After identifying each of the mistakes that Ben and luna made, find the correct area of the circle. Round your answer to the nearest hundredth.

Answer:

the number of athletes is 8

Estimated value of median is 44.7.

The graphic representation of data points arranged into specified ranges is called a histogram. The histogram, which re assembles a bar graph in appearance, contain a data series into an intuitive visual by collecting numerals data points and organizing them into logical bins or range

The middle value in a arrange  ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does. It reflects the midway of the data since it is the point above and below which half (50%) of the observed data falls.

l =  lower limit of median class, n = number of observations, f =  frequency of  median class, and h = class size. Median = [l + ((n/2) - cf)/f]h (assuming equal size classes).

According to question ,n =60 then median class = 25 to 45 because [tex]\frac{n}{2}[/tex]=30

l=25, f=7.5 ,cf =0.5 ,h = [tex]\frac{45-25}{4}[/tex]=5

so, median =

[tex]25+[\frac{(30-0.5)}{7.5}]*5\\44.7[/tex]

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To create the figure with the new scale of 1 unit = 3 yd. The steps are mentioned below.

Scale refers to the proportional relationship between the measurements of an object or a system and the corresponding measurements on a representation or a model of that object or system. It is commonly used in many fields, including mathematics, engineering, architecture, art, and geography.

In mathematics, scale can be expressed as a ratio or a fraction, which indicates how much the measurements on the representation or model have been reduced or enlarged relative to the actual measurements of the object or system. For example, a scale of 1:100 means that every measurement on the representation or model is 100 times smaller than the corresponding measurement on the actual object or system.

In art and architecture, scale is used to create a sense of proportion and perspective in a work. For example, an artist might use a smaller scale for a background object to make it appear farther away, while using a larger scale for a foreground object to make it appear closer.

To create the figure with the new scale of 1 unit = 3 yd. Here are the steps:

Determine the dimensions of the rectangle in yards using the original scale of 1 unit = 6 yd.

Divide the dimensions by 2 to get the new dimensions using the new scale of 1 unit = 3 yd.

Draw a rectangle on a new grid using the new dimensions.

If you want to place the rectangle in a specific location on the grid, you can use the coordinates on the grid to position it.

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According to the given information, the correct answer is Bus 18, with a median of 13.

What is median?

The median is a measure of central tendency in statistics. It is the value that separates the dataset into two equal halves, with half the values being greater than the median and half being less than the median.

To compare the travel times of the two buses and determine which typically has the faster travel time, we need to look at the measures of central tendency.

The two common measures of central tendency are mean and median.

For Bus 18, the median is 13, which means that half of the students take less than 13 minutes to travel to school and half take more than 13 minutes. The mean can be calculated by finding the sum of all travel times and dividing by the number of students, but this information is not provided in the given line plot.

For Bus 47, the median is 16, which means that half of the students take less than 16 minutes to travel to school and half take more than 16 minutes. The mean can be estimated by calculating the average of all the travel times, which is:

(4+6+10+10+12+12+14+14+18+18+22+22+28+28+28)/15 = 16

Therefore, the mean travel time for Bus 47 is also 16.

Comparing the median travel times, we can see that Bus 47 has a higher median of 16 compared to Bus 18's median of 13. This suggests that the travel times for Bus 47 are typically longer than those for Bus 18, and therefore Bus 18 typically has the faster travel time.

Therefore, the correct answer is Bus 18, with a median of 13.

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Please mark answer as brainliest

Answer:

  (c)  AE = x·cos(α)/sin(θ)

  (d)  BD = x·cos(α)cos(α-θ)/cos(θ)

Step-by-step explanation:

In the given diagram, you want expressions for (c) AE and (d) BD in terms of x, α, and θ.

The law of sines can be used in ∆ACE to give the measure of AE.

[tex]\dfrac{AE}{\sin(C)}=\dfrac{CE}{\sin(\theta)}\\\\\boxed{AE=\dfrac{x\,\cos(\alpha)}{\sin(\theta)}}\qquad\text{where $\sin(C)=\cos(\alpha)$ and $CE=x$}[/tex]

The length BD can be found in terms of AD and θ:

  BD = AD·tan(θ)

The length AD can be found in terms of AE and (α-θ):

  AD = AE·cos(α-θ)

Using the value of AE from part (c), we have ...

  BD = AE·cos(α-θ)·tan(θ) = x·cos(α)cos(α-θ)·tan(θ)/sin(θ)

  BD = x·cos(α)cos(α-θ)/cos(θ) . . . . . . . using tan/sin = 1/cos

__

Additional comment

We assume angle EAC is θ throughout, as it is in part (a).

