first term to build to the second term.

Plug in n = 2

f(n) = -4f(n-1) + n

f(2) = -4f(2-1) + 2 ..... n replaced with 2

f(2) = -4f(1) + 2

f(2) = -4*4 + 2 ......... f(1) replaced with 4; since f(1) = 4

f(2) = -16 + 2

f(2) = -14

The second term is -14

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

Repeat for n = 3

f(n) = -4f(n-1) + n

f(3) = -4f(3-1) + 3 ..... n replaced with 3

f(3) = -4f(2) + 3

f(3) = -4*(-14) + 3 ......... f(2) replaced with -14

f(3) = 56 + 3

f(3) = 59

The third term is 59

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

We keep going until we get to f(5)

Plug in n = 4

f(n) = -4f(n-1) + n

f(4) = -4f(4-1) + 4 ..... n replaced with 4

f(4) = -4f(3) + 4

f(4) = -4*(59) + 4 ......... f(3) replaced with 59

f(4) = -236 + 4

f(4) = -232

The fourth term is -232

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

Just one more section

Plug in n = 5

f(n) = -4f(n-1) + n

f(5) = -4f(5-1) + 5 ..... n replaced with 4

f(5) = -4f(4) + 5

f(5) = -4*(-232) + 5 ......... f(4) replaced with -232

f(5) = 928 + 5

f(5) = 933

The fifth term is 933

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

As you can see, recursive sequences can get tedious for fairly large values of n. We need to compute every term before f(5) to figure it out. So if your teacher needed you to compute something like f(10), then it would get even worse. Sometimes it's possible to find a closed formula for it, but it may be tricky to find.

Answer:

x=36°

Step-by-step explanation:

Find the answer with the theorems related to isosceles triangle and the exterior angle theorem

With a down payment of $15,000, an annual income of $90,000, and a 30-year mortgage rate of 5%, you should be able to afford a house with a median price of $350,000 in your area.

To determine how expensive of a house you can afford, we need to consider several factors, including your income, down payment, mortgage rate, and the median house price.

First, let's calculate the loan amount. Subtracting your down payment of $15,000 from the median house price of $350,000 gives us a loan amount of $335,000.

Next, we need to calculate your monthly mortgage payment. To do this, we will use the 30-year mortgage rate of 5%. Converting this annual rate to a monthly rate, we get 0.05/12 = 0.0042.

Using an online mortgage calculator, we can determine that the monthly mortgage payment for a $335,000 loan at a 5% interest rate is approximately $1,794.

To determine how much you can afford, we need to consider your income. Assuming an annual income of $90,000, we can estimate your monthly income by dividing it by 12, which gives us $7,500.

As a general rule, lenders typically recommend that your monthly mortgage payment should not exceed 28% of your monthly income. In your case, 28% of $7,500 is $2,100.

Since your estimated monthly mortgage payment of $1,794 is below $2,100, you should be able to afford a house with a median price of $350,000, given your income, down payment, and mortgage rate.

Learn more about down payment  here:-

https://brainly.com/question/28765137

#SPJ11

i believe its √49.

the square root of 49 is 7, and 7 is a rational number

Step-by-step explanation:

526 133 3821

P: 12345

j _o _I _n g _I _r l

o. n z-oo-o-m

The length of longer piece of metal rod on division into two pieces is 7.18 meters.

Let the measurement of first piece be x meters. So, the measurement of second piece will be -

Three times = 3x

0.16 meters longer = 3x + 0.16

Total measurement of second piece = 3x + 0.16 meters.

Now, total measurement = measurement of first piece + measurement of second piece

Total measurement = x + 3x + 0.16

9.52 = 4x + 0.16

4x = 9.52 - 0.16

4x = 9.36

x = 9.36/4

x = 2.34 meters

Length of longer piece = 3(2.34) + 0.16

Length of longer piece = 7.18 meters

Learn more about equations -

https://brainly.com/question/22688504

#SPJ4

Answer:

12/7

Step-by-step explanation:

Point C is at ( 0,0)

Point D is at ( 7,12)

The slope is given by

m = ( y2-y1)/(x2-x1)

m = ( 12-0)/(7-0) = 12/7

A normal distribution can appear utterly erratic due to a lack of data. Results from tests taken in class, for instance, are often regularly distributed.

