suppose a fair die is rolled twice, what is the probability that the sum of the two outcomes is 6, given that the sum is even

Answer:

3.054

i think

At most Josh can invite 14 friends to the party. If he invited that many friends, each will receive 3 granola bars and 4 fruit drinks.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of granola = 42

Number of fruit drinks = 56

The highest common multiples of 42 and 56.

14 x 3 = 42

14 x 4 = 56

Now,

The number of friends that can be invited is 14.

Where each friend gets an equal number of each item.

Thus,

At most Josh can invite 14 friends to the party.

The number of items each friend received is 3 granola bars and 4 fruit drinks.

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This is a table of values of three functions at selected values of x.

It is asking for h(f(-2))

Its saying, take f(-2), and take whatever you get from that and put it into h(x)

So, find f(-2).

Find x = -2, then see what f is there.

f(-2) = -1

So, find h(-1)

h(-1) = 0

Hope this helps :)

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- Jeron

The expected frequencies in a chi-square test is can contain fractions or decimal values

What is Chi-Square Test?

When the sample sizes are large, a chi-squared test is a statistical hypothesis test used in the study of contingency tables. To put it another way, the main purpose of this test is to determine if two categorical factors  have independent effects on the test statistic.

What is Expected Frequencies?

A theoretical frequency that we anticipate to show up in an experiment is known as an expected frequency.

Expected frequency = Expected percentage * Total count

The expected frequencies in a chi-square test is can contain fractions or decimal values

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A bijection between two sets is constructed below and also proved that it is both one-one and onto.

The phrase "one-to-one function" should not be mistaken with "one-to-one correspondence," which is used to describe bijective functions, in which each element in the codomain is a precise mirror image of a single element in the domain.

Any function that can work with the operations of two algebraic structures is said to be a homomorphism between them. An injective homomorphism is also referred to as a monomorphism for any commonly occurring algebraic structures, particularly vector spaces.

Let t∈T

Then,

t=2k+1, for some k∈Z

Let s=3k

Then,

s∈S and f(s)=2(s/3)+1

=2k+1

=t

Therefore, for every t∈T there exists s∈S such that f(s)=t

Thus, f is onto.

Hence,

f:S  ----> T is a bijective mapping

⇒|S|=|T|

Now, we have to define a mapping f:S ---?T

By f(x)=2(x/3)+1, ∀x∈S

Given,

S={3k|k∈Z} and T={2k+1:k∈Z}

We have to prove:

|S|=|T|

Let x, y∈ S with f(x)=f(y)

Then,

2(x/3)+1=2(y/3)+1

2(x/3)=2(y/3)

(x/3)=(y/3)

x=y

So, f is one-one

Now, we have proved that f is both one-one and onto.

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The shortest total length of the fence is 808 m.

What is a rectangle?

A rectangle is a quadrilateral with all four interior angles 90°.

Given that the area of the rectangular field is 800 m².

Let the length and the width of the rectangle be x and y.

Then, the area of the rectangle is:

A= xy

Or, xy = 800

x = 800/y     (1)

The perimeter of the triangle is:

2x +2y

Since the triangle is divided into three equal parts by fence, the total length of the fence is equal to the sum of the perimeter of the triangle and two times the length or width of the triangle.

Therefore, the total length of the fence is:

L = 2x + 2y + 2x

L = 4x +2y

Substitute x = 800/y into the above equation:

L = 4(800/y) + 2y

L = 3200/y +2y         (2)

Differentiate the equation with respect to y:

L' = -3200/y² +2

Substitute L'= 0 into the above equation:

0 = -3200/y² + 2

y² = 3200/2

y² = 1600

y = 400

Substitute y = 400 into equation (2):

L = 3200/400 + 2(400)

L = 8 + 800

L = 808

Hence, the shortest total length of the fence is 808 m.

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The area of the rectangle in centimeter square is 2013 cm².

The area of a rectangle is the product of its length and width.

If the values of area and one of the sides of a rectangle is given the other one can be found by forming a suitable equation.

The length and width of the given rectangle can be written in cm as follows,

The length is given as 24 × 2.54 = 60.96 cm

And, the width is 13 × 2.54 = 33.02 cm

Now, the area of the rectangle can be obtained by taking the product of length and width as follows,

Area = 60.96 × 33.02

        = 2012.89

Which can be approximated as 2013 cm².

