Select the postulate of equality or inequality that is illustrated.

5 = 5

the transitive postulate of equality
the multiplication postulate of inequality
comparison postulate
addition postulate of inequality
the symmetric postulate of equality
the transitive postulate of inequality
the reflexive postulate of equality

To calculate the probabilities, we can use the following information:

Total number of student athletes = 204

Number of students who play soccer = 52

Number of students who play volleyball = 31

Probability of a student playing both soccer and volleyball = 5/204

1.  Probability that a student plays both soccer and volleyball:

Let's denote the probability of playing both soccer and volleyball as P(Soccer and Volleyball). From the given information, we know that the number of students who play both soccer and volleyball is 5.

P(Soccer and Volleyball) = Number of students who play both soccer and volleyball / Total number of student athletes

P(Soccer and Volleyball) = 5 / 204

2.  Probability that a student plays volleyball:

We want to find the probability of a student playing volleyball, denoted as P(Volleyball).

P(Volleyball) = Number of students who play volleyball / Total number of student athletes

P(Volleyball) = 31 / 204

Therefore, the probability that a randomly selected student athlete in this school plays both soccer and volleyball is 5/204, and the probability that they play volleyball is 31/204.

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Here are a few 4/1 , 8/2 , 12/3

4, 8/2, 12/3 are equal to 4, when simplified, which means they are equivalent in nature.

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

If the denominator is 1, the numerator can be taken as 4, so the fraction would become \(\frac{4}{1}\) = 4

If the denominator is 2, the numerator can be taken as 8, so the fraction would become \(\frac{8}{2}\) = 4

If the denominator is 3, the numerator can be taken as 12, so the fraction would become \(\frac{12}{3}\) = 4

Thus, 4, 8/2, 12/3 are equal to 4, when simplified, which means they are equivalent in nature.

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First let's solve the given inequality:-

So the correct option is (D).

The slopes are best approximated as: The slopes are approximately -1.7, 0, and 1.7.

The formula to find the slope between two coordinates is expressed as:

Slope = (y₂ - y₁)/(x₂ - x₁)

The slope of each line above the x-axis are:

Slope 1 = (5 - 0)/(5 - 8)

Slope 1 = -1.7

Slope 2 = (5 - 5)/(5 - (-2))

Slope 2 = 0

Slope 3 = (5 - 0)/(-2 - (-5))

Slope 3 = 5/3 = 1.7

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The criteria that you can use to show these two triangles are congruent is A. AAS

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. It stands for "Angle, Angle, Side." Knowing two angles and one side is known as "AAS" (which is not between the angles). to make an AAS triangle work.

To find the other angle, add the three angles to 180°. then utilize the Law of Sines to determine each of the additional two sides. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

In conclusion, the correct option is A.

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Answer:

Step-by-step explanation:

(8 - 8i) + (1 + 6i)

8 + 1 - 8i + 6i

9 - 2i

Answer:

25 + 9^3

Step-by-step explanation:

Answer:

Step-by-step explanation:

divide by R

Answer:

\(\boxed{\sf \ \ \ answer \ b. \ \ +5 \ \ \ }\)

Step-by-step explanation:

Hello

let's assume that we are looking for x >=0

\(4x^2=100 <=> \dfrac{4x^2}{4}=x^2=\dfrac{100}{4}=25\\<=>\sqrt{x^2}=25\\<=> |x| = 5 <=> x = 5 \ or \ x=-5\)

Let's assume that we are looking for x>=0

so the correct answer is 5

Answer:

B. all expected frequencies > 5

Step-by-step explanation:

The expected number np(i) in any of the classes or cells should not be less than 5. So when the expected number np(i) in any  class is less than 5 , we may combine this class with one or more other classes to meet this requirement.

It is clear that chi square  will be small when all ni are close to their expected values npi. The chi square will become larger when the difference becomes larger. The chi square thus measures the amount of deviation ( or agreement ) between the observed and expected results.