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Answer:

exact form-512/7

decimal form-73.1

Mixed number form-73 1/7

Step-by-step explanation:

Answer: 7[tex]x^{2}[/tex]+13x-7

Step-by-step explanation: (3x + 7)(3x - 1) = 9[tex]x^{2} \\[/tex] + 18x - 7. (2x + 5)x = 2[tex]x^{2}[/tex]+5x. 9[tex]x^{2} \\[/tex] + 18x - 7 - (2[tex]x^{2}[/tex]+5x) = 7[tex]x^{2}[/tex]+13x-7

The x-intercepts (zeros), end behaviors, degree and multiplicity of the function f(x) = (x - 2)²·(x + 1)·(x - 4), can be used to graph the polynomial in factored form. Please find attached the graph of the polynomial created with MS Excel.

A zero is an input variable value that makes the value of the output to be zero. A root is a value that satisfies the equation.

The steps to graph the polynomial in factored form are;

1. Find the x-intercepts; The x-intercepts are obtained by setting each  factor as being equivalent to zero and solve for x. The values obtained are the x-intercepts or the zeros of the function.

The specified function, f(x) = (x - 2)²·(x + 1)·(x - 4), the zeros are; x = 2, (with a multiplicity of 2), x = -1, and x = 4.

2. Determine the end behavior of the function: The degree and leading coefficient of a polynomial determines the end behavior of the polynomial.
The degree of a function is the highest exponent of the function. The highest exponent of x in the function f(x) is 4, therefore, the degree of f(x) is 4.

The leading coefficient is the coefficient of the term with the highest exponent of x. The leading coefficient of f(x) is therefore, the coefficient of the term with the highest exponent of x, which is 1

3. Determine the multiplicity of the zeros: The number of times a factor appears in the factored form determines the multiplicity of the zero of the factor.

The zero of x = 2 in the function has a multiplicity of 2 indicating that the graph touch and bounces upwards on the x-axis at x = 2.

4. Determine the behaviour at the x-intercepts: The multiplicity of the zero determines the behavior of the graph at the x-intercept, such that an odd multiplicity indicates that the graph crosses the x-axis and an even multiplicity indicates that the graph touches the x-axis and bounces upwards or downwards at the point.

The information in the steps 1 – 4 can then be used to sketch the graph of the polynomial.

Please find attached the graph of the polynomial created with MS Excel,  using the function, f(x) = (x - 2)²·(x + 1)·(x - 4)

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Answer: ~1256.64

Step-by-step explanation:

The equation for the surface area of a sphere is 4πr². So you would substitute 10 in for r which would then be 4π10². That will get you 1256.63706 but rounded it would be approximately 1256.64.

Answer: [tex]\text{400}\pi \ \text{square inches}[/tex]

Step-by-step explanation:

Given: The radius of the sphere = 10 in.

The formula to calculate the surface area of the sphere is given by:

[tex]\text{Surface Area}=4\pi r^2[/tex], where r is the radius of the sphere.

For r = 10 in. we have

[tex]\text{Surface Area of the sphere}=4\pi (10)^2[/tex]

[tex]\implies \text{Surface Area of sphere}=4\pi (100)[/tex]

[tex]\implies \text{Surface Area of the sphere}=\text{400}\pi \ \text{square inches}[/tex]

Check the picture below.

so since ST is bisecting at the vertex T, that means that T will end up with twin angles and thus both triangles the yellow and green one since both are sharing the hypotenuse ST, both triangles are congruent by the HA theorem, and thus CPCTC.

Answer:

The GCF of 16 and 40 is 8. To calculate the greatest common factor of 16 and 40, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40) and choose the greatest factor that exactly divides both 16 and 40, i.e., 8.

Answer:

The GCF is 8 ; factored is 8(5+2)

Step-by-step explanation:

The gcf of 40 and 16 is 8.

Since 8*5 = 40 and 8*2 = 16:

40+16 = 8(5+2).

Answer:

x equals [tex]\frac{11}{2}[/tex]

Hope this helps!

Step-by-step explanation:

Cross multiply to get ( 4x + 8 = 6x - 3 )  =  ( 2x = 11 ) = ( x = [tex]\frac{11}{2}[/tex] ).

