In hours 3 3/8, John reads 4 1/2 chapters.
What is the unit rate in chapters per hour?
Write your answer as a fraction or a mixed number in simplest form.

All subjects or objects whose characteristics are being studied.

In statistics, a population consists of all subjects or objects whose characteristics are being studied. This means that a population can be defined as a group of individuals, objects, or events that have something in common.

For example, if you are conducting a survey on the opinions of people in a city, the population would be all the people living in the city. If you are studying the behavior of cats, then your population would be all cats. In short, the population is the group of individuals or objects that you are interested in studying.

In addition, the population can be further broken down into subgroups, such as males and females, different age groups, geographical regions, and so on. This is known as stratifying the population and can help researchers to better understand the characteristics of their population and make more accurate conclusions.

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The shapes C and F represent an enlargement of shape X by a scale factor of -1.

A dilation is defined as a non-rigid transformation that multiplies the distances between every point in a polygon or even a function graph, called the center of dilation, by a constant factor called the scale factor.

For a scale factor of -1, we have that the size remains constant, as |-1| = 1, hence the figure is just reflected.

Thus the shapes are given as follows:

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The conversions of the given lengths are:4.1 × 106 m = 4.1 × 103 km0.01 m = 10 mm4.2 × 10-10 m = 1.13 × 10-7 pm7.6 × 104 m = 7.6 × 102 hm.

The metric prefixes can be used to rewrite the given lengths in meters so that the numerical value is larger than one but less than 1000. The metric prefixes are used to indicate values that are greater or smaller than the unit in use.

Some of the common prefixes used are as follows:

PrefixSymbolMultiple of metermega M106kilok103hectoh102deca10-1deci10-2centi10-3milli10-6micro10-9nano10-12pico10-15femto10-18atto10-21zepto10-24yocto10-27

The given lengths are:4.1 × 106 m = ?0.01 m = ?4.2 × 10-10 m = ?7.6 × 104 m = ?

The conversions are given as follows: -

:4.1 × 106 m = 4.1 × 106 × 10-3 km = 4.1 × 103 km0.01 m = 10-2 m = 10 mm4.2 × 10-10 m = 4.2 × 10-10 × 1012 pm = 4.2 × 2.687 pm = 1.13 × 10-7 pm7.6 × 104 m = 7.6 × 104 × 10-2 hm = 7.6 × 102 hm.

Therefore, the conversions of the given lengths are:4.1 × 106 m = 4.1 × 103 km0.01 m = 10 mm4.2 × 10-10 m = 1.13 × 10-7 pm7.6 × 104 m = 7.6 × 102 hm.

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The given recurrence relation is (k + 2)(k + 1)a(k+2) = (k^2 - k + 1)a(k+1) - 17a(k). To find a6, we will apply the recurrence relation and perform the necessary calculations.

Using the given recurrence relation, we can calculate the values of a2, a3, a4, a5, and finally a6 by substituting the appropriate values. Starting from a0 = 2 and a1 = 3, we can iteratively apply the recurrence relation.

a2 = (0^2 - 0 + 1)a1 - 17a0 = 1 * 3 - 17 * 2 = -31

a3 = (1^2 - 1 + 1)a2 - 17a1 = 1 * (-31) - 17 * 3 = -80

a4 = (2^2 - 2 + 1)a3 - 17a2 = 3 * (-80) - 17 * (-31) = -319

a5 = (3^2 - 3 + 1)a4 - 17a3 = 7 * (-319) - 17 * (-80) = -1883

a6 = (4^2 - 4 + 1)a5 - 17a4 = 12 * (-1883) - 17 * (-319) = 720. Therefore, the value of a6 is 720.

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Answer:

x = 60.4

Step-by-step explanation:

First, let's remember the three different trigonometric functions: sine, cosine, and tangent. In this case, we would use cosine because the adjacent side to the angle and hypothenuse are used/given.

\(cos(22) = \frac{56}{x}\)

We need to set up a proportion because there is not much else you could do here.

\(\frac{cos(22)}{1} =\frac{56}{x}\)

Then, cross-multiply.

