Write 4.8 as a mixed number and as an improper fraction

The area of a sector of a circle is equal to the central angle multiplied by the radius squared, divided by 2. In this case, the sector of the circle has an area of 20 square feet, the radius is 5 feet, and we need to find the central angle.

The central angle will be 6.28 radians.

To find the central angle, we can rearrange the equation to solve for the angle:

Central Angle = (2 * Area) / (Radius^2)

Substituting the given values, we get:

Central Angle = (2 * 20) / (5^2)

Simplifying, we find that the Central Angle equals 6.28 radians.

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If Blake flips a fair coin , and stops flipping once he get head , then the fair value of the game is 7 .

The Fair Value /Expected value is a mathematical definition that refers to the average outcome of a random process, such as a game or an investment. It is calculated by taking into account all the possible outcomes of the process, weighting each outcome by its probability of occurrence, and summing up the results.

We know that every coin flip has a equal chance of being heads or tails.

So, the probability of getting a head on each flip = 0.5  ;

The expected value is calculated as :

⇒ P(n=1)×(2¹) + P(n=2)×(2²) + P(n=3)×(2³) + P(n=4)×(2⁴) + P(n=5)×(2⁵) + P(n≥6)×(2⁶)  ;

⇒ (0.5¹)×2 + (0.5²)×4 + (0.5³)×8 + (0.5⁴)×16 + (0.5⁵)×32 + (1-0.5-0.25-0.125-0.0625 - 0.03125)×64  ;

⇒ 5 + 0.03125 × 64   ;

⇒ 5 + 2

⇒ 7

Therefore , The Fair Value of this game is 7 .

The given question is incomplete , the complete question is

Blake flips a fair coin and stops flipping once he gets a head. He gets the minimum of $16 and $2ⁿ , where n is the total number of Blake's flips. For example, if Blake flips a head on the first try, then n=1. What is the fair value of this game?

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The measure of angle 2 is 38° and the value of x is 11

Geometry is a branch of mathematics concerned with the study of space, shapes, sizes, and positions of objects. It covers topics such as points, lines, angles, surfaces, and solids.

Check the attached image for labelling. From the figure:

u = 64° (base angles of an isosceles triangle are equal)

t = 180 - 64 - 64 = 52° (Sum of angles in a triangle)

y = 90 - t

y = 90 -52 = 38°

y =  m∠2  (base angles of an isosceles triangle are equal)

m∠2 = 38°

m∠2 = 3x + 5

3x + 5 = 38°

3x = 38 - 5

3x = 33

x = 33/3

x = 11

Therefore, the value of x is 11

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The side of the square cutout that gives the box the largest possible volume

Therefore the answer is d) 2450/27 in.

To find the side length of the square cutouts that give the box the largest volume, we need to find an expression for the volume of the box in terms of the side length of the square cutouts. We can start by subtracting four times the area of one square cutout from the total area of the tin sheet to find the area of the box sides. The volume of the box will then be equal to the area of the box sides multiplied by the height.

The side length of the square cutouts can be represented by x. The area of one square cutout is x^2, so the total area of the four cutouts is

4x^2

The area of the tin sheet is 8 * 15 = 120. The area of the box sides is then

120 - 4x^2

The volume of the box is then (120 - 4x^2) * 8, which we want to maximize. To do this, we can differentiate the expression for the volume with respect to x and set it equal to zero, then solve for x. The solution to this optimization problem is

x = 2450/27, which is the side length of the square cutouts that gives the box the largest volume.

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Answer:

5x>20 and  4

Step-by-step explanation:

x is how many packs Dave bought

5x>20 because he went over the 20 dollar budget

5(4) = 20

Buying 4 packs of cards wouldn't go above the budget, so he must've bought more than 4 packs of cards.

Answer:

Altitude: Segment from a vertex of a triangle that is perpendicular to the opposite side. This segment may be inside the triangle, on the triangle, or outside the triangle. Pictured below are the altitudes (represented as black segments) of acute, right, and obtuse triangles.