Answer:

11/2 or 5.5 (5 1/2 mixed)

Step-by-step explanation:

Cross multiplication ( a/b = c/d = a*d = c*b

(x+2)*4 = 3(2x-1) =

4x + 8 = 6x - 3

Move -3 to the left side (becomes positive since it is a negative)

4x + 8 + 3 = 6x

Move 4x to the other side

8+3 = 6x - 4x

Combine Like Terms

11 = 2x

Divide by 2

11/2 = x

Spanish playing cards have four suits: coins, cups, swords, and clubs, with each suit representing a different aspect of life, and consisting of ten numbered cards and three court cards.

Spanish playing cards traditionally have four suits: coins, cups, swords, and clubs. These suits are similar to the suits found in Italian and Latin American playing cards, but different from the suits found in French and German playing cards. The coins suit represents wealth and commerce, the cups suit represents love and pleasure, the swords suit represents warfare and justice, and the clubs suit represents agriculture and prosperity. Each suit typically contains ten numbered cards and three court cards: the knight, the queen, and the king.

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Answer:

24

Step-by-step explanation:

Because it has to be a equal side and 24 is even

and plus 24 is

The radius of the cylinder is approximately 9.02 mm.

What is cylinder?

A cylinder is a three-dimensional shape that consists of two parallel and congruent circular bases that are connected by a curved lateral surface. It can be thought of as a stack of circular discs or coins of equal size, with a constant distance between them. The axis that passes through the center of the circular bases is called the axis of the cylinder.

The formula for the volume of a cylinder is:

[tex]$$ V = \pi r^2 h $$[/tex]

where [tex]$V$[/tex] is the volume, [tex]$r$[/tex] is the radius, and [tex]$h$[/tex] is the height.

We can rearrange this formula to solve for the radius:

[tex]$$ r = \sqrt{\frac{V}{\pi h}} $$[/tex]

Substituting the given values, we get:

[tex]$$ r = \sqrt{\frac{4700}{\pi \cdot 31}} $$[/tex]

Simplifying this expression, we get:

[tex]$$ r \approx 9.02\ \text{mm} $$[/tex]

Therefore, the radius of the cylinder is approximately 9.02 mm.

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Answer:

85

Step-by-step explanation:

13(6)+7=85

:)

Answer:

85

Step-by-step explanation:

Let's calculate the working hours of the first 6 days:

[tex]13 * 6 = 78[/tex] hours

Now let's add that to the last 7 hours she worked:

[tex]78 + 7 = \fbox{85}[/tex] hours

Answer:

(4, 1 )

Step-by-step explanation:

3x - 5y = 7 → (1)

2x + 5y = 13 → (2)

the 'best' or 'simplest' way to solve this system is the elimination method

since the signs of 5y are opposites then adding will eliminate the y term

add (1) and (2) term by term to eliminate y

(3x + 2x) + (- 5y + 5y) = 7 + 13 , that is

5x + 0 = 20

5x = 20 ( divide both sides by 5 )

x = 4

substitute x = 4 into either of the 2 equations and solve for y

substituting into (2)

2(4) + 5y = 13

8 + 5y = 13 ( subtract 8 from both sides )

5y = 5 ( divide both sides by 5 )

y = 1

solution is (4, 1 )

Answer:

-3x^3y^2 - 4x^2y + 8y.

Step-by-step explanation:

When we distribute the negative sign to the terms inside the parentheses, we get:

(2x^3y^2 − 8x^2y + 4y) − (5x^3y^2 − 4x^2y − 4y) = 2x^3y^2 − 8x^2y + 4y - 5x^3y^2 + 4x^2y + 4y

Now, we can combine like terms. The terms with x^3y^2 are 2x^3y^2 and -5x^3y^2, which combine to give -3x^3y^2. The terms with x^2y are -8x^2y and 4x^2y, which combine to give -4x^2y. The terms with y are 4y and 4y, which combine to give 8y. Therefore, we have:

(2x^3y^2 − 8x^2y + 4y) − (5x^3y^2 − 4x^2y − 4y) = -3x^3y^2 - 4x^2y + 8y

Therefore, the simplified expression is -3x^3y^2 - 4x^2y + 8y.

The expression can be simplified by subtracting the coefficients of matching terms from the first and second parentheses. The simplified expression is -3x3y2 - 4x2y + 8y.

To simplify the expression (2x3y2 − 8x2y + 4y) − (5x3y2 − 4x2y − 4y), you must subtract each term in the second parentheses from the corresponding term in the first. In this case, it works as follows:

So, the simplified expression becomes −3x3y2 − 4x2y + 8y.

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List 4 provides space for the sample to remove 2 marbles from the bag and replace them.

In statistics and probability, a sample is a subset of a population that is selected for observation, analysis, or testing. The population refers to the entire group of individuals, objects, or events that share a common characteristic of interest, while the sample is a smaller group that is selected to represent the population.

