uppose the probability of an unsuccessful missile launch is 0.3. If missiles continue to be launched until an unsuccessful launch occurs, what is the probability that exactly 4 total launches will be performed (round off to first decimal place)

The interquartile range of the data shown in the box plot is 14.

In descriptive facts, the interquartile range is a measure of statistical dispersion, which is the spread of the data. The IQR may also be called the midspread, center 50%, fourth unfold, or H‑unfold. Its miles are defined as the difference between the 75th and 25th percentiles of the records.

To find the interquartile range (IQR), ​first, discover the median (middle price) of the lower and top 1/2 of the information. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.

If you have a set containing the information points 1, 3, five, 7, eight, 10, eleven, and 13, the primary quartile is 4, the second one quartile is 7.5 and the 0.33 quartile is 10.5. Draw these factors on various lines and you may see that those three numbers divide the number line in quarters from 1 to 13.

To find the Interquartile Range (IQR) you need to subtract points Q1 from Q3.

The ends of the box are the Q1 and Q3 points.

Q3 = 80

Q1 = 66

80-66= 14

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False. As you increase the sample size (n), assuming everything else remains the same, the width of the confidence interval decreases, not increases.

The width of a confidence interval is determined by several factors, including the sample size (n), the variability of the data, and the desired level of confidence. When all other factors remain constant, increasing the sample size (n) leads to a narrower confidence interval.

A larger sample size provides more information and reduces the uncertainty associated with estimating population parameters. This decrease in uncertainty leads to a smaller margin of error, resulting in a narrower confidence interval.

The relationship between the sample size and the width of the confidence interval can be understood by the formula for the margin of error. The margin of error is inversely proportional to the square root of the sample size. As the sample size increases, the square root of n increases at a slower rate, resulting in a smaller margin of error and narrower confidence interval.

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Answer:

y-intercept = -2

Step-by-step explanation:

The given equation of line is :

5x – 3y = 6 ...(1)

The general equation of line is given by :

y = mx +c ...(2)

Where

m is slope

c is y-intercept

Equation (1) can be written as :

-3y = 6-5x

\(y=\dfrac{6}{-3}-\dfrac{5x}{(-3)}\\\\y=-2+\dfrac{5x}{3}\\\\y=\dfrac{5x}{3}+(-2)\) ..(3)

Comparing equation (1) and (3).

y-intercept = -2

Hence, this is the required solution.

Answer: the answer is 55 degrees

Step-by-step explanation:

Answer:

600400

Step-by-step explanation:

The probability distribution of X is 0.5, 0.25, 0.25, and 0.125. Mean value ∑ X × P (X) = 1.875. Standard Deviation of X = 1.0533

a) For a fair coin,

P(H) = P(T) = 0.5

Outcome  X                            Probability

T                  1                                  0.5

HT              2                       0.5×0.5 = 0.25

HHT          3                       0.5×0.5×0.5 = 0.125

HHHT          4                           0.5×0.5×0.5×0.5 = 0.0625

HHHH          4                           0.5×0.5×0.5×0.5 = 0.0625

So, probability distribution of X is

X P(X)

1 0.5

2 0.25

3 0.125

4 0.0625+0.0625 = 0.125

b)

X     P(X)    X×P(X)         X2×P(X)

1     0.5     0.5          0.5

2     0.25      0.5               1

3     0.125    0.375         1.125

4     0.125       0.5            2

sum 1     E(X) = 1.87

c) Variance = E(X²) - E(X)²

= 4.625 - 1.875²

= 1.1094

Standard Deviation of X = √ Variance

= √1.1094

= 1.0533

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Answer:

Given :

The length of a rectangle is 4 cm more than its width

The area of the rectangle is 96 cm²

To Find :

Width of the rectangle.

Solution :

Let the length of the rectangle be x cm.

Let the breadth of the rectangle be y cm.