Step-by-step explanation:

Answer:

-3y

Step-by-step explanation:

-√(9y²) = -√((3y)²)

= -3y

Answer: $8000 is invested for 6 years

Step-by-step explanation:P=$3,000 r= 7%= 0.07 t= 4 n= 2

Answer:

aₙ = aₙ₋₁ - 3, a₀ = 8

Step-by-step explanation:

Minus three every time thus the recursive equation would be aₙ = aₙ₋₁ - 3, a₀ = 8

the cost of the system and the cost of the games is: $501. This can be solved using the concept of equation.

The connection between the two expressions on each side of the sign is represented by a mathematical equation. One variable and an equal sign are often present.

The total cost of the video game system and the several game = $668

Let, the cost of several game = x and

The cost of video game system = 3x

To find the cost of the system and the games

According to the problem,

or, x + 3x = 668

or, 4x = 668

or, x = $167

Hence, the cost of several game = $167 and

The cost of video game system = $3 × 167 = $501

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The Largest interval in which the solution of the differential equation is defined is (-5, 3).

dy/dt + 2(t + 1)y² = 0 and y(0) = -1/15

Now, dy/dt + 2(t + 1)y² = 0

dy/dt = -2(t + 1)y²

By separating variables

dy/y² = -2(t + 1) dt

Integrating both sides

∫dy/y² = -∫(t + 1) dt

-1/y = -(t²+2t) + c

y(t) = /(t²+2t - c)

We know, y(0) = -1/15

So, -1/15 = 1/(0+0-c)

c = 15

∴ y(t) = 1/(t² + 2t - 15)

Now, y(t) is defined if t² + 2t - 15 ≠ 0

Let t² + 5t - 3t - 15 = 0

(t + 5)(t - 3) = 0

t = -5, 3

So, the intervals are (-∞ , -5), (-5, 3) and (3, ∞)

As t = 0 lies in between (-5, 3) hence the interval in which the solution is defined is (-5, 3)

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The function for distance jogged is d(t) = 3.3t and the inverse of the function is d(t)⁻¹ = 3.3/t.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Let, 'd' be the distance covered in miles, and 't' is the time in hours.

Therefore, From the given information d(t) = 3.3t.

Let, d(t) = y.

So, y = 3.3t.

t = 3.3/y.

d(t)⁻¹ = 3.3/t.

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The number of cigarettes smoked in 1925 was approximately 1.3 billion.

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Given:-

[tex] \: [/tex]

[tex] \: [/tex]

To Find:-

[tex] \: [/tex]

By using formula:-

[tex] \: [/tex]

Solution:-

[tex] \rm{Speed = \frac{Distance}{time} }\\ = \rm{\cancel\frac{30}{3}} \\ \: \:\: \: \: \: \: \: \: \underline {\boxed{\rm \red{= 10km/hr}}}[/tex]

[tex] \: [/tex]

hope it helps!:)

The average speed of the cyclist is 10 km/hr.

Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.

As per the question,

Given that the distance is 30 km and the time is 3 hours.

To calculate the average speed of a cyclist, we can use the formula:

average speed = distance/time

Substitute the given values in the above formula,

average speed = 30 km / 3 hr

average speed = 10 km/hr

Therefore, the average speed of the cyclist is 10 km/hr.

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The of sum of the fraction 2 1/3 + 5 5/16 + 2/7  is 7 313/336

Fractions are represented as numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing

We want the of sum 2 1/3 + 5 5/16 + 2/7 =

For convenience sake, we can convert the mixed fractions to improper fractions. That is:

2 1/3 = 7/3

5 5/16 = 85/16

2 1/3 + 5 5/16 + 2/7 = 7/3 + 85/16 + 2/7

The LCM of 3, 16 and 7 is 336

                                = (7*112 + 85*21 + 2*48)/336

                                = (784 + 1785 + 96)/336

                                 = 2665/336

                                = 7 313/336

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The value of r is equal to the cube root of (V * (3π/4)).

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The estimated mean of the distribution for the given question will be 10.

