Consider n circles in a plane. Into how many regions will they divide the plane?
Suppose that n circles divide the plane into rn regions. Now you add another circle, C, that non-trivially intersects each of the first n circles. Start at any point on C and travel around C; you will cross one of the other n circles 2n times.
If p0 and p1 are two consecutive crossings, the arc of C from p0 to p1 divides one of the original rnregions into two smaller regions. You do this 2n times,that gives you a recurrence,
rn+1=rn+some simple function of n,
and you can fairly easily turn it into an expression for rn that is just a summation. If you do it right, it’s a summation that you can evaluate pretty easily in closed form to get a formula for rn.

70% of students had scores that were within (±) one standard deviation of the mean.

For the stated question-

Total number of students = 20

Scores received; 70, 60, 75, 68, 85, 86, 78, 72, 82, 88, 88, 73, 74, 79, 86, 82, 90, 92, 93, 73.

Mean = Sum of all/ Total number

Mean x = 79.7

standard deviation = 8.7

Thus, (±) one standard deviation SD of the mean becomes;

-1 SD; 79.7 - 8.7 ≈ 70.994

+1 SD; 79.7 + 8.7 ≈ 88.406

Thus, 71 to 88

Percentage = scores between  71 to 88/ total scores

Percentage = 14/20 x 100 %

Percentage = 70%

Thus, 70% of students had scores that were within (±) one standard deviation of the mean.

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7/11 is the probability of choosing a blue block.

Given:

a child has a box full of colored building blocks. he will choose one block without looking.

the odds against choosing a blue block are 47.

We need the probability of choosing a blue block,

Odds:

The odds of an event is the ratio of the probability of an event to the probability of its complement. In other words, it is the ratio of favorable outcomes to unfavorable outcomes.

The odds against choosing a blue block are 4/7 means. In 11 chances, 4 events will happen in which blue block will not be chosen and 7 events will happen in which blue blocks will be chosen.

So, the probability of not choosing the blue block is 4/11.

Probability of choosing blue block: complement of 4/11 which is equal to 7/11.

Hence we get the required answer.

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The following ways of measuring weight loss are more appropriate than correlation, i.e.,Skin calipers, Impedance scales, DEXA scanning, Body measurements.

Calories factor into the equation while trying to maintain a healthy weight. The key to losing weight is to burn more calories than you consume. You may do this by consuming fewer calories than you need and increasing the number of calories you burn via physical exercise.

A realistic, efficient, and lasting weight loss plan might be difficult to follow even if it may appear straightforward.

You don't have to do it by yourself, though. Seek advice from your doctor, family, and friends. Consider whether this is the right time and whether you're prepared to make the essential changes. Plan wisely as well: Consider how you'll respond to circumstances that put your determination to the test and the inevitable slight setbacks.

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With 98% confidence interval, all teenagers' mean number of hours watching TV per week will be (26.6,29.4).

98% confidence interval can be calculated as

Point estimate± Error margin

Point estimate=mean number of hours watching TV

students=28.

Error margin=1.4.

As per given data, the 98% confidence interval for all teenagers is

=28± 1.4

=(28-1.4,28+1.4)

=(26.6,29.4)

Statisticians use confidence intervals to assess the level of uncertainty in a sample variable. For instance, a researcher may select numerous samples at random from the same population and compute a confidence interval for each sample to estimate how each sample may correctly reflect the true value of the population variable. With certain intervals including the true population parameter and others not, each produced dataset is distinct. Confidence intervals are a set of values that are constrained by the mean of the statistic and are likely to include an unidentified population parameter. The confidence level is the proportion of likelihood, or certainty, that, after multiple draws from a random sample, the confidence interval would contain the true population parameter.

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The equation v in terms of other variables is v = kr/2h

It is a variable which is expressed in terms of other variables involved in the formula.

Formulas are written so that a single variable, the subject of the formula is on the L.H.S. of the equation. Everything else goes on the right side of the equation. We evaluate the formula by substituting for the literal numbers on the right hand side.

2(vh) / k = r

by cross multiplication

2(vh) = kr

divide both sides by 2h

v = kr/2h

In conclusion, v in terms of other variables is  kr/2h

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Step-by-step explanation:

|x+1|=2-5

|x+1|= -3

statement doesn't have solution

Answer:

No.