\(cos(22) * x = 56\)

Finally, divide both sides by cos(22). You'll probably need your calculator and make sure it's in degrees mode and not radians!

\(\frac{cos(22) * x}{cos(22)} = \frac{56}{cos(22)}\)

\(x = 60.4\)

Rounded to the nearest tenth, x = 60.4.

The length of the base of the triangle is √(2)/6, which can also be expressed as (√(2))/6.

In this case, we know the area (1/12 square centimeters), but we don't know the height or the base. However, we can use the fact that the area is equal to 1/2 times the base times the height to set up an equation:

1/12 = 1/2 x base x height

Now we need to solve for the base. We can do this by isolating the base on one side of the equation:

1/12 = 1/2 x base x height

1/6 = base x height

At this point, we need to make an assumption about the triangle.

We can use the Pythagorean theorem to solve for the length of h:

h² + (base/2)² = (base)²/4

Simplifying this equation, we get:

h² = (base)²/4 - (base)²/4

h² = (base)²/2

h = √((base)²/2)

h = base/√(2)

Now we can substitute this expression for h into our equation for the area:

1/6 = base x height

1/6 = base x (base/√(2))

Simplifying this equation, we get:

1/6 = (base²)/√(2)

Multiplying both sides by √(2), we get:

√(2)/12 = base²

Taking the square root of both sides, we get:

base = √(√(2)/12)

Simplifying this expression, we get:

base = √(2)/6

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Answer:

3x2+6x+4 2x

hope this helps !!

HAVE A AMAZING DAY

Answer:

(6x+7)/2x

Step-by-step explanation:

2/x+2 + 3/2x+1

2/x+2x/x + 3/2x+x/x   [Convert the bolded numbers into fractions with x in the denominator.

2/x+2x/x + 3/2x + x/x [Convert the bolded numbers so that the denominator becomes 2x]

4/2x+4x/2x + 3/2x + 2x/2x

4/2x+4x/2x + 3/2x + 2x/2x   [Now that all numbers have the same denominator, we can add the numerators]

(4+4x + 3 + 2x)

(6x+7)

(6x+7)/2x            [Place the denominator, 2x, back into the fraction]

Answer:

p = 15

Step-by-step explanation:

To find the value of p, you can follow opposite operations. What this means is you do the opposite of the equation.

In this instance, to find p, do 5 × 3

5 × 3 = 15, therefore 15 = p

Now we can check if the equation is correct by doing 15 ÷ 5

15 ÷ 5 = 3

So p = 15 is correct

Answer:15

Answer:

sinB = \(\frac{12}{13}\)

Step-by-step explanation:

sinB = \(\frac{opposite}{hypotenuse}\) = \(\frac{AC}{AB}\) = \(\frac{12}{13}\)

The Trigonometric ratios is 12/13

The branch of mathematics concerned with specific functions of angles and their application to calculations.

We have,

H= 13, B= 5 and P=12

So,

sin B= Perpendicular/ Hypotenuse

        = 12/13

hence, sin B=  12/13

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Answer:

3.14159...

Step-by-step explanation:

pi is not rational number

Answer:

A. 3.14......

Step-by-step explanation:

3.14159 is called pi! Pi is not rational, it is irrational.

Answer: 20 x 5280 = 105,600

Step-by-step explanation:

A sample statistic is a statistical finding based on small sample size.

A sample is only a small portion of the population. Let's imagine you were interested in determining the average income for all Americans in your population. Instead of knocking on every door in America because of time and money constraints, you decide to question 1,000 random people. Your sample consists of these a thousand persons.

Once you have your sample, you will obtain a statistic of some sort. Actually, a statistic is just a piece of data; in this case, it's the average salary. A sample statistic is one that is drawn from a portion of data or a population and contains statistical information (such as an average, median, or other types of statistics).

Your sample statistic might change greatly based on the things you select from the population because you are only working with a small portion of the total population. In actuality, there is some uncertainty in the majority of sample statistics.

It's extremely unlikely that the knowledge you gather from a few items will paint a complete picture or provide you with a precise explanation of what is happening in the population as a whole. While margins of error, confidence intervals, and many other statistical tools can help us quantify uncertainty, statistics is really just scientific guesswork.

