35 Points!!!! 7 2/5= 2/3x −4 1/2
Enter your answer as a mixed number in simplest form in the box.

The probability that headway is within 1 standard deviation of the mean value is 0.890.

What is mean value?

By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined.

The mean of a discrete probability distribution of a random variable X is equal to the sum over all possible values weighted by the likelihood of each value. To calculate the mean, one must multiply each potential value of X by its probability P(x), then add all of these products.

Given mean value is P( 0.995 ≤ x ≤ 1.445) = F(1.445) - F(0.995).

The cdf for the distribution is

[tex]F(x)=\left \{ {{1 -\frac{1}{x^6} ,x > 1} \atop {0,x\le 1}} \right.[/tex]

Now calculate the value of F(1.445) and F(0.995).

F(1.445) = 1 - (1/(1.445)⁶)

F(0.995) = 0

Now putting the value of F(1.445) and F(0.995) in  P( 0.995 ≤ x ≤ 1.445) = F(1.445) - F(0.995):

P( 0.995 ≤ x ≤ 1.445)

=1 - (1/(1.445)⁶)  - 0

=0.890

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In the scale drawing of the 2 pentagons the value of x is 3

To find the value of x in the pentagon, the scale factor is first determined

The scale factor is solved for as follows

AB * r = PQ

in the figure AB = 5 and PQ =2.5

5r = 2.5

r = 2.5 / 5

r = 0.5

Using the scale factor r = 0.5

6 * r = x

6 * 0.5 = x

3 = x

x = 3

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According to the empirical law of statistics, 99.7% of the males are between 54.5" and 81.5" tall.

The 68-95-99.7 rule, also known as the empirical rule, indicates where most of the values in a normal distribution are distributed: The majority of values—about 68%—fall within the range of the mean. The average value is within two standard deviations for about 95% of the data. Almost all values, 99.7% of them, fall within a 3 standard deviation range.

Here,

mean=68 inch

standard deviation=4.5 inch

The first part of the empirical rule states that 68% of the data values will fall within 1 standard deviation of the mean. To calculate "within 1 standard deviation," you need to subtract 1 standard deviation from the mean, then add 1 standard deviation to the mean. That will give you the range for 68% of the data values.

68−4.5=63.5

68+4.5=72.5

The range of numbers is 63.5 to 72.5

The second part of the empirical rule states that 95% of the data values will fall within 2 standard deviations of the mean. To calculate "within 2 standard deviations," you need to subtract 2 standard deviations from the mean, then add 2 standard deviations to the mean. That will give you the range for 95% of the data values.

68−2⋅4.5=59

68+2⋅4.5=77

The range of numbers is 59 to 77

Finally, the last part of the empirical rule states that 99.7% of the data values will fall within 3 standard deviations of the mean. To calculate "within 3 standard deviations," you need to subtract 3 standard deviations from the mean, then add 3 standard deviations to the mean. That will give you the range for 99.7% of the data values.

68−3⋅4.5=54.5

68+3⋅4.5=81.5

The range of numbers is 54.5 to 81.5

99.7% of the boys are between 54. 5 and 81. 5 inches tall using the empirical rule of statistics.

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26% of 78

= 26*(1/100)*78

=(26/100)*78

=0.26*78 = 20.28

so, the required answer is 20.28.

what is percentage?

answer: The quantity of something represented as if it were a portion of a sum total of 100; a portion or share of a whole.

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If Benjamin invested $20,000 in an account paying an interest rate of 7&5/8 % compounded monthly. The amount of money that Kehlani have in her account than Benjamin is: $322.83.

Using this formula to find the compounded amount

A = P(1+r/n)^nt

Where

A = Amount

r =Interest rate.

n =Number of years

P =Principal

Benjamin

P = $20,000

r = 7 5/8% = 7.625% = 0.07625

n = 12 months

t = 10 years

Hence,

A = 20,000 (1+0.07625/12)^12× 10

A = 20,000 (1+0.006354)^120

A = 20,000 (1.006354)^120

A = $42,768.42

Kehlani

P = $20,000

r = 7 3/4% = 7.75= 0.0775

n = 4 months

t = 10 years

Hence,

A = 20,000 (1+0.0775/4)^4× 10

A = 20,000 (1+0.019375)^40

A = 20,000 (1.019375)^40

A = $43,091.25

Difference:

Difference = $43,091.25 - $42,768.42

Difference = $322.83

Therefore the amount of money is $322.83.