List 4 provides space for the sample to remove 2 marbles from the bag and replace them.

Each element in List 4 represents a possible outcome of selecting 2 marbles from the bag, where the order of selection matters and replacement is allowed. For example, the first element in List 4, "G, O", represents the outcome of first selecting a green marble, then replacing it in the bag, and then selecting an orange marble.

The other lists represent possible outcomes of selecting 2 marbles, but some of them do not allow for replacement or do not include all possible orderings. For instance, List 1 only includes outcomes where both marbles are the same color, while List 2 does not include all possible orderings (e.g., it does not include the outcome "O, G").

Therefore, List 4 is the correct answer as it represents the sample space for selecting 2 marbles from the bag with replacement and includes all possible outcomes.

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Answer:

List 4

Step-by-step explanation:

List 4 provides space for the sample to remove 2 marbles from the bag and replace them.

What is sample?

In statistics and probability, a sample is a subset of a population that is selected for observation, analysis, or testing. The population refers to the entire group of individuals, objects, or events that share a common characteristic of interest, while the sample is a smaller group that is selected to represent the population.

According to question:

List 4 provides space for the sample to remove 2 marbles from the bag and replace them.

Each element in List 4 represents a possible outcome of selecting 2 marbles from the bag, where the order of selection matters and replacement is allowed. For example, the first element in List 4, "G, O", represents the outcome of first selecting a green marble, then replacing it in the bag, and then selecting an orange marble.

The other lists represent possible outcomes of selecting 2 marbles, but some of them do not allow for replacement or do not include all possible orderings. For instance, List 1 only includes outcomes where both marbles are the same color, while List 2 does not include all possible orderings (e.g., it does not include the outcome "O, G").

Therefore, List 4 is the correct answer as it represents the sample space for selecting 2 marbles from the bag with replacement and includes all possible outcomes.

The mean IQ score in the population is approximately 98, and the standard deviation is approximately 16.

Let μ = mean and σ = standard deviation of IQ scores in population.

Then we can write the two equations as :

⇒ P(X ≤ 80) = 0.13    ...equation(1)

⇒ P(X ≥ 128) = 0.03   ...equation(2)

we standardize the data by using the formula:

⇒ Z = (X - μ)/σ,

Where Z = standard normal variable.

Using the standard normal distribution, we know that P(Z ≤ -1.126) = 0.13,

So, -1.126 = (80 - μ)/σ   .....equation(3),

and we know that P(Z ≥ 1.881) = 0.03.

So, 1.88 = (128 - μ)/σ     ...equation(4),

⇒ μ = 128 - 1.881σ,

Solving equation(3) and equation(4),

We get,

⇒ σ ≈ 16.

Substituting σ = 16 into the equation(4),

We get,

⇒ μ = 128 - 1.881×16,

⇒ μ = 98.

Therefore, the mean IQ score = 98, and standard deviation is = 16.

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There are some traits that rectangles, squares, and rhombuses have in common. These are also some differences between them. Rectangles, squares, and rhombuses all have 4 sides. If a shape is a rectangle the diagonal sides will be congruent. If a shape is a square all the sides will be congruent, the shape will also have a right angle. The diaganles of a rombus are perpendicular.

If the sides of a right triangle are x, 3x+3, and 4x-3, the value of x is 7

In a right triangle, the Pythagorean theorem states that the sum of the squares of the two shorter sides equals the square of the longest side (the hypotenuse). Using this theorem, we can set up an equation as follows

x^2 + (3x+3)^2 = (4x-3)^2

Expanding the squares, we get

x^2 + 9x^2 + 18x + 9 = 16x^2 - 24x + 9

Simplifying and rearranging terms, we get

6x^2 - 42x = 0

Factorizing out x, we get

x(6x - 42) = 0

Therefore, x = 0 or x = 7. However, since the sides of the triangle cannot be zero, we must choose x = 7 as the solution.

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I have solved the question in general as the given question is incomplete:

The complete question is:

If the sides of a right triangle are x, 3x+3, and 4x-3, then what is the value of x?

For the given cyclic quadrilateral the missing values of  x is 82°,  y is 130° and z = 118°

In trigonometry, a set of fundamental identities is referred to as the "Circle identities" and connects the six trigonometric functions of an angle in a right-angled triangle.