Step-by-step explanation:

Below I should you two ways to get the correct answer.

The depth of the given rectangular lot is 60 yards.

Here, we are given that the area of a rectangular lot is 1,200 square yards.

Further the width of the lot is 60 feet

As the area and the width are given in different units, we first need to convert them into the same units.

Now, 1 foot = 0.33 yards

⇒ 60 feet = 0.33*60 yards

= 20 yards

Further, we know that the area of a rectangle is given by the formula-

area = length × breadth

Thus,

1,200 = 20 × breadth

1,200/20 = breadth

breadth = 60 yards

Thus, we find that the depth of the given rectangular lot is 60 yards.

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The difference between the value of two signed numbers and the absolute value is that

Positive and negative numbers are referred to as signed numbers. The number is automatically regarded as positive if no sign is present.

On a number line, positive numbers are those to the right of zero. Negative numbers are those to the left of 0

Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line.

A number can never have a negative absolute value.

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If Olive Construction Company won the job, there is a 0.4615 (or 46.15%) probability that Base Construction Company would not have submitted a proposal.

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.

The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

So, the probability that the base construction company did not bid:

[tex]\begin{aligned}& P(A \mid B)=\frac{P(B \mid A) P(A)}{P(B \mid A) P(A)+P\left(B \mid A^{\prime}\right) P\left(A^{\prime}\right)} \\& P\left(B^{\prime} \mid O\right)=\frac{P\left(O \mid B^{\prime}\right) P\left(B^{\prime}\right)}{P\left(O \mid B^{\prime}\right) P\left(B^{\prime}\right)+P(O \mid B) P(B)} \\& P\left(B^{\prime} \mid O\right)=\frac{(0.5)(0.3)}{(0.5)(0.3)+(0.25)(0.7)} \\& P\left(B^{\prime} \mid O\right)=\frac{0.15}{0.15+0.175} \\& P\left(B^{\prime} \mid O\right)=0.4615\end{aligned}[/tex]

Therefore, if Olive Construction Company won the job, there is a 0.4615 (or 46.15%) probability that Base Construction Company would not have submitted a proposal.

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The measured height of the tree is found as 3.2 yards.

Let 'h' be the height of the three.

Let distance between student A and tree =  x.

Using trigonometric relation;

tan 57 = h/x

x = h/tan 57   ......eq 1

tan 46 = h/(x + 1)

x + 1 = h/tan 46   ......eq 2

Equation eq 1 and eq 2.

h/tan 57 + 1 = h / tan 46

h / tan 46 - h / tan 57 = 1

Further solving,

h(tan 57 - tan 46) = tan 46.tan 57

h = tan 46 tan 57 / (tan 57 - tan 46)

h = 3.2 yards

Thus, the measured height of the tree is found as 3.2 yards.

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The complete question is-

Two students stand 1 yard apart and measure their respective angles of elevation to the top of a tree. Student A measures the angle to be 57°, and Student B measures the angle to be 46°.

What is h, the height of the tree? Use the law of sines to first find AT. Then use that measure to find the value of h.

A) 3.0 yards

B) 3.2 yards

C) 3.8 yards

D) 4.4 yards

Answer: 3.2 is correct

Step-by-step explanation:

edge 2023

The required evaluation to the given expression is 5/12.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

The expression is given in the question as:

1 3/4  - 1/3 (4)(3) - 1/3

We have to determine the evaluation to the given expression

As per the given question, we have

⇒ 1 3/4  - 1/3 (4)(3) - 1/3

⇒ 7/4  - 1/3 (12) - 1/3

Apply the subtraction operation,

⇒ 7/4  - 4 - 1/3

Take the LCM in the above fractions,

⇒ (21 - 12 - 4)/12

⇒ 5/12

Thus, the required evaluation to the given expression is 5/12.

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Answer: 11 miles each day for the remaining 5 days

Step-by-step explanation:

First, you subtract the miles already done (25) from the total (80) to get 55 (miles left to do) then next divide 55 by 5 (days left), and then your left with 11. Finally, check the work and see how 11x5=55 then 55+25=80.

