Determine which set of side measurements could be used to form a right triangle.

square root of 19 comma square root of 35 comma 54
square root of 15 comma 6 comma square root of 51
5, 8, 30
5, 6, 7

The value of the experimental probability of rolling a 6 is found as 1/5.

For the given question-

Thus, by the definition of the probability-

Probability (getting 6) = number of occurred outcomes/ Total outcomes

Probability (getting 6) = 18/90

Probability (getting 6) = 1/5

Thus, the value of the experimental probability of rolling a 6 is found as 1/5.

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0.1875 is  the probability of having a daughter .

Describe probability using an example?

Let X = No. of sons

n = 5 and p = 0.5, because probability of having son and daughter is same.

X follows Binomial distribution with parameter n and p. Then its pmf is,

P(X= x) = \binom{n}{x}p^xq^{(n-x)} \ \ \ \ \ x = 0,1,----5

Now,

P(X= 5) = \binom{5}{5}(0.5)^5 (0.5)^{(5-5)} \\ \\ \\ P(X= 5) = 0.03125

Probability of haveing at least four sons

P(X\ge4) = P(X=4) +P(X=5) \\\\ P(X\ge4) = 0.15625 + 0.03125 \\\\ P(X\ge4) = 0.1875

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According to the model, the value of -6(10b + 0.8) will be -60b - 4.8.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, this is illustrated as:.

= -6(10b + 0.8)

Open the parentheses

= -60b - 4.8

Therefore, the value is -60b - 4.8.

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Answer:

y = (2/3)y - 2

Step-by-step explanation:

Linear equations of the form y=mx+b, describe the slope, m, and the y-intercept, b (the value of y when x=0).  

Line K

y = -(3/2)x + 1 tells us that it has a slope of -(3/2) and crosses the y axis (x=0) at y = 1.  

Perpendicular Lines

Perpendicular lines have a useful property in that they have a slope that is the "negative inverse" of the line they are perpendicular to.  If, for example, we were ever asked  what is the slope of a line perpendicular to Line L (yes, it happens), we could, with minimal effort, respond "It is the negative inverse of -(3/2)," which is a slope of (2/3).

Line L

We just accidently answered a key question when we found the negative inverse of the slope for Line K, (2/3).  That will be the slope of Line L that will make it perpendicular to Line K.

Line L will have the form y = (2/3)x + b

This line will be perpendicular to Line K, no matter the value of b.  But we want a perpendicular line that goes through point (6,2), so we need to find a value of b that will force it to go through that point.

The role b has in our equation is simply moving it up or down.  If b were 0, the line will go through the origin (0,0).  If b were 5, it would interect the y axis at 5 (0,5).  We could draw a graph and get a pretty good idea what b would have to be for the line to go throgh (6,2), but most prefer the easier route:  Use the (x,y) value in the above equation and solve for b.  Its easy, and works great:

   y = (2/3)x + b for (6,2)

  2 = (2/3)(6) + b

   b = 2 - (2/3)*(6)

   b = 2 - 4

    b = -2

The equation for Line L is thus:  y = (2/3)y - 2

See the attached graph.  Included are equations [marked Demo Line 1 and 2] with 2 random values of b (1 and 0), in order to:

The fraction of the surface of the cube which is white is 14/27

Given 27 cubes of 1 centimetre are conjoined to form a large cube of 3x3x3

To maximise the value of the surface area, in this case, taken as white, other than the cube in the centre, the rest of the cubes must have their white surface area exposed.

• Total Number of cubes where white surface area is exposed is = 27 – 1 = 26

Although, on each surface of the 3x3x3 cube, there are 9 smaller cube surfaces, and there will be a total of 6 surfaces for the bigger cube.

•      Total number of cube surfaces exposed in blue = 9 * 6 = 54

• Therefore, the greatest fraction in blue= 26/54 = 13/27

Therefore the fraction of the surface of the cube is white is = 1-[tex]\frac{13}{27}[/tex]= 14/27

The fraction of the surface of the cube which is white is 14/27 is the answer

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The fraction of the surface area of the cube which is white is 14/27

Given 27 cubes of 1 centimetre are conjoined to form a large cube of 3x3x3

To maximise the value of the surface area, in this case, taken as white, other than the cube in the centre, the rest of the cubes must have their white surface area exposed.

• Total Number of cubes where white surface area is exposed is = 27 – 1 = 26

Although, on each surface of the 3x3x3 cube, there are 9 smaller cube surfaces, and there will be a total of 6 surfaces for the bigger cube.

•      Total number of cube surfaces exposed in blue = 9 * 6 = 54

• Therefore, the greatest fraction in blue= 26/54 = 13/27

Therefore the fraction of the surface of the cube is white is = 1-(13/27)

= 14/27

The fraction of the surface of the cube which is white is 14/27 is the answer.

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Answer:8r squared -16

Step-by-step explanation:

The relation is function because each value in the domain matches only one value in the range, the relationship described above can be thought of as a function.

Given that,

In the picture we can see the domain and range.

We have to find if the domain and range is function or not.

Each of the sets of domain values has precisely one range value, according to the mapping.