Thus it is a good approximation if all the expected values npi are sufficiently large and hence chi square distribution confirms with the ( k-1) degrees of freedom.

Answer:

Jose will have played the guitar for 9.1 hours during those 6 days.

Step-by-step explanation:

Given that this week Jose played guitar for 3/4 of an hour on Tuesday, an hour and a half on Thursday, and 2.3 hours on Saturday, to determine, if Jose plays guitar for the same amount of time next week, how many hours will he have practiced over these 6 days, the following calculation must be performed:

3/4 = 0.75

1/2 = 0.5

(0.75 + 1.5 + 2.3) x 2 = X

4.55 x 2 = X

9.10 = X

Therefore, Jose will have played the guitar for 9.1 hours during those 6 days.

Answer:

16%

Step-by-step explanation:

From the graph of distribution of the number of text messages

Young adults send more than 158 text messages per day is 16%

Given :

The distribution is approximately Normal, with a mean of 128 messages and a standard deviation of 30 messages.

Given 158 text messages . so x is 168

Now we find out z -score

\(z=\frac{x-mean}{standard\; deviation }\)

Replace the values and find out z

\(z=\frac{158-128}{30} =1\)

the value of z=1

Lets use the standard deviation table that gives area on the left

the table gives the percentage of adults less than 158

z-score value for z=1 is 0.8413

Now, percentage of young adults send more than 158 text messages  

Percent (more than 158)=1- P(less than 158)=\(1-0.8413=0.1587\)

To get percentage we multiply by 100

\(0.1587 \cdot 100= 15.87= 16\)

Young adults send more than 158 text messages per day is 16%

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Answer:

<

Step-by-step explanation:

-0.5 is greater than -0.64

We need to find the symbol -0.64 ,0-0.5. -0.64<0-0.5.

A number system is defined as a system of writing to express numbers.

We need to find which symbol is used between Minus zero point six four and minus zero point five.

-0.64 and -0.5

As we know that the integers are number with positive, Negative and zero.

-0.64<-0.5

On the number line the integer -0.64 lies on left of -0.5.

So -0.64 is less than -0.5.

Hence -0.64 is less than -0.5.

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Step-by-step explanation:

To multiply two numbers in scientific notation, you multiply their coefficients and add their exponents. Applying this rule, we get:

(4 x 10^11) (8 x 10^6) = (4 x 8) x (10^11 x 10^6) = 32 x 10^17

However, this result is not yet in scientific notation because the coefficient 32 is not between 1 and 10. To put it in scientific notation, we need to divide the coefficient by 10 and increase the exponent by 1. This gives:

32 x 10^17 = 3.2 x 10^18

Therefore, the product of (4 x 10^11) and (8 x 10^6) expressed in scientific notation is 3.2 x 10^18.

Note that in the prompt above, the value of x is given as: 16°

To answer the issue, we will first name all of the points supplied to us on the isosceles triangle, then identify O, and last discover the value of x. See the attached image.

As a result, an isosceles triangle has two equal sides and two equal angles. The term is derived from the Greek words iso (same) and skelos (skull) (leg). An equilateral triangle has all of its sides equal, whereas a scalene triangle has none of its sides equal.

In ΔAOB

OA =  OB = R, the radius of the circle O,

therefore, the ΔAOB is an isosceles triangle, with OA, OB as the congruent sides and AB as the base of the triangle.

Thus, ∠OAB = ∠OBA = 53°

Sum of all the angles of a triangle = 180°

∠O + ∠AOB + ∠OBA = 180°

We know ∠AOB = ∠OBA, therefore,

∠O + 2(∠AOB) = 180°

∠O + 2(53°) = 180°
∠O = 180 - 106

∠O = 74°

In ΔOBC,

BC is the tangent to the circle O, therefore,

∠OBC = 90°

Sum of all the angles of a triangle = 180°

∠O + ∠OBC + ∠OCB = 180°

74° + 90° + ∠OCB = 180°

∠OCB = 180° - 74° - 90°

∠OCB = 16°

Hence, the value of x is 16°.