Given information;

Scores from the sit and reach test weren't normally distributed.

To find what is the likely cause for this lack of normal distribution,

⇒ A normal distribution can appear utterly dispersed due to Insufficient Data. For instance, test scores in the classroom are often regularly distributed.

To learn more about normal distribution click here:

brainly.com/question/29509087

#SPJ4

Step-by-step explanation:

Question 3 :

We have ,

Multiplying all three equations ,

=> a × b × c = bc * ac * ab

=> abc = a²b²c²

=> abc/a²b²c² = 1

=> 1/abc = 1

=> abc = 1

\(\rule{200}2\)

The length of IKE is 2x - 12.

A condition on a variable that is true for just one value of the variable is called an equation.

Since KITE is a kite, we know that KT = IT and KE = IE. Let's call the length of these diagonals d. Then we have:

KT + TI = d

KE + EI = d

Substituting in the given values, we get:

x + 6 + 2x = d

2x + IE = d

Solving for d in the first equation, we get:

3x + 6 = d

Substituting this into the second equation, we get:

2x + IE = 3x + 6

Solving for IE, we get:

IE = x + 6

Therefore, IKE is equal to:

IKE = IT - IE

IKE = (d - KT) - (x + 6)

IKE = (3x + 6 - x - 6) - (x + 6)

IKE = 2x - 12

So, the length of IKE is 2x - 12.

Learn more about equation on:

https://brainly.com/question/27893282

#SPJ4

The value of the low tide at T is 0.25 foot

The alternating advance and retreat of seawater along a coastline is called a tide. High tide is when water advances to its furthest extent onto the shoreline. Low tide is when it recedes to its furthest extent. Some freshwater rivers and lakes can have tides, too. A high tide that is significantly higher than normal is called a king tide. It often accompanies a new moon and when the moon is closest to the Earth.

Given here the data for low tides at locations P,Q,R as 0.63, -0.94, -1.02

and simple mean of the four locations with  T included x as the low tide for T  is given as

-0.27= (0.63-0.94-1.02+x )/4

x-1.33= -1.08

    x   = 0.25

Hence, The value of the low tide at T is 0.25 foot

Learn more about low and high tides here:

https://brainly.com/question/14683300

#SPJ5

Answer:

A&D

Step-by-step explanation:

Lines with the same slope are parallel. 2x-5 and 2x+5 have the same slope

Answer:

A and D are parallel.

Step-by-step explanation:

Refer to the slope-intercept equation (y = mx + b).

M = the slope

If the slopes are equal, then the lines are parallel.

The slope for line A is 2, and so is the slope for line D.

Line A and line D are parallel.

Answer:

∆ABC=∆DBC

Step-by-step explanation:

The angle of ABC, which is 90° is the same as the angle DBC which is also 90°

Step-by-step explanation:

15 / (1/3)  is equal to  15 x 3/1  = 15 x 3 = 45

4/16(100)

Step-by-step explanation:

Answer:

4/16(100)

Step-by-step explanation:

Yes Jake is correct we the scales are accurately represented.

From the information, the original scale factor for a scale drawing of a square swimming pool is 1/90, and the length of the original drawing is measured to be 8 inches.

Therefore, the original length will be:

= 8 ÷ 1/90

= 8 × 90

= 720 inches

Therefore, Jack is correct.

Learn more about scale on:

brainly.com/question/25722260

#SPJ1

Answer:

11xy+2x

Step-by-step explanation:

x(11y + 2)

11y(x)+2(x)=11xy+2x

Hope this helps!

Please mark as brainliest if correct!

Answer:

\(11xy + 2x\)

Step-by-step explanation:

Using the distributive property means that we multiply everything that is inside the brackets with everything that is outside the brackets.

For this question that means that we will multiply \(x\) with both \(11y\) and 2:

\(x(11y + 2)\)

⇒ \(x \times 11y + x \times 2\)

⇒ \(11xy + 2x\)

Therefore \(x(11y + 2)\) rewritten using the distributive property is \(11xy + 2x\).

Learn more about the Distributive Property here:

https://brainly.com/question/27543580