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Answer:322

Step-by-step explanation:

If you are told 20% of people prefer all three forms of recreation is 60 when 60% of all college professors enjoy tennis, 65% enjoy bridge.

Given that,

Assume that 60% of all college professors enjoy tennis, 65% enjoy bridge, 50% enjoy chess, and 45% enjoy any certain pair of recreational activities.

We have to find if you are told 20% of people prefer all three forms of recreation, should you be suspicious.

We know that,

Let the total professors be  =100

n(tennis) = 60

n( bridege) = 65

n( chess)= 50

n( T U B) = 45, n(BU C) = 45, n(T UC)=45

n( T UBUC)= n(T) + n(B) + n(C) - n( T U B) - n( BU C) - n(TUC) + n(T∩B∩C)

100 = 60 + 65 + 50 - 45-45-45 +n(T∩B∩C)

n(T∩B∩C)=60

Therefore, If you are told 20% of people prefer all three forms of recreation is 60 when 60% of all college professors enjoy tennis, 65% enjoy bridge.

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The highest score is 12794706708

What is mean ?

The average of a set of data is referred to as the mean in statistics and arithmetic. The simple arithmetic mean, geometric mean, and harmonic mean are some of the methods that can be used to calculate the mean. The basic arithmetic mean involves adding the numbers together and dividing the result by the number of observations.

At first (remaining + top player) /888 = 14514514

So remaining + top = 12888888432

Now after removing top

Remaining/777 = 121212

Remaining = 94181724

So top = 12888888432 - 94181724

           = 12794706708

12794706708 is the score of the top player

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The likelihood that an event will occur—is determined. The most basic illustration is a coin toss. There are only two outcomes when you flip a coin: either it comes up heads or tails.

Here,

If the first die is red and the second one is green, then the sample space S is the following:

S=

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2, 1), (2,2), (2,3), (2,4), (2,5), (2,6), (3, 1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5, 1), (5,2), (5,3), (5,4), (5,5), (5,6), (6, 1), (6, 2), (6,3), (6,4), (6,5), (6,6)

Hence n(S)=36.

Let's list the losing combinations:

E={(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (2, 1),

(2, 3), (2, 5), (4, 1), (4, 3), (4, 5), (6, 1), (6, 3), (6,5)}

n(E)=15

There are 36 total possiblities.

Out of which, winning probability is 21.

=21/36

=7/12

Given that the winning combination is 21 and the total combination is 36, the chance of rolling a winning combination is 7/12.

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Angles 1 and 2 are neighboring, hence the fourth choice is accurate. Angles 1 and 2 are adjacent.

The term "Angle" refers to the separation between line segments or rays that converge at a single point.

The following may be said about angles 1 & 2:

In a line that proceeds from left to right, there is a ray in the middle that forms a right angle, a second ray between the two right angles, and one light that labels both the left angle and the right angle.

We can draw just as in the image.

Angles 1 and 2 are neighboring because they share a vertex, as seen in the image.

Angle 2 equals 90 degrees

Angle 1 equals 45 degrees

Angles 1 and 2 are adjacent, so option 4 is correct because it describes the relationship between them.

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Answers:

Ratios equivalent to 1/2 are...

Ratios equivalent to 3/9 are...

Ratios equivalent to 5/7 are...

===============================================

Explanation:

Let's see if 2/6 is equivalent to 1/2. For now, let's assume they are equal fractions. If so, then,

2/6 = 1/2

2*2 = 6*1 ... cross multiplying

4 = 6

The last equation is of course false, which then causes a domino effect to make the first equation false as well. This means 2/6 is not equivalent to 1/2.

You can use a calculator to find that

Which is another way to see how the fractions aren't the same.

----------------

Let's check to see if 2/6 is equivalent to 3/9.

2/6 = 3/9

2*9 = 6*3 ... cross multiplying

18 = 18

We get the same thing on both sides, which means the third equation is true. By extension, the first equation is true as well. We have shown that 2/6 and 3/9 are equivalent.

Take note how both of those fractions reduce to 1/3, which is another way to see how they are equivalent.

Yet another way is to use a calculator to find that

Both approximate decimal values involve '3's going on forever.

Apply any of the methods discussed to check the other values, so you can properly sort each ratio mentioned. Let me know if you have any questions.

Answer:

Step-by-step explanation:

false true true false

Answer:

false true true and false

Step-by-step explanation:

The equation to determine the number of players is (x-y)/z and there are 11 players in total.