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Based on the volume of the solid, the value of K is 8960.

The volume of the solid = volume of the cone + volume of the hemisphere

The volume of the cone = ¹/₃hπr²

The volume of the hemisphere = ²/₃πr³

where;

r is radius = 20 cm

h is the height of the cone = ?

The curved surface area of the cone = πrl

The curved surface area of the cone = 580π cm²

πrl =  580π

l = 580/20

l = 29 cm

h = √(29² - 10²)

h = 27.2 cm

The volume of cone = ¹/₃ * 27.2 * 20² * π

The volume of the cone = 3626.7π cm³

The volume of the hemisphere = ²/₃ * π * 20³

The volume of the hemisphere = 5333.3 cm³

The volume of the solid = 5333.3π cm³ + 3626.7π cm³

The volume of the solid = 8960π cm³

The volume of the solid is kπcm³ = 8960π cm³

K =  8960

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Answer:

no

Step-by-step explanation:

Answer:

Y2-y1

X2-×1 = m

-12-(-10)

11-5     = -2/3

m= -2/3

Step-by-step explanation:

Answer:

From the information given, we can draw the following diagram:

   S ------- P

       / \       / \

      /   \ QR /   \

     /     \ / /     \

    /       Q       \

   R-----------------P

           MN

Here, SP || QR, so we have ∠QSP = ∠PQR and ∠SPQ = ∠QRP.

Since m∠QRS = 120, we have m∠QRP = 360 - m∠QRS = 360 - 120 = 240.

Since m∠QPS = 135 and ∠QSP = ∠PQR, we have m∠PQR = 360 - m∠QPS = 360 - 135 = 225.

Let x = MN. Since MN is the median of the trapezoid, we have MP = NR = x.

Now, consider the triangles SPQ and RPQ. We have:

tan(∠SPQ) = x/12 (using the tangent ratio in triangle SPQ)

tan(∠RPQ) = x/12 (using the tangent ratio in triangle RPQ)

Since ∠SPQ = ∠RPQ (as they are corresponding angles), we have:

x/12 = x/12

x = 12

Therefore, MN = x = 12.

Answer:

Step-by-step explanation:

1. Get mileage per gallon by dividing miles traveled by gallons used

\(\frac{125}{5} = 25 mpg\\\)

2. Divide miles you want to travel by the mileage per gallon you got on the first step

\(\frac{400}{25} = 16 gallons\)

Answer:

3, 2√2, √7

Step-by-step explanation:

compute the square roots of the next three prime numbers:

√7

√11

√13

Therefore, the next three terms of the sequence are:

{1, √2, √3, 2, √5, √7, √11, √13}

chatgpt

chat

Answer:

I believe it'd 69.5

Step-by-step explanation:

if u use the equation 2x+5=134, you get 64.5 for Josh and 69.5 for eric

The total area of the shaded region for the region x = 5y³ , x = 5y² in the interval ( 5, 1 ) is equal to ( 5 / 12 ).

From the attached graph :

The area of the shaded region :

x = 5y³ , x = 5y² for the interval ( 5, 1 ) is equal to :

= \(\int\limits^1_0 {( 5y^{2 } - 5y^{3 }}) \, dy\)

=  [ ( 5y³/3 ) - ( 5y⁴ / 4 ) ]\(| \limits^1_0\)

Substitute the lower limit and upper limit we get,

= (5 /3 )( 1 )³ - 0  - ( 5 / 4 )( 1⁴) + 0

= ( 5 / 3 ) - ( 5 / 4 )

= ( 20 - 15 ) / 12

= 5 / 12

Therefore, the total area of the shaded region in the given graph for the lower and upper limit is equal to ( 5 / 12 ) .

The given question is incomplete, I answer the question in general according to my knowledge:

Find the total area of the shaded region x = 5y³ , x = 5y² for the interval

( 5, 1 ).

Graph is attached.

