1/7-3(3/7n-2/7) in simplest form

The theoretical probability of rolling each number ([tex]1[/tex] through [tex]6[/tex]) on a six-sided number cube is [tex]\(\frac{1}{6}\)[/tex]. The probability of rolling an even number ([tex]2, 4,[/tex] or [tex]6[/tex]) is [tex]\(\frac{3}{6}\)[/tex] or [tex]\(\frac{1}{2}\).[/tex]

Since there are six possible outcomes when rolling a six-sided number cube and each outcome is equally likely, the probability of rolling any specific number is calculated by dividing the number of favorable outcomes (which is 1 for each specific number) by the total number of possible outcomes (which is [tex]6[/tex]). Therefore, the theoretical probability [tex]\(P\)[/tex] for each roll is:

[tex]\[ P(1) = P(2) = P(3) = P(4) = P(5) = P(6) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{6} \][/tex]

To find the probability of rolling an even number, we consider the number of even outcomes ([tex]2, 4[/tex], and [tex]6[/tex]) and divide by the total number of possible outcomes:

[tex]\[ P(\text{even}) = P(2) + P(4) + P(6) = \frac{1}{6} + \frac{1}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2} \][/tex]

The experimental probability is calculated based on the results of the [tex]25[/tex]rolls. For each number, the experimental probability is the number of times that number was rolled divided by the total number of rolls ([tex]25[/tex]). For example, if the number [tex]1[/tex] was rolled [tex]4[/tex] times, the experimental probability of rolling a [tex]1[/tex] would be [tex]\(\frac{4}{25}\).[/tex]

The probability of rolling an even number based on observed frequencies would be the sum of the experimental probabilities of rolling a [tex]2, 4[/tex], or [tex]6[/tex]. If the number of rolls for each even number was [tex]\(x\), \(y\),[/tex] and [tex]\(z\)[/tex]respectively, then the experimental probability of rolling an even number would be [tex]\(\frac{x + y + z}{25}\).[/tex]

The experimental probability may differ from the theoretical probability due to random variation and the finite number of trials. In a small number of trials, the observed frequencies may not match the theoretical probabilities exactly. However, as the number of trials increases, the experimental probabilities should converge to the theoretical probabilities. This is due to the law of large numbers, which states that the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.

1) The precise difference is 158.268.

2) The difference when rounded to the nearest whole number is 159.

3) the difference using front-end rounding is 150.

1) To find the difference, subtract the smaller number from the larger number:

[tex]217.64 - 59.372 = 158.268[/tex]

2) First, let's round each of the numbers to the nearest whole number.

217.64 rounds to 218.

59.372 rounds to 59.

Now, subtract these rounded numbers:

[tex]218 - 59 = 159[/tex]

3) Front-end rounding means rounding the numbers based on the left-most digit (or most significant digit). For simplicity, we will keep the first digit and change the others to zeros.

217.64 can be rounded to 200.

59.372 can be rounded to 50.

Now, subtract these rounded numbers:

[tex]200 - 50 = 150[/tex]

In year 2000, the population was 15,000.

In year 2001, the population was 16,250.

In year 2002, the population was 17,500.

The population growth from year 2000 to year 2001 was (16,250-15,000) = 1,250.

The population growth from year 2001 to year 2002 was (17,500-16,250) = 1,250.

So the slope of the line would be m = 1250.

And y-intercept would be the initial population i.e. b = 15,000.

So the equation of line is y = 1250x + 15000.

Hence, n years after 2000, the population would be P = 1250n + 15000.

Answer:

The correct option is D.

Step-by-step explanation:

The correlation coefficient represent the relationship between two variables. It is denoted by r and the value of r lies from -1 to 1.

If r=-1 and close to -1, then it represents strong negative correlation.

If -1<r<0 and close to -0.5, then it represents weak negative correlation.

If r=0 and close to 0, then it represents no correlation.

If 0<r<1 and close to 0.5, then it represents weak positive correlation.

If r=1 and close to 1, then it represents strong positive correlation.

From the given graph it is clear than the data represents the strong positive correlation because the data set lie close to the positive strait line. So, the value of r is near to 1.

Option 1, 2 represent the negative correlation and option 3 represents weak positive correlation.

Since 0.95 close to 1, therefore it represents strong positive correlation.

Hence option D is correct.