Given: Lacrosse players raised $1581.75 to attend a tournament. They allocated $968.50 for the bus rental and $55.75 for each player's meals.

Let,

x = amount raised to attend a tournament.

y = amount allocated for bus rental

z = amount for each player's meals

Number of players = (x-y)/z

                               = (1581.75-968.50)/55.75

                               = 613.25/55.75

                               = 11

Therefore, the equation to determine the number of players is (x-y)/z and there are 11 players in total.

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The exponential equation that models the population of the bacteria is:

y = 5*(7)^x

The general exponential equation is of the form:

y = A*(b)^x

Where A is the initial value, b is the base, and x is the variable.

Initially, Zach counted 5 bacteria, then:

A = 5

And we know that after one hour, Zach saw 35 bacteria, then we can write the equation:

35 = 5*(b)^1

35 = 5*b

35/5  =b

7 = b

Then the exponential equation is:

y = 5*(7)^x

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Part a: All the students in a row = 36!.

Part b: 7 of the students in a row; 36 x 35 x 34 x 33 x 32 x 31 x 30.

Part c: women on the left = 20! x 16!

For the stated question-

The class contains-

Part a: all the students in a row.

Number of ways = 36!

Part b: 7 of the students in a row.

Number of ways = 36 x 35 x 34 x 33 x 32 x 31 x 30

Part c: All the students in a row if all the women are on the left and all the men are on the right.

women on the left = 20! x 16!

Thus, the number of ways in which all the students in a row if all the women are on the left and all the men are on the right is; 20! x 16!.

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Answer:

B. 100

Step-by-step explanation:

The lower extreme is the number in line with the left most dot.

15.87 % percent of batteries have lifetimes more than 561 days.

Given:

battery lifetime is normally distributed for large samples. the mean lifetime is 500 days and the standard deviation is 61 days.

μ = 500

σ = 61

we know that

z = X - μ / σ

z score :

A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.

Given X = 561 days

substitute

z = 561 - 500 / 61

= 61 / 61

z = 1

At z = 1 p value is 0.8413

1 - 0.8413 = 0.1587

= 0.1587 * 100 %

= 15.87 %

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The true statements regarding the linear function are given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the coefficients of the function are given as follows:

In this problem, the function crosses the y-axis at the origin, hence the intercept is given as follows:

b = 0.

When x increases by one, y increases by 2, hence the slope is of:

m = 2.

Considering the slope, it means that the ratio of the legs of the right triangle with it's hypotenuse along the line is of 2.

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a) The expected value for distribution A is equal to 1 and expected value for distribution B is equal to 3. b) The value of standard deviation of two distributions is same. c)  A is less than the expected value for the distribution B.

The calculation for expected value of distribution of A is given as,

E(X) = ∑[tex]^{n}[/tex][tex]_{i=1}[/tex]= [tex]X_{i}[/tex]. P (X=x)

       =0⋅ (0.50 )+1⋅(0.20)+....+4⋅0.05=1

E(X) = ∑i=1nXi.P(X=x)=0⋅(0.50)+1⋅(0.20)+....+4⋅(0.05)=1

The calculation for expected value of distribution of B is given as,

E(X)=n∑i=1 Xi.P(X=x)

      =0⋅(0.05)+1⋅(0.1)+....+4⋅(0.50)=3

E(X)=∑i=1nXi.P(X=x)=0⋅(0.05)+1⋅(0.10)+....+4⋅(0.50)

     =3

Therefore, the expected value for distribution A is equal to 1 and expected value for distribution B is equal to 3.

(b) The formula for standard deviation is given as,

σ=√E(X2)−E(X))2

The calculation for the E(X2) of distribution A is given as,

E(X2)=n∑i=1 X2i⋅P(X=x)

        =02⋅(0.50)+12⋅(0.20)2+.....+42⋅(0.05)=2.5

The calculation for the E(X2) of distribution B is given as,

E(X2)=n∑i=1 X2i⋅P(X=x)

        =02⋅ 0.05)+12⋅(0.10)+......+42⋅(0.50)

        =10.5

E(X2)=∑i=1nXi2⋅P(X=x)=02⋅(0.05)+12⋅(0.10)2+......+42⋅(0.50)

       =10.5

The value of standard deviation for the distribution A is given as,

σA=√2.5−12

   =1.225

The value of standard deviation for the distribution B is given as,

σB=√10.5−32

   = 1.225

Therefore, the value of standard deviation of two distributions is same.