Here given a quadrilateral inside the circle, we know that,

Sum of opposite angle of cyclic quadrilateral is 180 degree;

Then, x + 98° = 180°

          x = 82°

Opposite angle of 76° will be;  180° - 76° = 104°

Radius are same in ΔAOB, (See the below figure)

Then, a + a + 34° = 180°

          a = 73°

then, ∠OBC = 98° - a = 25°

and in ΔCOB, 25° + 25° + y° = 180°

Then, y = 130°

and in ΔDOA,  

∠OAD = 104° - 73° = 31°

Then, z = 118°

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Simplify figure for understanding-

The density of the material is 4 g/cm³.

What is the density of the material?

Density is a physical property that describes the amount of mass per unit volume of a substance. It is typically represented by the symbol "ρ" (rho) and is calculated by dividing the mass of an object by its volume. The units of density are usually expressed as mass per unit volume, such as grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³).

Density is defined as mass per unit volume. We can use the formula:

density = mass/volume

Substituting the given values:

density = 48g / 12cm³

Simplifying:

density = 4g/cm³

Therefore, the density of the material is 4 g/cm³.

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Let's first define some events:

A: The person has COVID-19.

B: The test result is positive.

Using the information provided, we can calculate the probability of a correct diagnosis using Bayes' theorem:

P(A|B) = P(B|A) * P(A) / [P(B|A) * P(A) + P(B|not A) * P(not A)]

where P(B|A) is the probability of a positive test result given that the person has COVID-19, P(A) is the prevalence of COVID-19 in the population (0.083 or 8.3%), P(B|not A) is the probability of a positive test result given that the person does not have COVID-19 (false positive rate, 0.05 or 5%), and P(not A) is the complement of P(A) (0.917 or 91.7%).

Plugging in the values, we get:

P(A|B) = (0.98 * 0.083) / [(0.98 * 0.083) + (0.05 * 0.917)]

= 0.6037 or 60.37%

Therefore, the probability that the diagnosis is correct is 60.37%, rounded to the nearest hundredth percent.

The two-column proofs of the segments are shown below

The proof is as follows

Statement                                                      Reason

ABCD and BCDE are parallelogram            Given

AG = BC                                                         Opposite sides of

                                                                       parallelogram            

ED = BC                                                         Opposite sides of

                                                                       parallelogram            

AG ≅ ED                                                         Substitution property (proved)

Proving that KLMN is a parallelogram

The proof is as follows

Statement                                                Reason

KL || NM  and ∠L ≅ ∠N                            Given

KN ≅ LM                                                   CPCTC

KL ≅ NM                                                   CPCTC

We've proved that the opposites sides are equal and parallel

So, KLMN is a parallelogram

Proving that STUV is a parallelogram

The proof is as follows

Statement                                                Reason

ST || VU  and W is midpoint of SU          Given

SW = UW                                                   Definition of midpoint

VW = TW                                                   Definition of midpoint

VU = ST                                                     CPCTC

VS = UT                                                     CPCTC

We've proved that the opposites sides are equal and parallel

So, STUV is a parallelogram

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Answer:

20 percent

Step-by-step explanation:

5/25=0.2

Answer:

25/30 which reduces to 5/6

Step-by-step explanation:

There is a net total of 30 students (25 for musical and 5 for play)

It's asking for the probability of someone who wants to do a musical getting selected, which would be 25 kids out of 30. Which reduces to 5/6

Answer:

Step-by-step explanation:

in the middle is 0 in the first one is -5 and last one is 5

Answer: a) Lower limit: (13.1 - 0.05) - (18.7 + 0.05) = -5.65 cm

Upper limit: (13.1 + 0.05) - (18.7 - 0.05) = -4.95 cm

Therefore, the lower limit of the difference is -5.65 cm and the upper limit is -4.95 cm.

b) Lower limit: (0.55 - 0.005) - (0.093 + 0.005) = 0.447 km

Upper limit: (0.55 + 0.005) - (0.093 - 0.005) = 0.457 km

Therefore, the lower limit of the difference is 0.447 km and the upper limit is 0.457 km.

c) Lower limit: (2539 - 0.5) - (1.229 + 0.001) = 2537.27

Upper limit: (2539 + 0.5) - (1.229 - 0.001) = 2541.27

Therefore, the lower limit of the difference is 2537.27 and the upper limit is 2541.27.

d) Lower limit: (8.3 - 0.1) - (15.9 + 0.1) = -7.7 m

Upper limit: (8.3 + 0.1) - (15.9 - 0.1) = -7.3 m

Therefore, the lower limit of the difference is -7.7 m and the upper limit is -7.3 m.

Step-by-step explanation: omg u made me so tired

Answer: 25 divided by 5 plus 6 times 2 minus 4 and 5 tenths

Step-by-step explanation: order of operations, PE(MD)(AS)