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Answer: This answer is 11 square units.

Step-by-step explanation:

Find the diagram attached

First we need to find the side length of the square with known areas.

Area of a square = L²

L is the side length of the square

For the green square

44 = L²

Lg = √44

For the purple square

Ap = Lp²

33 = Lp²

Lp = √33

Get the length (L) of the unknown square using pythagoras theorem;

Lg² = L²+Lp²

(√44)² = L²+(√33)²

44 = L²+33

L² = 44-33

L² = 11

Since Al = L²

Hence the area of the square adjacent to the third side of the triangle is 11 square units

Answer:

85 units

Step-by-step explanation:

Answer + Explanation:

Since you just flip the fraction if you have a negative power, you get

1.) 6 to the power of -1 = 1/6

2.) 6 to the power of -2 = 1/36

3.) 6 to the power of -3 = 1/216

4.) 6 to the power of -4 = 1/1296

Answer:

a little over 46 hours

Step-by-step explanation:

20            x

___   =   ___

3             7

20*7=140

3*x=3x

140/3=46.66666667

Answer:

10.9 pounds

Step-by-step explanation:

50 ÷ (2.3*2) = 10.869

First, let's calculate the monthly interest rate (i), which is the APR divided by 12 months:

i = APR / 12 months

i = 5.3% / 12

i = 0.00442 or 0.442%

Next, let's calculate the number of months (n) for the mortgage, which is 15 years multiplied by 12 months:

n = 15 years x 12 months/year

n = 180 months

Now, let's calculate the monthly payment (PMT) using the following formula:

PMT = P * i / \((1 - (1 + i)^(-n)\))

where P is the principal amount, i is the monthly interest rate, and n is the number of months.

PMT = $325,000 * 0.00442 / (1 - \((1 + 0.00442)^(-180)\)

PMT = $2,613.67 (rounded to the nearest cent)

Now, let's create the amortization table for the first two months:

Month | Payment | Interest | Principal | Remaining Balance

1 | $2,613.67 | $1,431.25 | $1,182.42 | $323,817.58

2 | $2,613.67 | $1,428.60 | $1,185.07 | $322,632.51

For each month, the Payment column shows the fixed monthly payment, the Interest column shows the calculated interest based on the remaining balance multiplied by the monthly interest rate, the Principal column shows the portion of the payment that goes towards reducing the principal, and the Remaining Balance column shows the remaining balance after subtracting the principal payment from the previous remaining balance.

The amortization table will continue in this manner for the remaining months until the mortgage is paid off.

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The interest and principal amounts for the first payment are:

Interest = $325,000 * 0.0044167 = $1,426.25

Principal = $2,549.67 - $1,426.25 = $1,123.42

Balance = $325,000 - $1,123.42 = $323,876.58

For the second payment, we start with the new balance of $323,876.58 and apply the formulas again:

Interest = $323,876.58 * 0.0044167 = $1,420.47

Principal = $2,549.67 - $1,420.47 = $1,129.20

Balance = $323,876.58 - $1,129.20 = $322,747.38

To complete the two-month amortization table, we need to calculate the monthly payment, as well as the principal and interest amounts for each payment.

The formula for calculating a fixed-rate mortgage payment is:

\(Payment = P * r * (1 + r)^n / [(1 + r)^n - 1]\)

Where:

P = Principal amount borrowed

r = Monthly interest rate

n = Total number of payments

First, let's calculate the monthly interest rate.

Since the APR is an annual rate, we need to divide it by 12 to get the monthly rate:

Monthly interest rate = 5.3% / 12 = 0.0044167

Next, we need to calculate the total number of payments.

