Is 2 an irrational number

Answer:

4

Step-by-step explanation:

2x5=10

5-1=4

2(4+1)=10

The pooled standard deviation will be True

The average range of all data points about their group mean is known as the pooled standard deviation (not the overall mean). It is the weighted average of the standard deviations for each group. Larger groups have a proportionately greater impact on the overall estimate because to the weighting.

Compare the ratio of the two sample standard deviations as a quick way to verify this. The ratio would be 1, or, in the event that the two are equal. However, we cannot anticipate the ratio to be exactly 1, as they are samples and as a result, there will be some mistake. A decent Rule of Thumb to apply is to see if the ratio falls between 0.5 and 2 when the sample sizes are nearly equal (granted, "nearly equal" is a bit imprecise, so frequently if sample sizes are small one requires they be equal). In other words, neither sample's standard deviation is greater than its counterpart.

Therefore, the pooled standard deviation will be True

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Answer:

AB = 142

Step-by-step explanation:

If M is the midpoint, then AM = MB

6x+5 = 7x -6

Subtract 6x from each side

6x-6x+5 = 7x-6x -6

5 = x-6

Add 6 to each side

5+6 = x-6+6

11=x

We want to find AB

AB = 6x+5+7x-6

AB = 13x -1

     = 13(11) -1

     =143-1

     = 142

According to the described way the volume of solid S is 156.25π.

Since the cross sections perpendicular to the x-axis and the base are semicircles, we know that the radius of each cross section is given by:

r = y = √(25 -\(x^{2}\) )  

where x is the distance from the center of the circle to the cross section, which lies along the x-axis.

The circle  \(x^{2}\)+ \(y^{2}\) = 25 has a radius of 5, and its center is at the origin (0,0). Thus, the farthest a cross section can be from the center of the circle is at x = 5 or x = -5.

To find the volume of the solid S, we need to integrate the area of each cross section over the range from x = -5 to x = 5. The area of each cross section is given by:

A = (1/2)πr^2

Substituting the expression for r above, we get:

A = (1/2)π(25 - x^2)

Integrating this expression over the range from x = -5 to x = 5 gives us:

V = ∫(-5)^5 (1/2)π(25 - x^2) dx

Using integration rules, we can evaluate this integral to get:

V = (1/2)π ∫(-5)^5 (25x - x^3) dx

V = (1/2)π [ (25/2)x^2 - (1/4)x^4 ]|_-5^5

V = (1/2)π [ (25/2)(5^2) - (1/4)(5^4) - (25/2)(-5^2) + (1/4)(-5^4) ]

V = (1/2)π [ 625/2 - 625/4 + 625/2 - 625/4 ]

V = (1/2)π (625/2)

V = (312.5/2)π

V = 156.25π

Therefore, the volume of solid S is 156.25π.

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Answer:

m = -4/3

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (-2,2) (1,-2)

We see the y decrease by 4 and the x increase by 3, so the slope is

m = -4/3

Answer:

The probability of this occurring is 1/7

Step-by-step explanation:

Okay, here is a probability question.

From the question, we can identify the following;

Total number of socks = 2 + 4 + 2 = 8 socks

Since we are not given the order in which the socks was worn, we can assume any order.

Let’s say the right leg socks was worn first.

From the question, the socks on the right leg is a brown one.

So now let’s calculate the probability of selecting a brown socks out of the mix

That would be ;

number of brown socks/ total number of socks = 4/8 = 1/2

Now, for the left foot, we are having white sock here.

Kindly recall that since we already have a sock on the right foot, we have 7 socks left to pick from.

Now we need the probability of picking a white sock from the total 7. That would be ; 2/7

So the probability of both action occurring is simply the product of both probabilities and that is ;

1/2 * 2/7 = 1/7

Answer:

.25

Step-by-step explanation:

hundredth's is the second place over so you look the the 3rd number. 4 or less it stays the same 5 or more you add one

To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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Answer:

y=mx+b

Step-by-step explanation:

b=1 (the point you start at - it's on the y-intercept

m=1/2

rise over run. rise/run

go up one, right 2

To find the point on the graph of $2y=\frac{f(2x)}{2}$, we can substitute $x=\frac{1}{2}$ and $y=\frac{f(2x)}{2}$ into the equation.