Case 1:

➣

➣  _____(1)

Case 2 :

We have the formula for area of the rectangle as follows :

Where,

l = length → x cm

b = breadth → y cm.

➣

➣

Substitute, x = 96/y in equation 1,

➣

➣

➣

➣

➣

Divide by minus sign,

➣

➣

➣

➣

➣

➣

➣

As per assumption, y = breadth of the rectangle.

•°• y = -12 is not acceptable.

Substitute, y = 8 in equation 1,

➣

➣

➣

➣

Step-by-step explanation:

Answer: $6

Step-by-step explanation:

 $5            $x

-------  =   -------

250          300

Cross multiply (means and extremes):

$5*300 = 250*x

1500 = 250x

1500/250 = x

$6 = x

Answer:

$6.50

I don't know if it is right, but here you go

Step-by-step explanation:

First thing we do is find how much 25 text messages cost

divide 200 by 4

=50 text messages for one dollar

divide by 2

=25 text messages for 0.50 cents

divide 325 by 25

=13

multiply by 0.50

=6.5

Answer

y=1/3x+1

Step-by-step explanation:

to be perpendicular, the slope has to be the opposite reciprocal

The relative frequency table is:

Class         Frequency  Relative frequency

40 - 50         4                     0.1

50 - 60          6                     0.15

60 - 70           11                     0.18

70 - 80            9                     0.23

80 - 90              7                    0.18

90 - 100             3                   0.08

The relative frequency measures how often a value appears relative to the sum of the total values. The class width is 10. The class width is the difference between the upper and lower boundary (e.g. 100 - 90).

Frequency is the number of times the numbers in the class interval appear in the data set. Relative frequency is the frequency of a class interval divided by the total frequency of the data set.

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For this study, we would use a t test for independent means to compare the job skills test scores of the workers who received the new job skill training program and those who received the standard job skills program.

For this study, we would use a t test for independent means. The reason for this is because the two groups of workers (the ones assigned to the new job skill training program and the ones receiving the standard job skills program) are independent of each other. The researcher randomly assigned the workers to each group, so there is no relationship or dependence between the two groups.

In a t test for independent means, we compare the means of two independent groups to determine if there is a statistically significant difference between them. We would calculate the t-statistic and the p-value to determine if the difference in job skills test scores between the two groups is significant or just due to chance.

In summary, for this study, we would use a t test for independent means to compare the job skills test scores of the workers who received the new job skill training program and those who received the standard job skills program.

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Answer:

g(x) = (3x-4)

Step-by-step explanation:

F(x) =  sqrt( 3x-4)

We are taking the square root of (3x-4)

so g(x) = (3x-4)

Answer:

A = l*w

A= 7*8

A= 56

56 is the area

The scores that need to be examined in order to determine the median value of n = 24 are the 12th and 13th values.

In order to determine the median value of n = 24, you would need to examine the 12th and 13th scores. This is because the median value is the middle number of a sequence of values, so when there is an even number of values, the median is the average of the two numbers in the middle. So in the case of n = 24, there are two values in the middle, the 12th and 13th numbers. To find the median, you would need to add the two values together and divide the result by two. This will give you the median value of the sequence. If there were an odd number of values instead of an even number, then the median would be the middle number rather than the average of two numbers.

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The factors of the given expression are 2av² and (2av³-9).

The given expression is 4a²v⁵-18av².

The factors are the polynomials which are multiplied to produce the original polynomial.

2av²(2av³-9)

Therefore, the factors of the given expression are 2av² and (2av³-9).

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After 35 minutes there will be 40 bacteria remaining.

The process of a constant percentage rate decrease in an amount over time is referred to as "exponential decay." The formula to calculate exponential decay is given as, \(N_t=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}}\). Here, Nt is the quantity after time t, N0 is the initial quantity, t1/2 is the half-life, and t is time.