Since this is a 15-year mortgage, and we're completing a two-month amortization table, the total number of payments is:

Total number of payments = 15 years * 12 months per year = 180

Number of payments for two months = 2

Now we can plug these values into the formula to calculate the monthly payment:

Payment = \($325,000 * 0.0044167 * (1 + 0.0044167)^180 / [(1 + 0.0044167)^180 - 1]\)

= $2,549.67

So the monthly payment is $2,549.67

Now we can use this value to complete the two-month amortization table:

Payment Interest Principal Balance

Month 1 $1,426.25 $1,123.42 $323,876.58

Month 2 $1,420.47 $1,129.20 $322,747.38

To calculate the interest and principal amounts for each payment, we use the following formulas:

Interest = Balance * Monthly interest rate

Principal = Payment - Interest

Balance = Balance - Principal

We start with the initial balance of $325,000 and apply the formulas for each payment.

The interest and principal amounts for the first payment are:

Interest = $325,000 * 0.0044167 = $1,426.25

Principal = $2,549.67 - $1,426.25 = $1,123.42

Balance = $325,000 - $1,123.42 = $323,876.58

For the second payment, we start with the new balance of $323,876.58 and apply the formulas again:

Interest = $323,876.58 * 0.0044167 = $1,420.47

Principal = $2,549.67 - $1,420.47 = $1,129.20

Balance = $323,876.58 - $1,129.20 = $322,747.38

And so on, for each subsequent payment.

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Answer:

No

Step-by-step explanation:

It is not because there is no patteren

Answer:

no its not because the difference between the terms are not the same

Step-by-step explanation:

20-14=6

14-9= 5

9-5=4

the differences are all different so the sequence is not arithmetic  

The probability that a sample of 10 items will contain at most 1 defective item is 0.7361

Consider X to denote the number of defective items which follows binomial distribution with sample size, n equals to 10.

The probability p of an item produced by a certain machine will be defective is 0.1.

Therefore, the probability q of an item produced by a certain machine will not be defective is:

(1−0.1)

=0.9

The probability of at most one defective item can be calculated as follows:

\(P(X\leq 1)=P(X=0)+P(X=1)\\\)

\(=^{10} C_{0} p^{0} (1-p)^{10} +^{10} C_{1} p^{1}(1-p)^{9}\)

\(=(0.9)^{10} +10(0.1)(0.9)^{9}\)

\(=0.7361\)

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Answer:

  a. 400 m

  b. 46.56 m

  c. 461 m

Step-by-step explanation:

The perimeter is the sum of the circumference of two semicircles and the two straight sections. Two semicircles add up to one circle.

The circumference of a circle is given by the formula ...

  C = 2πr

For an inner radius of 36.8 m, the circumference of the inner circle is ...

  C = 2π(36.8 m) = 73.6π m

The outer perimeter will have a radius that is the sum of the inner radius and the width of 8 track lanes.

  r = 36.8 m + 8(1.22 m) = 46.56 m . . . . . . . . . outer semicircle radius

The circumference of the outer circle is ...

  C = 2π(46.56 m) = 93.12π m

The straight sections are the same length on both perimeters. The sum of the two straight section lengths is ...

  2 × 84.39 m = 168.78 m

The inner perimeter is the sum of the inner circumference and the length of the straight sections:

  P = 73.6π m + 168.78 m ≈ 231.2 m + 168.8 m = 400 m

The inner perimeter is about 400 meters.

Above, we found the radius at the outside edge of the track to be 46.56 m.

The outer radius is 46.56 meters.

The outer perimeter is the sum of the outer circumference and the length of the straight sections:

  P = 93.12π m +168.78 m ≈ 292.5 m + 168.8 m ≈ 461 m

The outer perimeter is about 461 meters.

Answer:

Use the slope intercept formula!

Step-by-step explanation:

The measure of length PQ will be 22 units.

A triangle's third side is stated to be parallel to the line segment uniting its two midpoints, and it is also half as long as the third side.

Given:

PQ = 5x + 62, and MN = 6x-4

Now, using Mid- Point Theorem

PQ= 1/2 MN

-5x+ 62 = 1/2( 6x - 4)

-5x+ 62 = 3x - 2

-5x- 3x = -2 - 62

-8x = -64

x= 8

PQ= 5x+ 62 = -5(8) + 62 = -40 + 62 = 22

Hence, the measure of PQ is 22 units.

The missing image is attached below.