Answer:7.20

Step-by-step explanation:

The correct cost function for Vanessa’s clothing store per month is,

C = 7.20n + 825

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Vanessa is opening a clothing store. She plans to start by selling gym shorts.

Here, It costs her $4 for each pair of shorts, $3 for ink per shorts, and $0.20 a bag.

And, Vanessa also spends $750 on rent, $50 on electricity, and $25 on advertising each month.

Now, Let us assume that, n represent the number of things he sell.

Hence, We can formulate;

The correct cost function for Vanessa’s clothing store per month is,

C = (4 + 3 +  0.20)n + (750 + 50 + 25)

C = 7.20n + 825

Thus, The correct cost function for Vanessa’s clothing store per month is,

C = 7.20n + 825

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The answer is to this is B. 0

The above answer will be calculated as -

The seating capacity of the class that follows an AP is 5180.

An arithmetic progression(AP) is a sequence or series of numbers such that the difference of any two successive members is a constant. The first term is a, the common difference is d, n is number of terms.

For the given situation,

There are 10 seats in the first row, 13 seats in the second row, 16 seats in the third row and so on. There are 56 rows.

This statement follows as Arithmetic Progression.

The series is 10,13,16,.....

Here [tex]a=10, d= 3[/tex]

Number of rows, [tex]n = 56[/tex]

The formula of sum of n terms of an AP is

[tex]S_{n} =\frac{n}{2} [2a+(n-1)d][/tex]

On substituting the above values,

⇒ [tex]S_{56} =\frac{56}{2} [2(10)+(56-1)3][/tex]

⇒ [tex]S_{56} =28 [20+(55)3][/tex]

⇒ [tex]S_{56} =28 [185][/tex]

⇒ [tex]S_{56} =5180[/tex]

Hence we can conclude that the seating capacity of the class that follows an AP is 5180.

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Answer:

Step-by-step explanation:

tour answer would me a or 1:2

The answer to the above question can be explained as under -

Here, we need to convert large units into smaller units of same class i.e. to convert liters into milliliters.

We know that,

1 liter = 1000 milliliters

So, 2 liter of soda will have -

2 X 1 liter = 2 X 1000 milliliters

2 liters of Soda = 2,000 milliliters

Thus, the correct option will be = D) 2,000 ml

Answer: 3x^3-7x^2+5=7x^4+2x Is correct on edg

Step-by-step explanation:

True , Therefore, there are only three polygons with regular tessellations.

A semi-regular tessellation is a tiling of the plane by two or more regular polygons in such a way that every vertex has the same configuration of polygons in the same order. In other words, at every vertex, the same set of regular polygons meet in the same order.

Unlike regular tessellations, where only one type of regular polygon is used, semi-regular tessellations can use different regular polygons. However, the regular polygons used must have the same number of sides meeting at each vertex. For example, a semi-regular tessellation might use triangles and squares, with three triangles and one square meeting at each vertex.

Given data ,

There are actually infinitely many regular polygons that can make a regular tessellation. In fact, any regular polygon can be used to create a regular tessellation of the plane.

The number of polygons meeting at each vertex depends on the angle of the polygon, which is determined by the number of sides.

Only three regular polygons(shapes with all sides and angles equal) can form a tessellation by themselves—triangles, squares, and hexagons.

Hence , Equilateral triangles, squares and regular hexagons are the only regular polygons that will tessellate.

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[tex] |\Omega|=10\\ [/tex]

3a

[tex] |A|=4\\\\P(A)=\dfrac{4}{10}=\dfrac{2}{5}=40\% [/tex]

3b

[tex] |A|=3\\\\P(A)=\dfrac{3}{10}=30\% [/tex]

Answer:

a

Step-by-step explanation:

its a

The x-value is -b/(2a) = -8/(2·4) = -1.

The corresponding y-value is ...

... 4(-1)² +8(-1) -8 = 4 -8 -8 = -12

The y-value of the vertex is -12.