For the first situation, Nt=360, N0=900, t=10 minutes. Therefore, substituting the given values get the value of t1/2. So,

\(\begin{aligned}360&=900\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}} \\\frac{360}{900}&=\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}}\\0.4&=\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}}\\ \ln(0.4)&=\frac{10}{t_{1/2}}\ln(0.5)\\t_{1/2}&=10\times\frac{\ln(0.5)}{\ln(0.4)}\\&=7.6\end{aligned}\)

Now, for the second situation,  Nt=40.  We have to find the time at which there will be 40 bacteria remaining. Then,

\(\begin{aligned}40&=900\left(\frac{1}{2}\right)^{t/7.6}\\0.04&=\left(\frac{1}{2}\right)^{t/7.6}\\\ln(0.04)&=\frac{t}{7.6}\ln(0.5)\\t&=7.6\times\frac{\ln(0.04)}{\ln(0.5)}\\&=7.6\times4.64\\&=35.26\\&\approx35\end{aligned}\)

The answer is 35 minutes.

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The maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

maximize: z = c1x1 + c2x2 + ... + cnxn

subject to

a11x1 + a12x2 + ... + a1nxn ≤ b1

a21x1 + a22x2 + ... + a2nxn ≤ b2

am1x1 + am2x2 + ... + amnxn ≤ bmxi ≥ 0 for all i

In our case,

the given LP is:maximize: z = 36x1 + 30x2 - 3x3 - 4x

subject to:

x1 + x2 - x3 ≤ 5

6x1 + 5x2 - x4 ≤ 10

xi ≥ 0 for all i

We can rewrite the constraints as follows:

x1 + x2 - x3 + x5 = 5  (adding slack variable x5)

6x1 + 5x2 - x4 + x6 = 10  (adding slack variable x6)

Now, we introduce the non-negative variables x7, x8, x9, and x10 for the four decision variables:

x1 = x7

x2 = x8

x3 = x9

x4 = x10

The objective function becomes:

z = 36x7 + 30x8 - 3x9 - 4x10

Now we have the problem in standard form as:

maximize: z = 36x7 + 30x8 - 3x9 - 4x10

subject to:

x7 + x8 - x9 + x5 = 5

6x7 + 5x8 - x10 + x6 = 10

xi ≥ 0 for all i

To apply the simplex algorithm, we initialize the simplex tableau as follows:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

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

z |  0    |   0    |   0    |  36    |   30   |   -3   |   -4   |    0    |

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

x5|   0   |   1    |   0    |   1    |   1    |   -1   |   0    |    5    |

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

x6|   0   |   0    |   1    |   6    |   5    |   0    |   -1   |   10    |

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

Now, we can proceed with the simplex algorithm to find the optimal solution. I'll perform the iterations step by step:

Iteration 1:

1. Choose the most negative coefficient in the 'z' row, which is -4.

2. Choose the pivot column as 'x10' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 5/0 = undefined, 10/(-4) = -2.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to

make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

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

z |  0    |   0    |  0.4   |  36    |   30   |   -3   |   0    |   12    |

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

x5|   0   |   1    |  -0.2  |   1    |   1    |   -1   |   0    |   5     |

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

x10|   0  |   0    |   0.2  |   1.2  |   1   |   0    |   1    |   2.5   |

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

Iteration 2:

1. Choose the most negative coefficient in the 'z' row, which is -3.

2. Choose the pivot column as 'x9' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 12/(-3) = -4, 5/(-0.2) = -25, 2.5/0.2 = 12.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

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

z |  0    |   0    |  0.8   |  34    |   30   |   0    |   4    |   0     |

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

x5|   0   |   1    |  -0.4  |   0.6  |   1    |   5   |   -2   |   10    |

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

x9|   0   |   0    |   1    |   6    |   5    |   0   |   -5   |   12.5  |

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

Iteration 3:

No negative coefficients in the 'z' row, so the optimal solution has been reached.The optimal solution is:

z = 0

x1 = x7 = 0

x2 = x8 = 10

x3 = x9 = 0

x4 = x10 = 0

x5 = 10

x6 = 0

Therefore, the maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

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Answer: 59

Step-by-step explanation:

Answer:

x = 33

Step-by-step explanation:

b^2 = c^2− a^2 = 652 − 562 = 4225 − 3136 = 1089 =33^2

Answer:

a)2

b)4

c)6

Step-by-step explanation:

Answer:

D) (8,-22)

Step-by-step explanation:

I used my graphing calculator.