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Answer:

Step-by-step explanation:

Add like terms. 3x & 7x are like terms

3x +7x - 2 = 10x - 2

Answer:

0.2

Step-by-step explanation:

3x+7x-2

3x+7x-2=0

3x+7x=2

10x=2

x=2/10

x=\(\frac{1}{5}\)

Answer:

the angle that corresponds to AC IS PF

The width of the cooling tower at the base of the structure is 100 meters, rounded to the nearest whole number.

Given that the cooling tower's walls are modeled by where the measurements are in meters and the width of the

cooling tower at the base of the structure is required, we can find the width by using the formula for the area of a

trapezoid. The area of the trapezoid represents the area of the base of the cooling tower.

Area of a trapezoid = 1/2 × (a + b) × h

where a and b are the lengths of the parallel sides of the trapezoid and h is the height or perpendicular distance

between the parallel sides.

In this case, the parallel sides of the trapezoid are not given, but we are given the height of the cooling tower, which is

100 meters. We also know that the area of the base of the cooling tower is 10,000 square meters.

Therefore, we can use the formula for the area of a trapezoid to find the sum of the lengths of the parallel sides of the

trapezoid, which will give us the width of the cooling tower at the base.

Area of a trapezoid = 1/2 × (a + b) × h

10,000 = 1/2 × (a + b) × 100

100 = (a + b)/2

200 = a + b

Width of cooling tower at the base = (a + b)/2

Width of cooling tower at the base = 200/2

Width of cooling tower at the base = 100 meters

Therefore, the width of the cooling tower at the base of the structure is 100 meters, rounded to the nearest whole number.

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To prove that AC ⊕ EC, we need to show that quadrilateral DEFG being a rectangle and BC ⊕ DC implies that AC ⊕ EC.

To begin, we know that quadrilateral DEFG is a rectangle. In a rectangle, opposite sides are equal in length and parallel to each other.

Given that BC ⊕ DC, we can infer that BC and DC are not equal in length.

Since DEFG is a rectangle, this means that AB and DE are also not equal in length, as they are opposite sides. Similarly, AD and BC are not equal in length.

Now, let's consider triangle ABC. In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Applying this to triangle ABC, we have:

AB + BC > AC
AD + DC > AC

Since AB and DC are not equal in length, and BC and AD are not equal in length, we can conclude that AC is the longest side in triangle ABC.

Now, let's look at triangle CDE. Again, using the same rule for triangles:

AC + CE > EC
AD + DE > EC

Since AC is the longest side in triangle ABC, and AD is not equal in length to DE, we can conclude that AC is longer than EC.

Therefore, we have proved that if quadrilateral DEFG is a rectangle and BC ⊕ DC, then AC ⊕ EC.

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There are a total of 5 graduate assistantships available to be awarded to the 10 students who will be interviewed by the college. The number of ways that the assistantships can be awarded is determined by using the formula for combinations, which is:

nCr = n! / r! * (n - r)!

where n is the total number of items, r is the number of items being chosen, and ! denotes factorial, which means the product of all positive integers up to and including the given number.

In this case, we have:

n = 10 (number of students being interviewed)
r = 5 (number of assistantships available)

Using the formula, we can calculate the number of ways that the assistantships can be awarded as:

10C5 = 10! / 5! * (10 - 5)! = 252

Therefore, there are 252 ways that the assistantships can be awarded to the 10 students being interviewed by the college.

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The length of GH is 21 units.

The Secant-Secant Theorem states that "if two secant segments which share an endpoint outside of the circle, the product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment".

Using the theorem above, we can say:

HI * GI = JI * KI

Since KJ is 5 more than GH, we can say:

KJ = GH + 5

KI = KJ + JI

KI = GH + 5 + 46 = GH + 51

From the figure:

GI = GH + HI

Substituting into:

HI * GI = JI * KI

HI * (GH + HI) = JI * (GH + 51)

48 * (GH + 48) = 46 * (GH + 51)

48GH + 2304 = 46GH + 2346

48GH - 46GH =  2346 - 2304

2GH = 42

GH = 42/2

GH = 21 units

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Complete Question

Check attached image

Answer:

Three and five twelfths; 3 5/12; 41/12

Answer:

41/12

Step-by-step explanation: