Find the mean absolute deviation of the data below:

51, 79, 82, 60, 63, 65, 70, 70

The formula for a circle's arc length is L = r * θ, where L is the arc length, r is the circle's radius, and θ is the arc's central angle, expressed in radians.

We can calculate the radius of the circle by dividing the arc length by the central angle because we know the value of L (7 cm) and that can be calculated from the arc's measure (degrees or radians):

r = L / θ

It is crucial to keep in mind that in order to calculate the radius, you must first know the arc's central angle's measurement in radians.

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Answer:20

π

cm or about

62.8

cm.

Step-by-step explanation:

The formula for a circumference of a circle is

2

π

r

, where

r

is the radius. We can plug our known value of the radius (

10

cm) into the formula and solve.

Answer:

78.5

Step-by-step explanation:

Answer:

j = $7

b = $12

c = $15

Step-by-step explanation:

Let

j = cost of one pound of jelly

b = cost of one pound of Bonbon

c = cost of one pound of chocolate

First week:

two pounds of Jellies and two pounds of Bonbons for $38.

2j + 2b = 38

Second week:

two pounds of Jellies and four pounds of Chocolates for $74

2j + 4c = 74

Third week:

two pounds of Jellies, two pounds of Bonbons and one pound of Chocolates for $53.

2j + 2b + c = 53

Recall,

2j + 2b = 38

So,

38 + c = 53

c = 53 - 38

= 15

c = $15

Substitute c = 15 into

2j + 4c = 74

2j + 4(15) = 74

2j + 60 = 74

2j = 74 - 60

2j = 14

j = 14/2

= 7

j = $7

Substitute j = 7 into

2j + 2b = 38

2(7) + 2b = 38

14 + 2b = 38

2b = 38 - 14

2b = 24

b = 24/2

= 12

b = $12

Answer: The formula for simple interest is:

I = Prt

Where:

I is the interest earned

P is the principal (the initial amount deposited)

r is the interest rate (as a decimal)

t is the time period in years

Using this formula, we can calculate the interest earned by Patricio after 4 years:

I = Prt

I = 800 * 0.025 * 4

I = 80

So, after 4 years, Patricio will have earned $80 in interest. Adding this to the initial deposit of $800, the total amount of money he will have in the account is:

Total = P + I

Total = 800 + 80

Total = $880

Therefore, Patricio will have $880 in the savings account after 4 years.

Step-by-step explanation:

Answer:

$14,580

Step-by-step explanation:

To start off, 10% of 20,000-one easy way to do this is to multiply 20,000 by 0.1, which is 10% in decimal form

-In doing that, you get 2,000

-Now the question says that the value is depreciated which means it goes down in value, so subtract 2,000 from 20,000 to 18,000

-the value of the car after one year is now $18,000

Now, let's move to the second year.  This time find 10% of 18,000

-multiply 18,000 by 0.1 to get 1,800

-since the value is depreciating, or becoming less, we will subtract 1,800 from 18,000 to get 16,200

-the value of the car after two years is now $16,200

Finally, let's look at the value of the car after three years.  Only this time, we will now find 10% of 16,200

-multiply 16,200 by 0.1 to get 1,620

-since value is being depreciated, or lessened, we will once again be subtracting.  Subtract 1,620 from 16,200 to get 14,580

Therefore, the value of the car after three years is now $14,580.

Answer:

706 out 2201

Step-by-step explanation:

the total number of the passengers in the cabin out of the total number of the passengers that were on board.

I hope this helps you..!

the given differential equation dR/dx = a(R² + 16), where a is a non-zero constant, is R = -4/√\((16 - e^(2ax + C))\), where C is the constant of integration.

In the first part, the solution to the differential equation is R = -4/√\((16 - e^(2ax + C)).\)

In the second part, let's solve the differential equation step by step. We start by separating variables:

dR/(R² + 16) = a dx.

Next, we integrate both sides:

∫(1/(R² + 16)) dR = ∫a dx.

To integrate the left side, we can use a substitution. Let u = R² + 16, then du = 2R dR. This gives us:

(1/2) ∫(1/u) du = ∫a dx.

Simplifying the left side and integrating, we have:

(1/2) ln|u| = ax + C.

Substituting back for u and rearranging, we get:

ln|R² + 16| = 2ax + 2C.

Taking the exponential of both sides, we have:

|R² + 16| = \(e^(2ax + 2C).\)

Considering the absolute value, we can rewrite it as:

R² + 16 = \(e^(2ax + 2C).\)

Solving for R, we get:

R = ±√(e^(2ax + 2C) - 16).

Simplifying further:

R = ±√(e^(2ax + C) - 16).

Finally, we can rewrite it as:

R = -4/√(16 - e^(2ax + C)).

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Answer:

89,470

Step-by-step explanation:

Answer:

846x + 2123

 —————

     423  

Step-by-step explanation:

STEP

1

:

            8

Simplify   ———

           423

Equation at the end of step

1

:

              8

 (2x + 5) +  ———

             423

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  423  as the denominator :

              2x + 5     (2x + 5) • 423

    2x + 5 =  ——————  =  ——————————————

                1             423      

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(2x+5) • 423 + 8     846x + 2123

————————————————  =  ———————————

      423                423    

Final result :

  846x + 2123

 ———————————

     423  

Step-by-step explanation:

(f + g)(-1) = f(-1) + g(-1)

f(-1) = -1 -2 = -3

g(-1) = (-1)² + (-1) -6 = -6

(f+g)(-1) = -9

Answer:

(f + g)(- 1) = - 9

Step-by-step explanation:

note (f + g)(x) = f(x) + g(x)

f(x) + g(x)

= x - 2 + x² + x - 6 ← collect like terms

= x² + 2x - 8

To evaluate (f + g)(- 1) substitute x = - 1 into (f + g)(x), that is

(f + g)(- 1)

= (- 1)² + 2(- 1) - 8 = 1 - 2 - 8 = - 9

The HDD for the month of January in State College, PA is 930.

To calculate the HDD (Heating Degree Days) for the month of January in State College, PA, we need to subtract the average daily temperature from 65 degrees Fahrenheit, which is considered the standard temperature for indoor heating.

HDD = 65°F - 35°F
HDD = 30°F

Therefore, the HDD for the month of January in State College, PA is 30 degrees Fahrenheit.
Hi! To calculate the Heating Degree Days (HDD) for the month of January in State College, PA with an average outside temperature of 35 degrees F, follow these steps:

1. Determine the base temperature: In the US, the base temperature is commonly 65 degrees F.
2. Subtract the average temperature from the base temperature: 65 - 35 = 30 degrees.
3. Multiply the difference by the number of days in the month: January has 31 days, so 30 * 31 = 930.

So, the HDD for the month of January in State College, PA is 930.

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To calculate the HDD for the month of January in State College, PA, we need to first determine the base temperature. The base temperature is the temperature below which a building needs to be heated in order to maintain a comfortable indoor temperature. In this case, we will use a base temperature of 65 degrees F.

To calculate the HDD, we need to subtract the average daily temperature from the base temperature and sum up the values for each day of the month. If we assume that January has 31 days, we can calculate the HDD as follows:

HDD = (65 - 35) x 31
HDD = 930

So the HDD for the month of January in State College, PA is 930. This means that during the month of January, there were 930 heating degree days, which indicates the amount of heating required to maintain a comfortable indoor temperature. It is important to note that the HDD can vary depending on the base temperature used, so it is important to choose a base temperature that is appropriate for the climate and the building being heated.

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The value for x is 7π/6 and 11π/6.

sin2xsecx+2cosx=0

(2sinxcosx)(1/cosx)+2cosx=0

sinxcosx/cosx+2cosx=0

So,

2sinx+2cosx=0

2(sinx+cosx)=0

(2(sinx+cosx))²=0

4(sin²x+cos²x+2sinxcosx)=0

hence,

(sin²x+cos²x+2sinxcosx)/4=0/4

sin2x+cos2x+2sinxcosx=0

1+sin2x=0

sinx=−1/2

=7π/6 and 11π/6

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Answer:

A line traveling to the left with an open dot on x=1.

Explanation:

The inequality x < 1 basically means "less than 1." On number lines, the further left you go, the smaller the number becomes, and the further right you go, the larger the number becomes. So we know that because it's less or smaller than 1, then the line will be to the left. On the other hand, the inequality does not have a line under it to indicate a "less than or equal to 1," just "less than." Therefore, the dot is open. If there were a line under the inequality, then it would indicate "less than or equal to 1" and the dot would be closed.

Answer:

J =51

Step-by-step explanation:

Your welcome! Have a great day!

Answer:

$15.65 per hour

Step-by-step explanation:

125.20 / 8 = 15.65

Check

15.65 x 8 = 125.20

The height of the cylinder is the sum of the diameters of the spherical balls, which is 7cm+7cm+7cm=21cm.

The radius of the cylinder is half of the diameter of the spherical balls which is 3.5cm.

The volume of cylinder is given by the formula:

The volume of sphere is given by the formula:

There are three(3) spherical balls in the cylinder, thus, the volume of the 3 spherical balls will be:

Hence, the volume of the space inside the cylinder, not filled by the balls is:

2 pounds is equivalent to approximately 9 cups. both are unit of measurement of weight.

There are several ways to convert weight measurements, such as pounds, to volume measurements, such as cups. However, it is important to note that the conversion will vary depending on the substance being measured.

In general, one pound of a dry ingredient such as flour or sugar is equivalent to approximately 2 cups. Therefore, 2 pounds is equivalent to approximately 4 cups. However, this conversion may vary depending on the substance and the measurement method.If you are measuring a liquid, 1 pound is equivalent to 16 ounces.

1 cup is equivalent to 8 ounces. Therefore 2 pounds is equivalent to 32 ounces or 4 cups.It's also important to note that weight measurements are more precise than volume measurements, as volume measurement can be affected by factors such as how tightly packed the ingredient is, so it is best to use weight measurements for accurate measurements.

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-8 = -7 + X

- 8 + 7 = X (Adding 7 to both sides of the equation)

-1 =x (Subtracting)

The answer is x=-1.

the answer of -8 = -7 +Xx is x= -1

The elements of the complement of set K (K') are {1, 4, 6, 8, 9}.

The elements of the complement of set K (K'), we need to determine all the elements in the universal set that are not in set K.

The universal set, denoted as U, is defined as the set of positive integers less than 10.

The elements in the universal set U are {1, 2, 3, 4, 5, 6, 7, 8, 9}.

Set K is defined as the set of prime numbers.

The prime numbers less than 10 are {2, 3, 5, 7}.

To find the complement of set K (K'), we need to identify all the elements in the universal set U that are not in set K.

K' = U - K

Substituting the values, we have:

K' = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 3, 5, 7}

Performing the set difference operation, we remove the elements in set K from the universal set U:

K' = {1, 4, 6, 8, 9}

These are the positive integers less than 10 that are not prime numbers.

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15y - 9 < 36

add 9 to both-side of the equation

15y < 36 + 9

15y < 45

Divide both-side of the equation by 15

y < 3

Answer:15%

Step-by-step explanation:

Therefore, Caleb paid approximately $14,067.90 for the shares.

Let's assume the amount Caleb paid for the shares is represented by the variable "x". According to the given information, his selling price was 130% of the amount he paid.

Selling price = 130% of the amount paid

$18,189.27 = 1.3 * x

To find the amount he paid for the shares, we can solve the equation for "x" by dividing both sides by 1.3:

x = $18,189.27 / 1.3

Calculating this, we find:

x ≈ $14,067.90

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Answer:

Common difference=5.

Answer: The answer is B) y < 0

Answer: B

Step-by-step explanation:

Two tangent segments both have a length of 12 and form a 60° angle where they meet at P and the distance of point P from the circle is 24 units.

When two tangent segments meet at a point P, they form a right angle. A segment from the center of the circle to the point of intersection is perpendicular to the tangent lines. So, in the present scenario, the angle between the two tangent segments is 60°. Therefore, the angle that each of these tangent segments makes with the line joining the center of the circle to P is 30° (as per the properties of 30-60-90 triangles).