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Doing a change of units, we can see that 2.11 yd³ is equivalent to 1.7513 m³

We know that the relation between one yard and one meter is:

1yd = 0.91m

Then the relation between one cubic yard and one cubic meter is:

(1yd)³ = (0.91m)³

1 yd³ = 0.83 m³

Now we can perform a change of units between the volume in yards and the volume in meters, we will get:

2.11 yd³ = 2.11*(0.83 m³) = 1.7513 m³

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The measure of UV is 0.9

Similar triangles are triangles that have the same shape, but their sizes may be different. The ratio of the corresponding sides of similar triangles is equal.

For similar triangle to have thesame shape, this means that they will have thesame angles but different sides.

Therefore , 1.8/10 = UV/5

1.8 × 5 = 10UV

9 = 10UV

divide both sides by 9

UV = 9/10

UV = 0.9

therefore the measure of UV is 0.9

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The value of \(f\) is \(0\), by using the concept of slope of a line.

The equation to find the slope of a line is given by:

\(\(\text{slope} = \frac{{y_2 - y_1}}{{x_2 - x_1}}\)\)

Given that the slope is -8 and the points (-7, f) and (-6, -8) lie on the line, we can substitute the coordinates into the equation:

\(\(-8 = \frac{{-8 - f}}{{-6 - (-7)}}\)\)

Simplifying the equation:

\(\(-8 = \frac{{-8 - f}}{{1}}\)\)

Multiply both sides by 1:

\(\(-8 = -8 - f\)\)

Rearranging the equation:

\(\(-8 + 8 = -f\)\(0 = -f\)\)

The concept used in this problem is finding the slope of a line using two given points. The slope represents the rate of change of the line, indicating how much the line rises or falls for each unit of horizontal distance.

By substituting the coordinates of the two given points (-7, f) and (-6, -8) into the formula, we can calculate the slope.

Thus, the value of \(f\) is \(0\).

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The area of the kite is 38 mm squared.

A kite is a quadrilateral with two pairs of adjacent sides equal. The diagonals of a kite are perpendicular. The vertex angle are bisected by the diagonals.

It has two pairs of consecutive equal sides and perpendicular diagonals.

Therefore,

area of a kite = ab / 2

where

Therefore,

a = 9.5 mm

b = 4 mm

Therefore,

area of a kite = 9.5 × 4 / 2

area of a kite = 38 / 2

area of a kite = 19 mm²

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Answer:

The area of the kite would be 19 mm².

Step-by-step explanation:

A kite is a quadrilateral with two pairs of equal-length adjacent sides. The diagonals of a kite are perpendicular to each other and intersect at a right angle, dividing the kite into four right triangles. The area of a kite can be calculated by finding the product of the lengths of its diagonals and dividing it by 2.

If we assume that the height and width you provided are the lengths of the diagonals, we can calculate the area using the following formula:

Area = (height * width) / 2

Substituting the given values:

Area = (9.5 mm * 4 mm) / 2

= 38 mm² / 2

= 19 mm²

Therefore, if the height and width represent the lengths of the diagonals, the area of the kite would be 19 square millimeters.

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The probability that the third largest observation in the sample is less than 0.7 is  0.2401 =  24.01%.

The sample size n = 5,

Therefore the order statistics will be represented as X₁, X₂, X₃, X₄, and X₅.

Probability that X₃ is less than 0.7:

Since X₃ is the third largest observation =  (X₁ and X₂) < 0.7.

The probability that X₃ is less than 0.7 is (0.7)² = 0.49.

.

The probability that both X₁ and X₂ are less than or equal to 0.7 is (0.7)² = 0.49 because in a continuous uniform distribution, the probability of any single observation being less than 0.7 is 0.7 - 0 = 0.7.

We then get the product of both cases:

Probability = 0.49 * 0.49 = 0.2401

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Answer:

Step-by-step explanation:

LCM of 7/12 and 5/6

12: 12, 24

6: 6, 12

LCM: 12