Which graph shows the solution to the given system of inequalities? [y<6x+1 y<-3.2x-4

Solution :

Given information :

A sample of n = 10 adults

The mean failure was 24 and the standard deviation was 3.2

a). The formula to calculate the 95% confidence interval is given by :

[tex]$\overline x \pm t_{\alpha/2,-1} \times \frac{s}{\sqrt n}$[/tex]

Here, [tex]$t_{\alpha/2,n-1} = t_{0.05/2,10-1}$[/tex]

                       = 2.145

Substitute the values

[tex]$24 \pm 2.145 \times \frac{3.2}{\sqrt {10}}$[/tex]

(26.17, 21.83)

When the [tex]\text{sampling of the same size}[/tex] is repeated from the [tex]\text{population}[/tex] [tex]n[/tex] infinite number of [tex]\text{times}[/tex], and the [tex]\text{confidence intervals}[/tex] are constructed, then [tex]95\%[/tex] of them contains the [tex]\text{true value of the population mean}[/tex], μ in between [tex](26.17, 21.83)[/tex]

b). The formula to calculate 95% prediction interval is given by :

    [tex]$\overline x \pm t_{\alpha/2,-1} \times s \sqrt{1+\frac{1}{n}}$[/tex]

   [tex]$24 \pm 2.145 \times 3.2 \sqrt{1+\frac{1}{10}}$[/tex]

   (31.13, 16.87)

Answer:

135.7 yd²

Step-by-step explanation:

Surface area of the cone,

πr²+πrl

= π×3²+π×11.4×3

= 43.2π

= 135.7 yd² (rounded to the nearest tenth)

Answer:

the probability of taking a clear picture of a California candor is .24

Answer:

a

Step-by-step explanation:

B isn't a geometric sequence as it's last term doesn't follow the rule

C is an arithmetic sequence

D is an arithmetic sequence too

Answer:

4^15

Step-by-step explanation:

We know a^b^c = a^(b*c)

4^3^5

4^(3*5)

4^15

Se necesitan 10 micros si queremos que cada 3 micros transporten 90 pasajeros.

En principio, sabemos que 300 pasajeros pueden transportarse en 4 microbuses.

Entonces, el numero de pasajeros que va por cada micro será el cociente entre el numero de pasajeros y el numero de micros:

N = 300/4 = 75

Queremos responder:

¿Cuántos micros se deben aumentar para  que por cada 3 micros se transporten 90 pasajeros?

Definamos X como el numero de grupos de 3 micros que tendriamos en esta situación.

Entonces 300 sobre X, debe ser igual a 90 (el numero de pasajeros que va en cada grupo de 3 micros)

300/X = 90

300 = 90*X

300/90 = X = 3.33...

Notar que el número total de micros sera 3 veces X:

3*X = 3*3.33.... = 10

Se necesitan 10 micros.

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Explanation:

Add up the values to get

1.96+1.81+1.97+1.83+1.87+1.84+1.85+1.94+1.96+1.81+1.86+1.95+1.89= 24.54

Then divide over 13 (the number of values) to get 24.54/13 = 1.8876923 which is approximate.

So the mean is approximately 1.8876923

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

Now make a spreadsheet as shown below

We have the first column as the x values, which are the original numbers your teacher provided. The second column is of the form (x-M)^2, where M is the mean we computed earlier. We subtract off the mean and square the result.

After we compute that column of (x-M)^2 values, we add them up to get what is shown in the highlighted yellow cell at the bottom of the column.

That sum is approximately 0.04403076924

Next, we divide that over n-1 = 13-1 = 12

0.04403076924 /12 = 0.00366923077

That is the sample variance. Apply the square root to this to get the sample standard deviation. This is the point estimate of the population standard deviation. As the name implies, it works for samples that estimate population parameters.

sqrt(0.00366923077) = 0.06057417576822

This rounds to 0.061 which is the final answer.

Answer:

4y

They would have the same value if a number was substituted for y

Step-by-step explanation:

y+y+2y =

Combine like terms

4y

These are all like terms

They would have the same value if a number was substituted for y

Let y = 5

5+5+2(5) = 5+5+10 = 20

4(5) =20

Answer:

Step-by-step explanation:

I assume the sequence is 0, 2, 4, 6

nth term = 2(n-1)

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

Work Shown:

sin(angle) = opposite/hypotenuse

sin(29) = x/24

24*sin(29) = x

x = 24*sin(29) ..... exact value

x = 11.635430885912 .... approximate value

x = 11.6

To get the approximate value, you'll need a calculator. Make sure the calculator is in degree mode.

Answer:

soory i dont know just report me if you angry

Answer:

The shopping time (in minutes) of the nine shoppers are:

15, 16, 18, 20, 22, 25, 27, 28, 29 (just to make it easier to read, I rearranged  everything from least to greatest.)

We can see, that 3 shoppers shopped for 15-20 minutes.

And, 3 shoppers shopped for 21-26 minutes.

And finally, 3 shoppers shopped for 27-32 minutes.

So the answer for all 3 of the boxes is 3.

Let me know if this helps.