Given that $(9,7)$ is on the graph of $y=f(x)$, we can substitute $x=2$ and $y=7$ into the equation $2y=\frac{f(2x)}{2}$. Plugging in the values, we have: $2(7)=\frac{f(2\cdot 2)}{2}$. Simplifying the equation: $14=\frac{f(4)}{2}$. Multiplying both sides by $2$, we get: $28=f(4)$.  Therefore, the point on the graph of $2y=\frac{f(2x)}{2}$ is $(4,28)$. The sum of the coordinates of that point is $4+28=32$.

So, the sum of the coordinates of the point is $32$, where given that the point $(9,7)$ is on the graph of $y=f(x)$, there is one point that must be on the graph of $2y=\frac{f(2x)}2 2$.

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Answer:

c

Step-by-step explanation:

math

The area to the left of z1 is 0.0228 and the area to the left of z2 is 0.9772. Therefore, the area between z1 and z2 is:

0.9772 - 0.0228 = 0.9544

So approximately 95.44% of women have heights between 60 and 70 inches.

Given that the heights of college women are normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches, we can use the properties of the standard normal distribution to answer the following questions:

a) What percentages of women are taller than 65 inches?

Since the distribution is symmetric about the mean, we know that 50% of women are taller than 65 inches, and 50% are shorter than 65 inches.

b) What percentages of women are shorter than 65 inches?

As mentioned above, 50% of women are shorter than 65 inches.

c) What percentages of women are between 62.5 inches and 67.5 inches?

To answer this question, we need to find the area under the normal distribution curve between the z-scores corresponding to 62.5 and 67.5 inches, respectively. The z-scores can be calculated as follows:

z1 = (62.5 - 65) / 2.5 = -1
z2 = (67.5 - 65) / 2.5 = 0.8

Using a standard normal distribution table or calculator, we can find that the area to the left of z1 is 0.1587 and the area to the left of z2 is 0.7881. Therefore, the area between z1 and z2 is:

0.7881 - 0.1587 = 0.6294

So approximately 62.94% of women have heights between 62.5 and 67.5 inches.

d) What percentages of women are between 60 inches and 70 inches?

Using the same approach as in part c), we can calculate the z-scores for 60 and 70 inches:

z1 = (60 - 65) / 2.5 = -2
z2 = (70 - 65) / 2.5 = 2

The area to the left of z1 is 0.0228 and the area to the left of z2 is 0.9772. Therefore, the area between z1 and z2 is:

0.9772 - 0.0228 = 0.9544

So approximately 95.44% of women have heights between 60 and 70 inches.
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Answer:

-3

Step-by-step explanation:

To determine the time the power came back on, we need to determine how much time has passed since the power went out and the alarm clock reset where the power came back on at 17.79 hours or 17 hours and 47 minutes (17:47).

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Step-by-step explanation:

Well, since this is a 45, 45, 90 triangle, it means that the given side and y have the same length.

Y = 1.5sqrt(2)

this means that X, the hypotenuse is equal to 1.5sqrt(2)^2 + 1.5sqrt(2)^2 = X^2

X is equal to 2.44948974278

Answer:

Step-by-step explanation:

2) ∠A + ∠B = 146       {Exterior angle theorem}

5y + 3 + 4y + 8 = 146

5y + 4y + 3 + 8 = 146           {combine like terms}

         9y + 11 = 146

               9y = 146 -11

               9y = 135

                 y = 135/9

y = 15

3) m∠A = 5y + 3

              = 5*15 + 3

              = 75 + 3

∠A = 78

4) m∠B = 4y + 8

            = 4*15 + 8

            = 60 + 8

      m∠B = 68

5) m∠ACB + m∠A + m∠B = 180   {Angle sum property of triangle}

 m∠ACB  + 78 + 68 = 180

           m∠ACB + 146 = 180

                       m∠ACB = 180 - 146

                      m∠ACB = 34

Answer:

Brad has been on the team for 8 years. Apply that and that means that Anderson has been on the soccer team for 2 years.