Every domain value in a relation must have precisely one range value in order for it to be referred to as a function. It is not recommended to assign or map a domain value to more than one range value.

Therefore, The relation is function because each value in the domain matches only one value in the range, the relationship described above can be thought of as a function.

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Answer:

m = -2

Step-by-step explanation:

slope of AB

(4-3)/(-1-2)= 1/-3 = -1/3

parallel lines have the same slope

slope of CD = -1/3

we can now find the line that passes through the point C

y-5= -1/3(x-4)

y = -1/3 x +4/3 +5

y = -1/3 x + (4+15)/3

y = -1/3 x + 19/3

this line must passes also through the point D

we know its y, so:

7 = -1/3 x + 19/3

(7 * 3) = (-1/3 x + 19/3) * 3

21 = - x + 19

x = 19 - 21

x = -2

The commission earned by selling the merchandise worth $3000 is $270

The percentage of the commission earned by the salesman is 9%

The worth of the merchandise is $3000

A sales commission is typically an amount paid to an employee upon completion of a task for the sale of a specified quantity of goods or services.

Therefore, the commission earned can be found using the formula,

              Commission = SP x CP

where SP is the selling price and

          CP is the commission percentage.

Let us substitute the known values in the above equation, we get

              Commission = 3000 x 9%

                                    = 3000 x 9/100

                                    = 30 x 9

                                    = $270

Therefore, the commission earned is $270

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Answer:

a = 9 ; b = 26 ; c = 24

Step-by-step explanation:

(x^2+3x+2x+6)(x+4)

(x^2+5x+6)(x+4)

x^3+5x^2+6x+4x^2+20x+24

x^3+9x^2+26x+24

All the angles in a triangle add up to 180 degrees.

40 + x + (5x + 14) = 180

54 + 6x = 180

6x = 126

x = 21 degrees

Answer:

x=21

Step-by-step explanation:

a triangle adds up to 180 degree so to find x we will use the formula

(5x+14)+x+40=180

subtract 40 from each side so we have

(5x+14)+x=140

we have 2 terms with the same factor (x) so combine like terms

6x+14=140

subtract 14 from both sides

6x=126

divide both sides by 6

x=21

check your answer

5(21)+14

105+14=119

119+ 21+40=180

so x is equal to 21

f(n) = 8.3 + 2.1(n−1) function models the nth term of the sequence 8.3, 10.4, 12.5, 14.6.

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given,

The sequence below shows a certain company's expected net worth in millions of dollars after 1, 2, 3, 4 years, etc....

8.3, 10.4, 12.5, 14.6,...

The given sequence is a arithmetic sequence.

The first term is 8.3

The common difference is 2.1

The nth term of arithmetic sequence aₙ=a+(n-1)d

the nth term of this sequence=8.3+(n-1)2.1

f(n)=8.3+(n-1)2.1

Hence, f(n) = 8.3 + 2.1(n−1) function models the nth term of the sequence 8.3, 10.4, 12.5, 14.6.

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By comparing the fractions of rocks that skip over the poind for Jessica and Henry, we will see that Jessica gets more rocks to skip over the pond.

We know that for every 9 rocks that Herny throws, 5 skip over the pond. Then the fraction for Henry is:

H = 5/9

While for Jessica we know that for every 12 that she throws, 7 skip over the pond, so her fraction is:

J =  7/12

Now we only need to see which one of the fractions is larger.

If we simplify both we will get:

H = 5/9 = 0.556

J = 7/12 = 0.583

So we can see that Jessica's fraction is larger, which means that she will get more rocks.

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[tex]{ \pink{ \boxed{ \blue{ \sf{x = 2}}}}}[/tex]

Step-by-step explanation:

[tex]{ \red{ \sf{3x + 4x - 2 = 12}}}[/tex]

[tex]{ \red{ \sf{7x = 12 + 2}}}[/tex]

[tex]{ \red{ \sf{7x = 14}}}[/tex]

[tex]{ \red{ \sf{x = \frac{14}{7}}}} [/tex]

[tex]{ \blue{ \boxed{ \green{ \sf{x = 2}}}}}[/tex]

The equation → x - 4/5 - x + 1/6 = 1/3 will have infinitely many solutions.

A equation in mathematics is a mathematical statement depicting that the values of two mathematical expressions are equal. Some examples representing equations are -

y = 5x + 4

2x + 3y = 5x + 8π

cos(ny) = sin(πx)

Given is the following equation -

x - 4/5 - x + 1/6 = 1/3

We have -

x - 4/5 - x + 1/6 = 1/3

x - x - 4/5 + 1/6 = 1/3

- 4/5 + 1/6 = 1/3

Now, [x] will cancel out for ever possible value of [x], therefore, it will have infinitely many solutions

Therefore, the equation → x - 4/5 - x + 1/6 = 1/3 will have infinitely many solutions

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Normal distributions are frequently employed in the natural and social sciences to describe real-valued regressors with uncertain distributions, normal distributions are essential to statistics.

The central limit theorem is one reason they are significant.

This claim argues that, in some circumstances, the average of many samples (observations) of a random variable with finite variance and mean is itself a random variable, whose distribution tends to become normal with an increase in sample size.