Answer:

x < -4

Step-by-step explanation:

-3x > 12

-----   ----

-3      -3

12 ÷ -3 = -4

Which means:

x < -4

(The sign changes because the equation is divided by a negative number)

Hope this helped.

Answer:

x <-4

Step-by-step explanation:

-3x > 12

Divide each side by -3. remembering to flip the inequality

-3x/-3 > 12/-3

x <-4

Answer:

Step-by-step explanation:

(x-2)(x+4)=x^2+4x-2x-8=0=> x =2, x=0

Answer:

A

Step-by-step explanation:

Answer:

3.5 inches

Step-by-step explanation:

Sample mean basically means that we need to find the average of the samples.

So the formula for finding average is

Number of observations/ Number of Occurrences

So when we add the values together we get

42.

So there are 12 numbers

So, 42/12 =

3.5 inches

The sample mean of the heights of the plants in Susan's garden is

3.5 inches.

Here,

Susan randomly selected a sample of plants to determine the average height of the total 35 plants in her garden.

She measured the heights (in inches) of 12 randomly selected plants and recorded the data:

1.0, 1.4, 1.8, 2.0, 2.5, 3.5, 4.2, 4.5, 4.8, 5.0, 5.3, 6.0

We have to find the sample mean of the heights of the plants in Susan's garden.

What is Average?

Average value in a set of given numbers is the middle value, calculate as dividing the total of all values by the number of values.

Now,

The recorded data is;

1.0, 1.4, 1.8, 2.0, 2.5, 3.5, 4.2, 4.5, 4.8, 5.0, 5.3, 6.0

To find the sample mean of the heights of the plants in Susan's garden we have to find the average of the recorded data.

Formula for average = [tex]\frac{sum of number of observation}{ number of occurrence}[/tex]

Hence, Average = [tex]\frac{1.0+ 1.4+1.8+2.0+ 2.5+3.5+4.2+4.5+ 4.8+ 5.0+ 5.3+ 6.0}{12} = \frac{42}{12} = 3.5[/tex]

Therefore, The sample mean of the heights of the plants in Susan's garden is 3.5 inches.

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9514 1404 393

Answer:

  (d) 6√3

Step-by-step explanation:

There are several ways to work multiple-choice problems. One of the simplest is to choose the only answer that makes any sense. Here, that is 6√3.

y is the hypotenuse of the medium-sized right triangle, so will be longer than that triangle's longest leg. y > 9

The only answer choice that meets this requirement is ...

  y = 6√3

__

In this geometry, all of the right triangles are similar. This means corresponding sides have the same ratio. For y, we're interested in the ratio of long leg to hypotenuse.

  long leg/hypotenuse = y/(9+3) = 9/y

  y² = 9(9+3) = 9·4·3

  y = 3·2·√3 . . . . . . take the square root

  y = 6√3

__

Additional comments

You may notice that y is the root of the product of the longer hypotenuse segment (9) and the whole hypotenuse (9+3 = 12). We can say that y is the "geometric mean" of these segment lengths. Similarly (pun only partially intended), x will be the root of the product of the short segment (3) and the whole hypotenuse (12)

  x = √(3·12) = 6

This is another "geometric mean" relation.

Further, the altitude will be the geometric mean of the two segments of the hypotenuse:

  h = √(9·3) = 3√3

A way to summarize all of these relations is to say that the legs of the right triangle that are not the hypotenuse are equal to the geometric mean of the segments of the hypotenuse that the leg intercepts.

  x = √(3·12)

  y = √(9·12)

  h = √(3·9)

Answer:

a) To show that we can use the 1 proportion z-interval, we know that 250 ( size sample) is big enough to approximate the binomial distribution ( tolerance-intolerance) to a normal distribution.

b) See step by step explanation

CI 90 %  =  (  0,296 ; 0,392)

c) We can support that with 90 % of confidence we will find the random variable between this interval ( 0,296 ; 0,392)

d) the CI 95 % will be wider

Step-by-step explanation:

Sample Information:

Sample size n  =  250

number of people with milk intolerance  x = 86

p₁  =  86 / 250    p₁ = 0.344    and   q₁ =  1  - p₁   q₁ = 0,656

To calculate 90 % of Confidence Interval   α = 10%  α/2 = 5 %  

α/2 = 0,05     z(c) from z-table is:  z(c) =  1.6

Then:

CI 90 %  =  (  p₁  ±  z(c) * SE )

SE =  √ (p₁*q₁)/n   =  √ 0,225664/250

SE = 0,03

CI 90 %  =  (  0,344  ±  1,6* 0,03 )

CI 90 %  =  (  0,344 - 0,048 ;  0,344 + 0,048)

b) CI 90 %  =  (  0,296 ; 0,392)

a) To show that we can use the 1 proportion z-interval, we know that 250 ( size sample) is big enough to approximate the binomial distribution ( tolerance-intolerance) to a normal distribution.

c) We can support that with 90 % of confidence we will find the random variable between  this interval (  0,296 ; 0,392) .

d) CI 95 %      then significance level α = 5 %   α/2 = 2.5 %  

α/2  =  0,025      z(c) = 1.96   from z-table

SE = 0,03

And  as 1.96 > 1.6    the CI 95 % will be wider

CI 95% =  ( 0,344 ±  1.96*0,03 )

CI 95% =  (  0,344 ± 0,0588 )

CI 95% =  ( 0,2852 ; 0,4028 )

Answer:

The volume of the resulting solid is π/2 cubic units.