(c) The expected value for distribution A is less than the expected value for the distribution B. The standard deviation is same for both distributions; the spread between both the distributions is same. Therefore, the distribution B is better than distribution A.

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The graph shows a negative correlation, and it is a non-linear model.

What is positive and negative correlation?

When two variables behave in unison, rising or falling in lockstep with one another, there is a positive correlation. When two variables move in opposition to one another—that is, when one rises, the other falls—this is known as a negative correlation.

As given data from the graph, y values goes decrease with increasing x values.

So, we can conclude that the graph shows a negative correlation.

And, the given data in the graph are not linear.

Hence, the graph shows a negative correlation, and it is a non-linear model.

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Answer:

The graph shows a negative correlation, and it is a non-linear model.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Let x be that number.

(x^2) - 40 = 3x

x^2 - 40 = 3x

x*2-3x-40=0

(x-5)(x+8)=0

x=5

The null hypothesis must be rejected as there is enough evidence that the diameter differs from 0.5 inches.

Given values are

The population mean is  0.5 inches

The Null hypothesis is  : H₀ : μ = 0.5 inches

The Alternative hypothesis is  given by Hₐ : μ ≠ 0.5 inches

Now let us consider the parameter given:

sample size is  n =  15  

test statistics is  t =  1.66

The level of significance : α = 0.05

The degree of freedom: df = n-1 = 15 -1 =14

Calculating the critical value : [tex]t_\frac{\alpha}{2} ,df[/tex] = 2.145

We are using the critical value of [tex]t_\frac{\alpha}{2}[/tex] as the test is one-tailed .

Comparing the value of  t and [tex]t_\frac{\alpha}{2}[/tex] we can see that : [tex]t < t_\frac{\alpha}{2}[/tex]

Hence the null hypothesis can be rejected.

Given that the value of t does not fall within the range covered by (i.e., the range from -2.145 to the bottom of the normal distribution curve), we are unable to reject the null hypothesis.

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The value of u that completes the ordered pairs is -9

From the question, the points are given as

(9, u) and (10, -1)

Slope = 8

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (9, u) and (10, -1)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (9, u) and (10, -1)

Substitute the known values in the above equation

So, we have the following equation

8 = (u + 1)/(9 - 10)

Evaluate

u + 1 = -8

So, we have

u = -9

Hence, the value of u is -9

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The room is 10 ft by 12 ft

The area of the room = 120 sq ft

1 yard= 3 feet

1 square yard=9 sq feet

The area of the room = 120 sq ft or 120/9=13.33 sq yards

Answer: 13.33 sq yards

Answer:

it is linear

Step-by-step explanation:

if you add x on both sides, you can get rid of the -x on the left side, and you are left with a linear equation in slope intercept form

y=7/3x

Answer:

Step-by-step explanation:

rawr u fel me

The revised values of the mean and standard deviation are respectively; 154 cm and 5 cm

Let us assume that the number of Patients is denoted as P. We are given;

Mean = 156 cm

We know that mean here is gotten from the formula;

Mean = Total height/number of patients

Thus;

Total Height = 156P  cm

We are told that each height was measured 2 cm more. Thus;

Total height reduction = 2P cm

Thus;

Actual Total Height = 156P - 2P = 154P cm

Mean = 154P/P  = 154  cm

Therefore, as each reading and mean both have shifted by 2 then Standard deviation will remain same as 5cm

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Answer:

6

Step-by-step explanation:

8 * (1.0 - .25) = 6

Answer: 6

Step-by-step explanation: 8 - 4 is equivalent to 8 - 50%, cut 4 in half which gives 2, 2 is 25% of 8, so 8 - 2 = 6

The given study is an example of longitudinal developmental design.

Longitudinal developmental research design  analyzes progress by observing or measuring a group of people over time. As a consequence, it assesses changes in behavior according  to age over time by examining one group of participants of about the same age.

The same people's behavior is examined over time using longitudinal research designs. For instance, using our example of examining the relationship between intellect and aging, a scientist would carry out a longitudinal study to see whether 20-year-olds lose IQ as they get older.

Hence we get the required answer.

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Answer:

y = x + 5.25

Step-by-step explanation:

y - 8.25 = (x - 3)

y - 8.25 = x - 3

y = x + 5.25

Could you please give me brainliest for this? Thank you!

Answer:

y = x + 5.25

Step-by-step explanation:

y - 8.25 = x - 3    Add 8.25 to both sides of the equation

y = x + 5.25