That's how to get the answer :)

The required system of equation for the cost of shirt and tie are-

For the stated question-

Let 's' be the cost of each shirt.

Let 't; be the cost of each tie.

Then, the equations become-

4s + 2t = 95

3s + 3t = 84 are the required system of equation.

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The statement that is true about the triangle ABC with vertices A(-6, 6), B(4, 2), and C(-4, 0) is C. Since two of the sides have slopes that are negative reciprocals, it is a right triangle.

Right triangles are triangles with have perpendicular relationships

The lines will be checked for perpendicularity by calculating the slopes, if any two slopes are negative reciprocals then they are perpendicular and the triangle is a right triangle'

the points A(-6, 6), B(4, 2), and C(-4, 0)

Using point A(-6, 6) and B(4, 2)

m = (y₂ - y₁) / (x₂ - x₁)

m = (4 - 6) / (2 - -6)

m = -1/2

Using point B(4, 2), and C(-4, 0)

m = (y₂ - y₁) / (x₂ - x₁)

m = (4 - -4) / (2 - 0)

m = 2

Comparing the slopes shows that slopes calculated are negative reciprocals

Therefore the triangle is a right triangle

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The social security and Medicare deductions for the following employee are  $7768 and $1816 respectively.

What is arithmetic?

Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, mathematical process, and extraction of roots

Main body:

Cumulative Earnings before this pay period = $128,300

pay amount this period = $3000

tax rate of 6.2% on social security = 6.2%

effective earning = 128300 = 3000

                           = 125300

social security deduction = 6.2 % of 125300

⇒ 6.2 *125300 /100

⇒$7768

Medicare deductions = 1.45%

⇒ 1.45*125300/100

⇒$1816

Hence , the social security and Medicare deductions for the following employee are  $7768 and $1816 respectively.

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Answer:

A. Symmetric Property

Step-by-step explanation:

The Symmetric Propertry states that if x = y, then y = x.

Since XY = WX, and WX = XY, its the Symmetric Property.

The distance covered by the car with 12 gallons of gasoline is 200 miles.

Given,

Distance travelled by a car with full  tank gasoline = 300 miles

The capacity of the car's tank = 18 gallons

We have to find the distance covered by the car with 12 gallons of gasoline;

Here,

x be the distance covered by the car with 12 gallons of gasoline

Then,

300/18 = x/12

x = (300 x 12) / 18

x = (300 x 2) / 3

x = 100 x 2

x = 200 miles

That is,

The car will cover 200 miles with 12 gallons of gasoline.

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The probability of scoring exactly​ 80%  is  0.04395  as per the given data.

Given: 10 true-false questions

So, we will have 50% chances (probability = 0.5) of being correct.

P( 80% score) = P( 8 answers correct)

As we observe, if X= number of correct answers, then X~ Binomial (n=10, p=0.5)

So, P(  80% score) = P( 8 answers correct)

= 0.0439453125

= 0.04395

Potential is described by probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events.

Probability basically refers to the degree to which something is likely to occur. With the help of this fundamental theory of probability, which is also used to describe the probability distribution, you will discover the possible results for a random experiment. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

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The three numbers that are in the ratio 7:3:2 are 70, 30, and 20.

A ratio in mathematics demonstrates how many times one number is present in another.

For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

So, let 7x, 3x, and 2x be the three numbers.

7x+2x = 9x is the product of the lowest and greatest number.

In accordance with:

9x-30=2(3x)

To make the equation easier:

9x-30=6x

30 extra on both sides:

9x=6x+30 or,9x-6x=30

3x=30, x=10,

So, the numbers will be:

7x=7(10) = 70

3x=3(10) = 30

2x=2(10) = 20

Therefore, the three numbers that are in the ratio 7:3:2 are 70, 30, and 20.

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The probability flipping of four coin that will give head is 0.93

Probability:

In statistics, Probability defines the possible way of occurring a particular event.

Given,

A flipped coin can land in one of two states: heads or tails.

Here we need to find the probability while flipping four coins then  how many of these coins land in the heads state.