Step-by-step explanation:

I dont know how to explain lol i made an equation and figured it out

Step-by-step explanation:

let x be the number of years that Zach has been on the soccer team and y the number of years Anderson has been on the soccer team.

So, reading our problem it seems that

x=5y-2

x+y=10

replacing x on the second formula we take that 5y-2+y=10

6y-2=10

6y=12

y=2

so x=5y-2=5*2-2=10-2=8

Parallel lines are two straight lines that never cross. For this to happen, the lines have to have the same slope.

In this case, the equation given is in what's called "slope-intersect" form. The general form of the slope intercept formula is y=mx + b where m is the slope of the line and b is the point on the Y-axis where the line crosses.

The equation given is y=5x+3 and since the 5 is in the place of m from the general equation, 5 is the slope. Since parallel lines have the same slope, 5 is the answer.

Slope-Intercept Form:

When we're given a linear equation we can immediately see if it's in the slope-intercept form if it follows the format  y=mx+b. As long as y does not have a coefficient the slope and y-intercept are the values of m and b.

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Answer:

Yes you are correct :)

Step-by-step explanation:

Used a graphing calculator

Answer:

h > 24

Step-by-step explanation:

h/3 > 8

so basially you move the number three from the left side to the right side

so from division to multiplication

h > 8 x 3
h > 24
Solved !

Hope it helped ! Have a nice day !

The slope ratio for a line that makes an angle of 30 with the positive direction of the x-axis is 1:√3

The slope of a line is nothing but the change of the line in the y-coordinate concerning the change in the x-axis. So the slope is simply nothing but a ratio of change in the y-axis to change in the x-axis which is also called slope ratio.

m = change in y / change in x

tan 30= 1/√3 = change in y / change in x

tan 30= 1: √3

So the ratio of an angle of 30-degree slope will be 1:√3

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Answer:

12 minutes till 88 liters

Step-by-step explanation:

Answer:

When the diameter is known, the formula is Radius = Diameter/ 2.

When the circumference is known, the formula is Radius = Circumference/2π.

When the area is known, the formula for the radius is Radius = ⎷ (Area of the circle/π).

Answer:

$75.6

Explanation:

If the original cost was $70 and it was marked up 20%, the price after this is calculated as:

$70 + $70(0.2) = $70 + $14 = $84

Where $70(0.2) = $14 is the amount added to the original when it is marked up 20%.

Then, it was discounted 10%, we get that the selling price is

$84 - $84(0.1) = $84 - $8.4 = $75.6

Where $84(0.1) = $8.4 is the discount made on the initial price.

Therefore, the answer is $75.6

Answer:

$16 dollars because I got it right

Answer:

138

Step-by-step explanation:

$ 11.50 x 12 = 138

Answer:

its A 7.51

Step-by-step explanation:

The intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

To show that a1 ≤ a2 ≤ ... ≤ an ≤ ..., we need to use the fact that the sequence of intervals is nested, meaning that each interval is contained within the next one.

First, we know that I1 contains I2, so every point in I2 is also in I1. That means that a1 ≤ a2 and b1 ≥ b2.

Now consider I2 and I3. Again, every point in I3 is also in I2, so a2 ≤ a3 and b2 ≥ b3.

We can continue this process for all the intervals in the sequence, until we reach In. So we have:

a1 ≤ a2 ≤ ... ≤ an-1 ≤ an

and

b1 ≥ b2 ≥ ... ≥ bn-1 ≥ bn

This shows that the endpoints of the intervals are ordered in the same way.

Given that I₁ ⊇ I₂ ⊇ ... In ⊇ ... is a nested sequence of intervals and In = [an; bn], we can show that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... as follows:

Since the intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

Continuing this pattern for all intervals in the sequence, we can conclude that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... .

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