Hence, the area of the rectangle is obtained as 2013 cm².

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Using the equation we know that the flowerbed is 2250 feet away from the hive.

A mathematical assertion that has an "equal to" symbol between two expressions with equal values is known as an equation.

As in 3x + 5 Equals 15, for instance.

So, let's say the flowerbed is feet away from the hive.

The bee travels directly from its hive at a speed of 20 feet per second to a flowerbed before returning at a speed of 12 feet per second.

Time = distance/speed

Therefore, the bee needed x/20 seconds to get to the flowerbed and x/12 seconds to fly back to the hive.

The bee spends a total of 20 minutes, or 2060 seconds, or 1200 seconds away from the hive. I

t spends 15 minutes, or 1560 seconds, at the flowerbed.

Consequently, the equation will be:

x/20 + x/12 + 900 = 1200

3x + 5x/60 = 300

8x = 60 * 300

8x = 18000

x =  18000/8

x = 22550

Therefore, using the equation we know that the flowerbed is 2250 feet away from the hive.

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Complete question:
A bee flies at 10 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 20 ​minutes, and then flies directly back to the hive at 8 feet per second. It is away from the hive for a total of 22 minutes.

What equation can you use to find the distance of the flowerbed from the​ hive?

The height, ab, is 6 cm

The volume of the pyramid is 100 cm3.

we know that

ABC is a right triangle and we know that

∠ACB=45°

AC=hypotenuse------ 6√2 cm

sin 45=AB/AC----- AB=AC*sin 45----> AB=6√2*√2/2----> AB=6 cm

AB=6 cm

we already know that the formula for getting the volume of a pyramid

volume of the pyramid=(1/3)*Area of the base*height

We will now Substitute all the values in the formula;

area of the base=50 cm²

height=6 cm

so

volume of the pyramid=(1/3)*50*6---->

1/3*300

300/3

1=00 cm³

volume=100 cm³

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Answer:

6, 100

Step-by-step explanation:

right on edge

The interquartile range of the given data set is 2.16.

The given data is 2.35, 1.56, 1.77, 2.45, 6.02, 4.38, 2.77, 5.23, 2.22 and 3.26.

The Interquartile Range (IQR) formula is a measure of the middle 50% of a data set. The smallest of all the measures of dispersion in statistics is called the Interquartile Range. The difference between the upper and lower quartile is known as the interquartile range.

Formula to find the interquartile range is Interquartile range = Upper Quartile - Lower Quartile =Q2=Q3-Q1

The  order of the given data is 1.56, 1.77, 2.22, 2.35, 2.45, 2.77, 3.26, 4.38, 5.23, 6.02.

Here,

Q1= 1/4 (n+1) = 11/4= 2.75

= 2.22

Q3 = 3/4 (n+1) = 8.25

= 4.38

Q2 =4.38-2.22

= 2.16

Therefore, the interquartile range of the given data set is 2.16.

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If X is a normally distributed random variable and X ~ N(μ, σ), then the z-score is:                              z = x−μ/ σ

The z-score indicates the number of standard deviations that the value x is above (right) or below (left) the mean μ. Values ​​of x greater than the mean have positive z values, and values ​​of x less than the mean have negative z values. The z-score of x is zero if x is equal to the mean.

The standard normal distribution is the normal distribution of standardized values ​​called z-scores. Z-scores are measured in units of standard deviation. For example, if the normal distribution has a mean of 5 and a standard deviation of 2, then the value 11 is 3 standard deviations above (or to the right of) the mean. Here's the calculation:

                      x = μ + (z)(σ)  

                         = 5 + (3)(2)

                         = 11

The standard normal distribution has zero mean and one standard deviation. The transformation

                                    z= x − μ/σ

gives the distribution Z ~ N(0, 1). The value x comes from a normal distribution with mean μ and standard deviation σ.

The next two videos explain what it means to have a "normal" distributed data set.

If X is a random variable and follows a normal distribution with mean µ and standard deviation σ, the rule of thumb states within 1 standard deviation of the mean.

About 95% of the x-values ​​lie between –2σ and +2σ of the mean µ (within two standard deviations of the mean).