Consider the below figure for reference. Let the center of the circle be O, and the point of intersection of the two tangent segments be P. Join OP. Now, the line OP is perpendicular to the tangent lines since it is drawn from the center of the circle to the point of intersection. We can divide the right-angled triangle OPB into two 30-60-90 triangles by drawing a perpendicular line from point P to line OB. Since OB is 12, then OP is twice as long, i.e. 24.

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The probability density function (pdf) of the largest of the five waiting times is given by: f(x) = 4/10^5 * x^4, where x is a real number between 0 and 10. The expected value of the largest of the five waiting times is 8.33 minutes.

The pdf of the largest of the five waiting times can be found by considering the order statistics of the waiting times. The order statistics are the values of the waiting times sorted from smallest to largest.

In this case, the order statistics are X1, X2, X3, X4, and X5. The largest of the five waiting times is X5.

The pdf of X5 can be found by considering the cumulative distribution function (cdf) of X5. The cdf of X5 is given by: F(x) = (x/10)^5

where x is a real number between 0 and 10. The pdf of X5 can be found by differentiating the cdf of X5. This gives: f(x) = 4/10^5 * x^4

The expected value of X5 can be found by integrating the pdf of X5 from 0 to 10. This gives: E[X5] = ∫_0^10 4/10^5 * x^4 dx = 8.33

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Systematic random sampling is sometimes used in place of simple random sampling due to its efficiency, representativeness, ease of implementation, and cost-effectiveness.

Systematic random sampling is sometimes used in place of simple random sampling for several reasons, including:
Efficiency:

Systematic random sampling can be more efficient than simple random sampling, as it involves selecting elements at regular intervals from the population.

This often reduces the time and effort needed to collect data compared to simple random sampling.
Representativeness:

Systematic random sampling may provide a more representative sample of the population.

By selecting elements at regular intervals, it ensures that different segments of the population are included, reducing the potential for sampling bias.
Ease of implementation:

Systematic random sampling is relatively easy to implement, as it involves fewer random selections compared to simple random sampling.

This makes it more practical for large populations or when a sampling frame is not readily available.
Cost-effectiveness:

Systematic random sampling can be more cost-effective than simple random sampling.

Since the process is more efficient, it may require fewer resources, such as time and personnel, to collect data.

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Given that a circle with radius 20 has a corresponding angle of 305°.

To find the coordinates of a point on the circle, we use the formula:`(r cos (θ), r sin (θ))`Here, `r = 20` and `θ = 305°`.

Substituting the values of `r` and `θ` in the formula, we get:`(20 cos (305°), 20 sin (305°))`

Using the values of trigonometric ratios, we can write:cos(305°) = cos(360° - 305°) = cos(55°) ≈ -0.5736sin(305°) = sin(360° - 305°) = sin(55°) ≈ 0.8192

Hence, the coordinates of a point on a circle with radius 20 corresponding to an angle of 305° are approximately `(-11.47, 16.38)`.

The coordinates of a point on a circle with radius 20 corresponding to an angle of 305° are approximately `(-11.47, 16.38)`

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Answer:

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

Using the Commutative property of addition, which states that the order of addends does not affect the sum, you can rewrite:

Now, the expression becomes:

Next, apply the Associative property of addition, which states that the grouping of addends does not affect the sum.

You can rearrange the terms as follows:

Then, combine the like terms:

Now the expression matches the given form:

This shows that the two expressions are equivalent using the Commutative and Associative properties of addition.

Answer:

a) 34.3%

b) 49%

Step-by-step explanation:

In order to find the probability of a sequence of events, we need to multiply each individual probability by the others in decimal form. Therefore, we need to turn these probabilities into decimal form by dividing them by 100 like so..

70% / 100 = 0.70

Now we multiply all of them together and multiply the product by 100 to get the percentage.

0.70 * 0.70 * 0.70 = 0.343

0.343 * 100 = 34.3%

34.3% is the probability of it raining on all three days. Now to find the probability of it raining on two consecutive days we do the same but multiply only 2 probabilities

0.70 * 0.70 = 0.49

0.49 * 100 = 49%