Because of this, distributions of physical quantities that are meant to be the culmination of multiple separate processes, such as error margins, frequently resemble normal distributions.

Only the normal distribution has additional cumulants after the first two that are zero. It is also the continuous distribution with the highest level of entropy for a given mean and variance.

Assuming that the mean and variance are finite, Geary has shown that the normal distribution is the only distribution in which the mean and variance calculated from a collection of independent drawings are independent of one another.

The normal distribution is a form of elliptical distribution. The normal distribution is symmetric about its mean and non-zero over the whole real line.

Consequently, it could not be an appropriate model for variables that are inherently positive or highly skewed, such as a person's weight or the value of a share.

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The list of the members of the national education association is the Population.

Given, that a list of the members of the national education association is obtained and the questionnaire is mailed to 2500 teachers chosen at random from the list.

1347 teachers from those 2500 teachers return the questionnaire.

So, as we know that

A population is the group that you want to draw conclusions about.

Here, we want to know the opinions of American school teachers about establishing a national test.

So, The list of the members of the national education association is the Population.

Also, 1347 responses which we got is the sample.

Hence, The list of the members of the national education association is the Population.

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If a coin is weighted so that the probability of heads is five times the probabily of tails, that means :

+) P(head) + P(tail) = 1
+) P(head) = 5P(tail)

Therefore, P(head) = 5/6 ; P(tail) = 1/6

For both head and tail to be flipped, the events must happen together.

Therefore, we have the probabilty that both head and tail is flipped = 5/6 x 1/6 = 5/36.

Answer: 45 minutes

Step-by-step explanation:

She rides 150/20 minutes per mile which is 7.5 minutes per mile. So it would take her 45 minutes to ride 6 miles because 6 × 7.5 = 45.

840 are  4-letter passwords can be formed using the letters by permutation .

What are some examples of permutation?

We are to count all possible 4-letter passwords that can be generated from the letters a, b, c, d, e, f, g .

There are 7 letters in total.

      n = 7 r = 4

 P(n , r ) = 7!/( n - r )!

  P( 7 ,4 ) = 7!/( 7 - 4)!

              = 7!/3!

             = 7 * 6 * 5 * 4 * 3 * 2 * 1/3!

              = 7 * 6 * 5 * 4

               = 840

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Answer:

Step-by-step explanation:

The number of fliers that he has not posted is 9

What is proportion?

Proportion can be defined as the mathematical comparison of two elements or numbers.

From the information given, we have that;

• Total number of fliers is 45

• First week, 1/3 of the floors were posted

• This week, 3/5 of the remaining were posted.

To determine the number of fliers remaining, we have that;

Remaining fliers for the First week

= 45 × 1/3

Multiply and find the quotient

= 15 fliers

Fliers remaining after the last week

= 15 × 3/5

Multiply and find the quotient

= 45/5

= 9 fliers

Thus, the number of fliers the he has not posted is 9

Answer:

1/23

Step-by-step explanation:

The subtraction of the polynomials (1.3t³ + 0.4t² - 24t) and (0.6t² + 8t - 18) is given as follows:

1.3t³ - 0.2t² - 32t + 18.

Polynomials are subtracted subtracting the like terms, which are the terms that have the same symbolic variable and the same exponent.

For this problem, the subtraction is given by the expression presented as follows:

(1.3t³ + 0.4t² - 24t) - (0.6t² + 8t - 18).

The like terms of the expression are given as follows:

Hence the result of the subtraction of the polynomials is given as follows:

1.3t³ - 0.2t² - 32t + 18.

The problem asks for the subtraction of the polynomials (1.3t³ + 0.4t² - 24t) and (0.6t² + 8t - 18).

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Answer:

1, 3, 7 (<5 is also congruent to <5, but this is not a choice.)

Step-by-step explanation:

The angles congruent to <5 are:

<1 by corresponding angles.

<3 by alternate interior angles.

<7 by vertical angles.

<5 by the theorem: congruence of angles is reflexive.

Answer:

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A double-blind placebo control group study is used to control for observer bias and eliminate testing effects. So option c is correct.

A double-blind placebo control group study is one in which subjects are randomly assigned to either a control group, who receive a placebo, or an experimental group, who receive the treatment being studied. The researcher is not aware of which subjects are in which group, and neither are the subjects. This design is used to control for observer bias and eliminate testing effects.

This type of study is important because it allows researchers to test the efficacy of a new treatment without the risk of bias. By eliminating the possibility that the researcher or the subjects will know who is receiving the treatment and who is receiving the placebo, any expectations or preconceptions about the treatment can be avoided. This type of study is also important because it helps to control for the placebo effect, which is the phenomenon whereby subjects in the control group may experience some benefits from the placebo itself.

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She needs to complete 20 laps for a total distance of 0.5 kilometer.

1 kilometers = 1000 meters

0.5 kilometers = 500 meters

Length of swimming pool = 25 meters

That means, she covers 25 meters in 1 lap.

Laps to cover 500 meters = 500/25

                                            = 20

Hence, she needs to do 20 laps.

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