About 99.7% of the x-values ​​lie between –3σ and +3σ of the mean μ (within 3 standard deviations of the mean) .

Almost all x-values ​​are within 3 standard deviations of the mean.

1) +1σ and -1σ have z-scores of +1 and -1 respectively.

2) +2σ and -2σ have Z-scores of +2 and -2 respectively.

3) +3σ and -3σ have Z-scores of +3 and -3 respectively.

The rule of thumb is also known as the 68-95-99.7 rule.

The exact value used to calculate the median; further decreasing the minimum value or increasing the maximum value will not change the median value. Therefore, the median does not use all the information in the data and is therefore shown to be less efficient than the mean or average, which uses all the values ​​in the data. To calculate the average, add the observations and divide by that number.

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Answer:

x=22.5 please mark me as brainlyiest

Step-by-step explanation:

2(x-3)=49

2x-6=49

2x=55

x=22.5

Answer: x=10   x=-4

Step-by-step explanation:

[tex](x-3)^2=49\\\\(x-3)=7^2[/tex]

Extract the square root of both parts of the equation:

[tex]\sqrt{(x-3)^2}=\sqrt{7^2} \\\\x-3=б7\\\\x-3=7\\x-3+3=7+3\\x=10\\\\x-3=-7\\x-3+3=-7+3\\x=-4[/tex]

Answer:

Step-by-step explanation:

pemdas - parenthesis , exponet, multiply, divide, add, subtract. your answer is 3.5

To get the slope, use the slope-intercept form and calculate the reciprocal of the slope of the given line .The slope of any line perpendicular to Y = 7x + 8 is -7.

The equation of any line perpendicular to Y = 7x + 8 is in the form of y = mx + b where m is the slope.

To get the slope, use the slope-intercept form and calculate the reciprocal of the slope of the given line.

The slope of the given line (Y = 7x + 8) is 7. Therefore, the slope of the line perpendicular to it is the reciprocal of 7, which is -7.

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Answer: 2x(x^-4)(x^-2)

Answer:

y= -9

Step-by-step explanation:

slope intercept form is y=mx+b

m is slope

b is y intercept

slope formula is y2-y1/x2-x1

-9-(-9)/-9-(1)

0/-10

0 is the slope

y=0x+b

-9=0(-9)+b

-9=b

hopes this helps

The congruence theorem that justifies the similar triangles of triangles EFH and GFH is given as follows:

D. AAS.

For the triangles EFH and GFH in this problem, we have that:

These three features are used to identify the congruence theorem as follows.

Then the congruence theorem that justifies the similar triangles of triangles EFH and GFH is the Angle-Angle-Side theorem, given by option D, as:

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337 were senior citizens.

What is the system of equations?

A system of equations, also known as an equation system or a set of simultaneous equations, is a finite set of equations for which common solutions are sought.

Here, we

Let

x = the number of adult tickets sold

y = the number of senior tickets sold

483 people paid admission => a total of 483 tickets were sold and

x + y = 483

the total receipts were $7548

24x + 12y = 7548

by solving the system of equations

x + y = 483....(1)

24x + 12y = 7548....(2)

From equation (1), we get

x = 483-y....(3)

Now, we put the value of x in equation (2) and we get

24(483 - y) +12y = 7548

11592 - 24y + 12y = 7548

12y = 4044

y = 337

Now, we put the value of y in equation (1) and we get

x = 483 - 337

x = 146

Hence, 337 were senior citizens.

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Answer:

The strongest correlation is 0.87. In general, a correlation is a measure of the strength and direction of a linear relationship between two variables. Correlation values range from -1 to 1, with -1 indicating a perfect negative linear relationship, 0 indicating no linear relationship, and 1 indicating a perfect positive linear relationship. Among the numbers you have provided, 0.87 is the only one that is greater than 0, indicating a positive linear relationship between the two variables. This means that as one variable increases, the other variable also tends to increase. This is the strongest possible positive linear relationship, making 0.87 the strongest correlation among the numbers you have provided.

Step-by-step explanation:

Answer:

he perimeter of the equilateral triangle is $3(x + 1) = 3x + 3$.

Step-by-step explanation:

The perimeter of the equilateral triangle is $3(x + 1)$ since the sides are all equal and there are three sides. The perimeter of the other triangle is $2x + x + 4x - 7$, which is also equal to $3(x + 1)$

The 6th term of the geometric sequence is -1/2.