Mean = 13 + 52 + 48 + 28 + 28 + 23 + 14 + 13 + 10 + 4 + 2 + 4 + 2 + 1 + 1 + 0 + 2 + 0 + 0 + 0 + 1 + 1 + 1 + 1 + 1

Total number =25

Now, divided the sum by 25

We get, the mean is equal to 10.

In mathematics, particularly in statistics, there are various types of means. Every mean serves to condense a specific set of data, frequently to help understand the overall significance of a particular data set. Only numerical variables, whether continuous or discrete, can be used to calculate the mean. Simply dividing the total number of values in a data set by the sum of all of the values yields it. The calculation can be performed on unprocessed data or data that has been combined into a frequency table.

Note that the illustration for graph is: (check the attached image)

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The LCM of 1-x^2 and (x-1)^3 is (x-1)^3.

To find the LCM, we take the polynomial with the highest degree (which determines the degree of the LCM) and then make sure that it contains all the terms from the other polynomials.

The degree of (x-1)^3 is 3 and the degree of 1-x^2 is 2.

So, we take (x-1)^3 as the starting point for the LCM and then add any missing terms from 1-x^2.

In this case, (x-1)^3 already contains all the terms from 1-x^2, so the LCM is (x-1)^3.

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Answer:

  angle JKL is 22°

Step-by-step explanation:

You want the measure of exterior angle JKL represented by (5x-3)°, given that the remote interior angles of ∆IJK are I = (2x +8)° and J = (x -1)°.

The exterior angle is equal to the sum of the remote interior angles:

  angle JKL = angle I + angle J

  5x -3 = (2x +8) +(x -1)

  5x -3 = 3x +7 . . . . . . . . . simplify

  2x = 10 . . . . . . . . . . . add 3-3x

  x = 5 . . . . . . . divide by 2

  5x -3 = 5(5) -3 = 22 . . . . . degrees

Angle JKL is 22 degrees.

__

Additional comment

It is helpful to draw a figure. The attached figure is not to scale, but the angle measures are appropriately labeled.

The unlabeled interior angle at K is supplementary to the labeled exterior angle there. That same interior angle is also supplementary to the sum of the other two interior angles, since the sum of all the angles is 180°. Two angles supplementary to the same angle are congruent. This means the exterior angle JKL is congruent to the sum of the two marked interior angles. It's a simple relation, easy to derive, and useful to remember.

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In order to divide the amount Rs.60 in the ratio 1:2

We take x as the variable that replicates the 1st amount + 2nd amount = Rs.60

Putting the values into a equation we get

1x + 2x = 60

3x = 60

x = [tex]\frac{60}{3}[/tex]

x = 20

Hence the amounts are ,

1x = 20

2x = 2 x 20 = 40

The cumulative frequency distribution table is present below. Cumulative frequency for speed less than 30 is 4 , less than 60 is 20 , less than 90 is 80 less than 120 is 100. So, correct answer is option (b).

The cumulative frequency of a variable's value is the number of values in the collection of data that are less than or equal to the variable's value. Example: Let the raw data be 2, 2, 1, 5, 5, 6, 5, 3, 7, 7, 5, 6. Cumulative frequency of 3 = 4. Cumulative frequency is a frequency distribution table for the predecessor total. The final value is always equal to the sum of all observations, since all frequencies have already been added to the previous sum. We have a data corresponds to the frequencydistribution.

Speed Number of cars

0-29 4

30-59 16

60-89 60

90-119 20

We have to construct the cumulative frequency distribution for the above frequency distribution.Using the above rules we can construct distribution as,

Speed Number of cars Cumulative Freq

0-29 4 4

30-59 16 16 + 4 = 20

60-89 60 60 + 20= 80

90-119 20 20 + 80 = 100

-----------

Total 100

Thus , cumulative frequency for speed less than 30 is 4 , less than 60 is 20 , less than 90 is 80

less than 120 is 100.

Hence, we got the required cumulative frequencies for frequency distribution.