Step-by-step explanation:

Please refer to the diagram below.

The shell method is given by:

[tex]\displaystyle V = 2\pi \int _a ^b r(x) h(x)\, dx[/tex]

Where the representative rectangle is parallel to the axis of revolution, r(x) is the distance from the axis of revolution to the center of the rectangle, and h(x) is the height of the rectangle.

From the diagram, we can see that r(x) = (2 - x) and that h(x) is simply y. The limits of integration are from a = 0 to b = 1. Therefore:

[tex]\displaystyle V = 2\pi \int_0^1\underbrace{\left(2-x\right)}_{r(x)}\underbrace{\left(x - x^2\right)}_{h(x)}\, dx[/tex]

Evaluate:

[tex]\displaystyle \begin{aligned} V&= 2\pi \int_0 ^1 \left(2x-2x^2-x^2+x^3\right) \, dx\\ \\ &= 2\pi\int _0^1 x^3 -3x^2 + 2x \, dx \\ \\ &= 2\pi\left(\frac{x^4}{4} - x^3 + x^2 \Bigg|_0^1\right) \\ \\ &= 2\pi \left(\frac{1}{4} - 1 + 1 \right) \\ \\ &= \frac{\pi}{2}\end{aligned}[/tex]

The volume of the resulting solid is π/2 cubic units.

Answer:

pi/2

Step-by-step explanation:

I always like to draw an illustration for these problems.

For shells method think volume of cylinder=2pi×r×h

Integrate(2pi(2-x)(x-x^2) ,x=0...1)

Multiply

Integrate(2pi(2x-2x^2-x^2+x^3 ,x=0...1)

Combine like terms

Integrate(2pi(2x-3x^2+x^3) ,x=0...1)

Begin to evaluate

2pi(2x^2/2-3x^3/3+x^4/4) ,x=0...1

2pi(x^2-x^3+x^4/4), x=0...1

2pi(1-1+1/4)

2pi/4

pi/2

Answer:

8 113/1000(as a mixed number)      8113/1000(as an improper fraction)

Step-by-step explanation:

1. Convert 0.113 to a fraction...113/1000

2. As there is no further simplification needed, add 8 to 113/1000....8 113/1000

3. To convert 8 113/1000 from a mixed number to an improper fraction, multiply 8 (the whole number) and 1,000(the denominator)...8,000. Then add 113 (the numerator) to 8,000...8113. After that, you put 8113 over the denominator of the previous mixed number, getting 8113/1000 as the improper fraction.

Answer:

582-600

1,234-1,200

640-600

770-800

1,104-1,100

no bc it is not no no no no no no no

9514 1404 393

Answer:

corresponding: (1, 5), (2, 6), (3, 7), (43°, 4)4)

Step-by-step explanation:

In this geometry, "corresponding" angles are in the same direction from the point of intersection of the transversal with the parallel line.

"Alternate" refers to angles on opposite sides of the transversal. "Interior" and "exterior" refer to angles between and outside of the parallel lines, respectively.

Here, we list all angle pairs in each classification, so you can answer questions 1-12 based on this list.

alternate interior: (2, 4), (3, 5)

alternate exterior: (1, 7), (43°, 6)

corresponding: (1, 5), (2, 6), (3, 7), (43°, 4)

__

Additional classifications are also used:

consecutive (same-side) interior: (2, 5), (3, 4)

consecutive (same-side) exterior: (1, 6), (43°, 7)

vertical: (1, 3), (2, 43°), (4, 6), (5, 7)

linear pairs: (1, 2), (1, 43°), (2, 3), (3, 43°), (4, 5), (4, 7), (5, 6), (6, 7)

Answer: y = 7x + 18

Step-by-step explanation:

y = mx + b, (-2,4), m = 7

4 = 7(-2) + b

4 = -14 + b

b = 18

y = 7x + 18

Answer:

Step-by-step explanation:

8/5 = 16/10 = 24/15

8:5 = 16:10 = 24:15

Answer:

2016

Step-by-step explanation:

using USA dollars:

$42000 x .072 (7.2%) = 3024 total commission

3024 x 2/3 = 2016 brokers amount

Answer:

The probability will 4.32%.

The probability that all four are brown is 35/8,64,501.

Given that, A group of hens lays 69 eggs in a single day. On one particular day, there were 7 brown eggs and 62 white eggs.

Probability without replacement means once we draw an item, then we do not replace it back to the sample space before drawing a second item. In other words, an item cannot be drawn more than once.

If four eggs are selected at random, without replacement, the probability that all four are brown is 7/69 × 6/68 × 5/67 × 4/66

= 7/69 × 3/34 × 5/67 × 2/33

=7/23 × 1/17 × 5/67 × 1/33

=35/8,64,501

Therefore, the probability that all four are brown is 35/8,64,501.

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