Here we have to find the a6the term of the geometric sequence.

Data given:

The series = 512/243, -128/81, 32/27.....

The formula to find the nth term of the geometric sequence:

[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]

where [tex]a_{n}[/tex] = nth term of the sequence

a = first term of the sequence

r = common ratio

common ratio(r) = -128/ 81 ÷ 512/ 243

                       = -128/81 × 243/512

                       = -3/4

Now we have to find the 6th term of the series.

[tex]a_{6}[/tex] = 512/ 243 (-3/4[tex])^{6-1}[/tex]

   = 512/243 (-3/4[tex])^{5}[/tex]

  = 512/243 × 243/1024

  = -512/1024

  = -1/2

Therefore the 6th term is -1/2.

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Answer:

I have no idea sorry

Step-by-step explanation:

i'm in middle school

Answer:

17

Step-by-step explanation:

15 + 17 + 19= 51

The probability that they will each win a game = 0.24

Given,

The probability that Trevor will win the game p = is 0.6

The formula we will use for calculating Trevor losing the game

⇒ q = 1 - p

Now the probability of Trevor losing the game ⇒ q = 1 - 0.6

= 0.4

Now the probability that Brian wins = 0.4 when Trevor loses and the probability that Trevor wins = 0.6 when Brian loses the game.

Now the four possibilities that will decide the outcome for 2 ping pong games-

Total probability = 0.36 + 0.24 + 0.24 + 0.16

= 1

Therefore, the probability that they each win one of the games = is 0.24

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We can eliminate a variable by adding the two equations, doing that we will find the solution (4, 1.5)

Here we have the following system of equations:

-3x - 8y = -24

3x - 5y = 4.5

To eliminate a variable, we can simply add the two equations and the variable x will be eliminated, let's do that:

(-3x - 8y) + (3x - 5y) = -24 + 4.5

Grouping like terms we get:

(-3x + 3x) + (-8y - 5y) = -19.5

0 - 13y = -19.5

Now we can solve this for y:

y = -19.5/-13 = 19.5/13 = 1.5

To get the value of x, we need to replace the value of y in one of the equations:

-3x - 8*(1.5) = -24

-3x = -24 + 8*1.5

-3x = -12

x = -12/-3 = 4

The solution is (4, 1.5)

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The theorems used are:

First blank: side-angle-side theorem

Second blank: CPCTC

Third blank: 200 feet

Fourth blank: 1,700 feet.

Wen two triangles have a pair of included congruent angles and two pairs of corresponding congruent sides, then both triangles are congruent to each other by the side-angle-side theorem.

Furthermore, if two triangles are known to be congruent to each other, the CPCTC states that "corresponding parts of corresponding triangles are congruent". This means all angles and all sides that corresponds to each other are congruent.

Therefore:

Using the side-angle-side theorem it can be shown that the two triangles are congruent to each other.

Then using CPCTC , the length of the road from the intersection to the first turn would be 200 feet.

The total length of the tour would be = 2(200 + 300 + 350)

= 1,700 feet.

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Using, SAS it can be shown that the two triangles formed are congruent. Then using ,-CPCTC the length of the road from the intersection to the first turn can be found to be 200 feet. Thus, the total length of the tour is 1,700 feet.

The SAS Triangle Theorem indicates that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

By the use of the corresponding parts of congruent triangles are congruent (CPCTC) rule, we can state that the missing side is 200 feet. If that is the case, then the total distance traveled can be obtained by adding all the lengths of triangles:

=200 + 200 + 300 + 350 + 350 + 300

= 1,700 feet.

Hence, te total length of the tour is 1,700 feet.

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Answer:

Domain: [-3,100] if continuous. {x|x=-3,-2,0,1,4,100} if discrete.

Range: [0,100] if continuous. {y|y=0,10,19,77,100} if discrete.

Step-by-step explanation:

Answer: Neither.

Step-by-step explanation: I believe it's neither because I plotted the given points below and it gave me this for the result:

Hope this helps! :)

Answer:

[tex]f(x) = 32(3x-1)[/tex]

Step-by-step explanation:

I just plugged in values of x into the different functions provided this function check out. Also charge your computer