Answer:

The y-value of the vertex is [tex]-12[/tex]

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

[tex]f(x)=a(x-h)^{2}+k[/tex]

where

(h,k) is the vertex of the parabola

In this problem we have

[tex]f(x)=4x^{2}+8x-8[/tex] -----> this a vertical parabola open upward

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]f(x)+8=4x^{2}+8x[/tex]

Factor the leading coefficient

[tex]f(x)+8=4(x^{2}+2x)[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side

[tex]f(x)+8+4=4(x^{2}+2x+1)[/tex]

[tex]f(x)+12=4(x^{2}+2x+1)[/tex]

Rewrite as perfect squares

[tex]f(x)+12=4(x+1)^{2}[/tex]

[tex]f(x)=4(x+1)^{2}-12[/tex]

The vertex is the point [tex](-1,-12)[/tex]

The y-value of the vertex is [tex]-12[/tex]

Answer:C

Step-by-step explanation:

Original size of the picture

A regular  quadrilateral prism has 12 edges. It is given perimeter of the base 32 cm. Length of each edge of base will be 32÷4=8 cm. The 4 edges at the top will also have the same number of edges that is 4 with measure 8cm each.

Given: The height of the prism is 2 times greater than the length of the base edge.Height of prism = 2(8)= 16cm. Number of edges  with measure 16 cm is 4.

Sum of all the 12 edges= 8+8+8+8+16+16+16+16+8+8+8+8=128 cm.

A) The event is "tossing a number cube once"

The sample space of this event is {1,2,3,4,5,6}.

The expected value of this event is  

[tex]1\times \frac{1}{6}+2\times \frac{1}{6}+3\times \frac{1}{6}+4\times \frac{1}{6}+5\times \frac{1}{6}+6\times \frac{1}{6}\\ \\ =\frac{1}{6}+\frac{1}{3}+\frac{1}{2}+\frac{2}{3}+\frac{5}{6}+1\\ \\ =\frac{7}{2} = 3.5[/tex]

Since 3.5 is not in the sample space of the event. Therefore, option (A) is not correct.

(B) The event is "Flipping a coin"

Sample space of this event is {HH,TT,HT,TH}

Since sample space of this event is not numbers, therefore, this cannot be the correct option either.

(C) The event is, "Randomly picking a number between 1 and 9, inclusive."

The sample space of this event is {1,2,3,4,5,6,7,8,9}.

Expected value of this event is [tex]\frac{1}{9}(1+2+3+4+5+6+7+8+9) = \frac{1}{9}(45) = 5[/tex]

Since 5 is the expected value and it is present in the sample space for this event. Therefore, option (C) is a correct choice.

(D) The sample is "Randomly picking a number between one and ten, inclusive".

The sample space of this event is {1,2,3,4,5,6,7,8,9,10}.

Therefore, expected value of the event is [tex]\frac{1}{10}(1+2+3+4+5+6+7+8+9+10) = \frac{1}{10}(55)=5.5[/tex]

Since 5.5 is not present in the sample space of this event. Therefore, option (D) is not correct either.

Hence, the correct choice is option (C).

Answer:  0.04

Step-by-step explanation:

Given : Sample size : n= 150

No. of females in the sample  : x= 90

Proportion of females = [tex]\hat{p}=\dfrac{x}{n}=\dfrac{90}{150}=0.6[/tex]

Standard error of proportions :

[tex]SE=\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex] , where [tex]\hat{p}[/tex] = sample proportion and n= sample size .

Substitute the corresponding values , we get

[tex]SE=\sqrt{\dfrac{0.6(1-0.6)}{150}}[/tex]

[tex]SE=\sqrt{\dfrac{0.6 (0.4)}{150}}[/tex]

[tex]SE=\sqrt{0.0016}=0.04[/tex]

Hence, the standard error of the proportion is 0.04 .

The standard error of the proportion is 0.04

Since the random sample is 150 people and the number of female in the sample is 90 people

First step is to determine the sample proportion (p)

[tex]Sample proportion (p) =90/150[/tex]

[tex]Sample proportion (p) =0.6[/tex]

Now let determine the standard error of the proportion  using this formula

[tex]Standard error= \sqrt{p(-p)/n}[/tex]

Where:

[tex]p=Sample proportion (p)=0.6[/tex]

[tex]p=(1-0.6)= 0.4[/tex]

[tex]n=150[/tex]

Let plug in the formula

Standard error=\sqrt{(0.6) (0.4)/150}[tex]Standard error=\sqrt{(0.6) (0.4)/150}[/tex]

[tex]Standard error= \sqrt{0.24/150}[/tex]

[tex]Standard error= \sqrt{0.0016}[/tex]

[tex]Standard error= 0.04[/tex]

Inconclusion The standard error of the proportion is 0.04

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