Answer:

D

Step-by-step explanation:

First, we know that angle B is congruent to angle E.

2x + 40 = 5x + 10

2x + 30 = 5x

30 = 3x

x = 10

Angle B and Angle E = 60 degrees

Angle C = 14 degrees

Remember that the interior angles of a triangle always add up to 180 degrees. Now that we know 2 of the 3 angles of these triangles, and because they are congruent, all that's left to do is find Angle A/D by setting up a simple equation.

60 + 14 + D = 180

74 + D = 180

D = 106

Angle D = 106 degrees

Hope this helps!

Answer:

Step-by-step explanation:

<E = <A                property of congruency.

<A = 5x + 10        Comes from the fact that <A and <E are equal.

Three angles of the triangle are given. They add to 180 degrees.

2x + 40 + x + 4 + 5x + 10 = 180         Combine like terms

8x + 54 = 180                                     Subtract 54 from both sides.

8x + 54 - 54 = 180 - 54                      Combine  

8x = 126                                              Divide by 8

8x/8 = 126/8

x = 15.75

<B = <D                                               Congruency and parallel lines

<D = 2x + 40                                       Substitute for x

<D = 2*15.75  +  40                             Combine

<D = 31.5 + 40

<D = 71.5

Answer:

2 Eggs

Step-by-step explanation:

Since it takes her 4 eggs for 2 batches you divide 4 by 2 and get two eggs per batch

The frequency distribution consists of class intervals and their corresponding frequencies. The class intervals are 1-5, 6-10, 11-15, and 16-20, and their respective frequencies are 1, 2, 3 and 4. The total number of observations (N) is given as 10.

1. To calculate the standard deviation, we need to follow a step-by-step process. First, we calculate the midpoint of each class interval by taking the average of the lower and upper limits. Then, we calculate the product of the midpoint and its corresponding frequency for each class interval. Next, we sum up all these products. We divide this sum by the total number of observations (N) to find the mean.

2. Now we subtract the mean from each midpoint, square the differences, and multiply them by their respective frequencies. Then, we sum up these values. To obtain the variance, we divide this sum by the total number of observations (N). Finally, the standard deviation is calculated by taking the square root of the variance.

3. In summary, to calculate the standard deviation for the given frequency distribution, we find the mean by calculating the sum of the products of midpoints and frequencies divided by the total number of observations. Then, we calculate the sum of the squared differences between each midpoint and the mean, multiplied by their respective frequencies. The variance is obtained by dividing this sum by the total number of observations, and finally, the standard deviation is obtained by taking the square root of the variance.

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Answer:

B!!!!!

Step-by-step explanation:

1/5

Step-by-step explanation: 3+3=6

Answer:

1. X= - 2, Y = 8

2. X= - 1 Y = 7

3. X= 0, Y = 6

4. X = 1, Y = 5

5. X = 2, Y = 4

6. X = 3, Y = 3

Answer:

Hope this helps any!

Step-by-step explanation:

What you do is you would add the -4w to w.

Then you would add 6 to -11

5w=-5

w=-1(I think)

Answer:

green and blue marbles are same in number so their ratio will be 1

Step-by-step explanation:

total marbles = 22

red = 8

blue = 7

green = total - (red + blue) = 22 - (8 + 7) = 22 - 15 = 7

ratio of blue marbles to green marbles =

blue : green

7: 7 = 1