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Complete question:

Construct the cumulative frequency distribution that corresponds to the given frequency distribution. Number Speed of cars 0-29 4 30-59 16 60-89 60 90-119 20 a)Speed Cumulative Frequensy

Less than 30 100

Less than 60 80

Less than 90 82

Less than 120 1

b)Speed Cumulative Frequency

Less than 30 4

Less than 60 20

Less than 90 80

Less than1 20 100

c) speed Cumulative Frequency

Less than 30 0.04

Less than 60 0.20

Less than 90 0.80

Less than120 1.00

jill wants to make a blend of mango and papaya juices and store it in a container that can hold no more than a total of 32 ounces. So,  m + p ≤ 32 inequalities represents this scenario.

A relationship that compares two numbers or even other mathematical expressions in an unequal way is known as an inequality in mathematics. The majority of the time, size comparisons between two numbers on the number line are made. Less than, larger than, less than or equal to, and more than or equal to are the four fundamental inequalities. A mathematical connection between two expressions is known as an inequality, and it is shown using one of the following: "≤" , "≥" , "<" and ">".

Given that,

Number of mango = m

Number of papaya = p

The limit of juices should be less than or equal to 32 ounces
Thus, the sum of mass of mangoes and papaya should be less than  or equal to 32 ounces.

So, m + p ≤ 32

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The complete question is as follows:

The most likely way Alcmaeon will try to solve this mystery about the sudden death of the goats would be by taking blood samples to analyze a possible disease or epidemic in the goat herd.

The best option to decipher the cause of death of the Cleatus goats is to take a sample from one of the goats to do an autopsy and identify the possible cause of death. Additionally, you can take blood samples to analyze a possible disease or infection that has caused the death of the sheep.

This would be the most effective way of detecting a possible cause of death as it allows Cleatus to know if the goats left alive are sick or at risk of dying from a disease.

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The length of side VY is 25.

A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those equal lengthed n sides).

Suppose that length of each side of that figure be of u units, then we have the perimeter as:

P=u+u+...+u (n times) = n xu

units.

Given;

The perimeter of the rectangle below is 120 units

The two sides of rectangle are 2y+3 and3y+2

Now,

2l+2b=120

2(2y+3)+2(3y+2)=120

4y+6+6y+4=120

10y+10=120

y+1=12

y=11

VY=2y+3

VY=2*11+3

VY=25

Therefore, the length according to given perimeter will be 25units.

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The correct graph for the supplements is attached below.

A bar chart is a graph that uses bars to represent and compare data. The length of the bar represents the magnitude of the data being displayed, with longer bars indicating larger values.

Bar charts can be used to display data for one or more categories, and can be either vertical or horizontal. They are commonly used to compare and visualize the distribution of categorical data.

The correct bar graph that shows the distribution of the supplements have been shown in the image that is attached to the answer that we have here.

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A library manager is interested in the number of people using the library. She decides to perform a count every 28th day for one year, starting next Monday. The systematic sampling method is this.

Hence, option (a) is the correct choice.

The library manager employs systematic sampling as a sample approach.

Systematic sampling is a form of probability sampling approach in which sample members are drawn from a larger population at random but with a set, periodic interval.

The sampling interval is determined by dividing the population size by the desired sample size.

Systematic sampling is a technique for picking a sample from a larger population at regular intervals. In this scenario, the library manager selects a sample of library users by tallying the number of persons every 28th day.

It is a systematic sampling approach since the intervals (28th day) are fixed and systematic.

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Both of these procedures start by drawing two arcs to the sides of the point and they both have six angles.

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The following are the two similarities between drawing a perpendicular line through a point on a line and drawing one through a point of a line:

Both of these procedures start by drawing two arcs to the sides of the point and they both have six angles.

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Answer: Its perimeter is 45 cm.

Step by step explanation:

Data :

We have a triangle with a measure of 15 cm

We must simplify taking into account that it is an equilateral triangle, all its sides are equal, therefore the perimeter is the sum of its sides:

[tex]\bf P= 15 + 15 + 15[/tex]

[tex]\boxed{\bf \: P = 45 \: cm}[/tex]

Rpt: Its perimeter is 45 cm.