A researcher wants to test the claim that convicted burglars spend an average of 18.7 months in jail. She takes a random sample of 11 such cases from court files and finds x=20.6 months and s=8 months. Test the claim that u=18.7 months at the 0.05 significance level.

Answer:

The area of the shaded region between [tex] \\ z = 1.23[/tex] and [tex] \\ z = 0.86[/tex] is [tex] \\ P(0.86 < z < 1.23) = 0.08554[/tex] or 8.554%.

Step-by-step explanation:

To solve this question, we need to find the corresponding probabilities for the standardized values (or z-scores) z = 1.23 and z = 0.86, and then subtract both to obtain the area of the shaded region between these two z-scores.

We need to having into account that a z-score is given by the following formula:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]

Where

A z-score indicates the distance of x from the mean in standard deviations units, where a positive value "tell us" that x is above [tex] \\ \mu[/tex], and conversely, a negative that x is below [tex] \\ \mu[/tex].

The standard normal distribution is a normal distribution with [tex] \\ \mu = 0[/tex] and [tex] \\ \sigma = 1[/tex], and has probabilities for standardized values obtained using [1]. All these probabilities are tabulated in the standard normal table (available in any Statistical book or on the Internet).

Using the cumulative standard normal table, for [tex] \\ z = 1.23[/tex], the corresponding cumulative probability is:

[tex] \\ P(z<1.23) = 0.89065[/tex]

The steps are as follows:

Following the same procedure, the cumulative probability for [tex] \\ z = 0.86[/tex] is:

[tex] \\ P(z<0.86) = 0.80511[/tex]

Subtracting both probabilities (because we need to know the area between these two values) we finally obtain the corresponding area between them (two z-scores):

[tex] \\ P(0.86 < z < 1.23) = 0.89065 - 0.80511[/tex]

[tex] \\ P(0.86 < z < 1.23) = 0.08554[/tex]

Therefore, the area of the shaded region between [tex] \\ z = 1.23[/tex] and [tex] \\ z = 0.86[/tex] is [tex] \\ P(0.86 < z < 1.23) = 0.08554[/tex] or 8.554%.

We can see this resulting area (red shaded area) in the graph below for a standard normal distribution, [tex] \\ N(0, 1)[/tex], and  [tex] \\ z = 0.86[/tex] and [tex] \\ z = 1.23[/tex].

Answer:

part a: 52%

part b: 0.4

part c: 0.24

Step-by-step explanation:

For part one, you find the frequency of the number of people that are less that 20. You add the number of tics in each bar and you divide by the total.

so for part a it is (7+6+9+4)/ (7+6+9+4+4+12+8)

for part b you add up the values that are greater than 25(less than 35)

(12+8)/total

part c you find the number of people between 25 and 30

that's 12

over total

12/total

Answer:

(d - 4) / c

Step-by-step explanation:

The slope of the line in terms of c and d is (d - 4) / c.

Here, we have,

To find the slope of the line in terms of the coordinates of the point (c, d), we can use the slope-intercept form of a line, y = mx + b, where m represents the slope.

In the given equation, y = kx + 4, we can see that the coefficient of x is k, which represents the slope of the line.

Since the line contains the point (c, d), we can substitute these values into the equation:

d = kc + 4

To isolate the slope term, we rearrange the equation:

d - 4 = kc

Now, divide both sides by c:

(d - 4) / c = k

Therefore, the slope of the line in terms of c and d is (d - 4) / c.

To learn more on slope click:

brainly.com/question/3605446

#SPJ2

Answer: Point slope form is y-y1=m(x-x1)

Step-by-step explanation:

Here y1=4

x1=-11

m i.e slope=-2

And there you go.

Answer:

  12 cm

Step-by-step explanation:

The rule regarding secants and/or tangents is that the product of distances from their common point to the two intersection points with the circle is the same.

For the tangent the "two" intersection points with the circle are the same point, so ...

  product of tangent lengths = product of secant lengths

  (8 cm)(8 cm) = (4 cm)(4 cm +x)

Dividing by 4 cm gives ...

  16 cm = 4 cm + x

  12 cm = x

Answer:

Probability = 4%

Step-by-step explanation:

For each answer, there are only two possible outcomes. Either it is correct, or it is not. The probability of an answer being correct is independent of other answers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Each question has 5 possible answer:

The person guesses, so [tex]p = \frac{1}{5} = 0.2[/tex]

2 questions:

This means that [tex]n = 2[/tex]

Find the probability that both responses are correct.