In order to calculate the probability of these event, we have to know the values of the sample space and the possible number of events,

Here the value of sample space is written as,

S = {HHHH, TTTT, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, HTHT, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH}

So, the value of n(S) = 16

The possible number of way to obtain the head state is,

E = {HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, HTHT, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH}

the value of n(E) = 15.

Therefore, the probability of getting head state is

=> P(E) = 15/16

=> P(E) = 0.93

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Answer:

Step-by-step explanation:

Base angles are congruent.

[tex]\tt y=128^o[/tex]

Let's solve for x first:-

[tex]\tt x+y=180^o[/tex]

[tex]\tt x=180-y[/tex]

[tex]\tt x=180-128[/tex]

[tex]\tt x=52^o[/tex]

Therefore, x = 52° and y = 128°

_________________

Hope this helps you!

Have a nice day! :)

Answer:

3/4 = 12/16, y = 2, w = 2.5, 20/2.5 = x/9

Step-by-step explanation:

The first question is asking which is proportional.

B. 3/4 = 12/16

We know this is proportional because 4 can be multiplied by 4 to get 16, and the same can be applied to 3 to get 12.

The second question is asking for the missing value of y.

3/12 = y/8

y = 2

We can solve this by looking at the 12 and the 8.

8 is 2/3 of 12.

2/3 of 3 is 2

The third question is asking for the missing value of w.

5/w = 8/4

w = 2.5

We can solve this by looking at the 8/4.

8/4 is the same as 2/1.

Using this, we can conclude that w = 2.5

The fourth question is asking for the correct proportion.

If Mr. Argo can go 20 miles on 2.5 gallons of gas:

20/2.5

And he wants to know how many miles he can go with 9 gallons:

x/9

We can use the equation: C. 20/2.5 = x/9

Hope this helps!!

The value of sides of the right triangle are a = 3 units, b = 12.47 units and c = 11.21 units.

For the given question-

The length of the side are-

a = 3 units

Angle B = 64°.

Then,

Applying trigonometric properties-

Tan B = b/a

b = a tan B

b = 3 tan 64°

b = 12.47 units

Now,

Sin B = b/c

c = b sin B

c = 12.47 sin 64°

c = 11.21 units.

Thus, the value of sides of the right triangle are a = 3 units, b = 12.47 units and c = 11.21 units.

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The slope and intercept of the line will be 2 and 80 respectively.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that, the total amount of tourist spending in Florida from 2013 to 2017 can be predicted using the equation y=2x+80, where x is the number of years since 2013, to the tune of billions of dollars.

Compare the equation with the standard equation,

y=mx+ c

Where m is the slope and c is the intercept of the line.

Thus the slope and intercept of the line will be 2 and 80 respectively.

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Answer:

w=7/2=3.5

Step-by-step explanation:

width =w

length = l = 2w+2

25=2(l+w)= 2(2w+2+w) =2(3w+2)=6w+4

25=6w+4

6w=21

w= 21/6 = 7/2

Answer:

[tex]\huge\boxed{\sf 3}[/tex]

Step-by-step explanation:

y = 3x + 5

Comparing it with standard form of slope-intercept equation i.e. y = mx + b.

Where,

m = slope = 3

b = y-intercept = 5

A line that is parallel to this line will have the same slope as this line.

So, it will also have a slope of 3.

[tex]\rule[225]{225}{2}[/tex]

The value of the mentioned expression is -43.24.

To solve the expression, firstly rewriting the equation followed by keeping the values of x, y and z at their respective places.

Equation = (4x³ - 10)/(3y² + 5) - (4x³ (z² - 8))/(y³ + 5)

Now keeping the values of each variable in the equation

Equation = (4×2³ - 10)/(3×(-5)²) - (4×2³ ((-7)² - 8))/((-5)³ + 5)

Taking cube and square on Right Hand Side of the equation

Equation = (4×8 - 10/(3×15)) - (4×8 (49 - 8))/(25 + 5)

Solving the bracket first where we will perform multiplication on the Right Hand Side

Equation = (32 - 10/45) - ((32 × 41)/30)

Equation = 22/45 - 1312/30

Now performing division on Right Hand Side of the equation

Equation = 0.49 - 43.73

Performing subtraction on Right Hand Side of the equation

Equation = -43.24

Hence, the value is -43.24.

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