This is P(X = 2).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{2,2}.(0.2)^{2}.(0.8)^{0} = 0.04[/tex]

As a percent:

Probability = 4%

Answer:

[tex] P= 2*Lenght + 2*Width[/tex]

Since the perimeter is 56 inches we can solve for the lenght with this equation:

[tex] 56 in = 2*12in + 2*Length[/tex]

And solving for the length we got:

[tex] Length = \frac{56in -24 in}{2} 16 in[/tex]

So then the lenght = 16 inhes and the width of 12 inches

Step-by-step explanation:

For a rectangle of width 12 inches and lenght y inches we know that the perimeter is given by:

[tex] P= 2*Lenght + 2*Width[/tex]

Since the perimeter is 56 inches we can solve for the lenght with this equation:

[tex] 56 in = 2*12in + 2*Length[/tex]

And solving for the length we got:

[tex] Length = \frac{56in -24 in}{2} 16 in[/tex]

So then the lenght = 16 inhes and the width of 12 inches

Answer:

4z + 2 - 5/2z

Step-by-step explanation:

8z^2 + 4z -5

divided by 2z

8z^2 /2z = 4z

4z/2z =2

5/2z = 5/2z

Putting them back together

4z + 2 - 5/2z

Answer:

A   4z + 2 - 5/2z

Step-by-step explanation:

Answer:2

Step-by-step explanation:

3y+ 7= 13

3y= 13 - 7

3y= 6

Y = 6/3

Y= 2

Answer:

  the sum is 01011000₂ = 88

Step-by-step explanation:

For numbers of magnitude less than 128, it is convenient to use an 8-bit representation. I find it works will to convert back and forth through the octal (base-8) representation, as each base-8 digit converts nicely to three (3) base-2 bits.

  61 = 8·7 +5 = 075₈ = 00 111 101₂

  27 = 8·3 +3 = 033₈ = 00 011 011₂

Then ...

  [tex]\begin{array}{cc|ccc}&61&&00111101\\+&27&+&00011011\\ &\overline{88}&&\overline{01011000}\end{array}[/tex]

__

Starting from the right, we can convert the binary back to octal, then to decimal by considering 3 bits at a time:

  01 011 000₂ = 130₈ = 1·8² +3·8 +0 = 64 +24 = 88

The binary sum is the same as the decimal sum.

Answer:  C

Step-by-step explanation:

In order to find the inverse, transpose the matrix then find the determinant of each 2 x 2 matrix within it.

[tex]Q=\left[\begin{array}{ccc}2&2&3\\1&1&1\\3&2&1\end{array}\right] \qquad \rightarrow \qquad Q^T=\left[\begin{array}{ccc}2&1&3\\2&1&2\\3&1&1\end{array}\right][/tex]

[tex]det\left[\begin{array}{cc}1&2\\1&1\end{array}\right] =\bold{-1}\qquad det\left[\begin{array}{cc}2&2\\3&1\end{array}\right]=\bold{-4}\qquad det\left[\begin{array}{cc}2&1\\3&1\end{array}\right] =\bold{-1}\\\\\\\\det\left[\begin{array}{cc}1&3\\1&1\end{array}\right] =\bold{-2}\qquad det\left[\begin{array}{cc}2&3\\3&1\end{array}\right]=\bold{-7}\qquad det\left[\begin{array}{cc}2&1\\3&1\end{array}\right] =\bold{-1}\\[/tex]

[tex]det\left[\begin{array}{cc}1&3\\1&2 \end{array}\right] =\bold{-1}\qquad det\left[\begin{array}{cc}2&3\\2&2\end{array}\right]=\bold{-2}\qquad det\left[\begin{array}{cc}2&1\\2&1\end{array}\right] =\bold{0}[/tex]

[tex]Q^{-1}=\large\left[\begin{array}{ccc}1&-4&1\\-2&7&-1\\-1&-2&0\end{array}\right][/tex]

Answer:

[tex]x=35^\circ[/tex]

Step-by-step explanation:

From the diagram which I have drawn and attached below:

[tex]56^\circ+y+51^\circ=180^\circ$ (Sum of Angles on a Straight Line)\\y=180^\circ-(56^\circ+51^\circ)\\y=73^\circ[/tex]

Next, in the triangle, the sum of the three interior angles:

[tex]y+x+72^\circ=180^\circ\\$Since y=73^\circ\\73^\circ+x+72^\circ=180^\circ\\x=180^\circ-(73^\circ+72^\circ)\\x=35^\circ[/tex]

The value of angle x is 35 degrees.

Answer:When n is an odd number, [tex]\sqrt[n]{a}[/tex] is a real number for all values of a. Then, the domain is the real domain.

Answer:

B

Step-by-step explanation:

Answer:

A) cluster sampling ( b ) and systematic sampling ( e )

B ) Randomly selecting precincts increases the likelihood that the people polled represent the population well. ( c )

Step-by-step explanation:

Cluster sampling is a type of sampling plan used when there is an internally heterogeneous groups can be found inside a population that is supposed to be mutually  homogeneous . while systematic sampling is a type of probability sampling that involves the selection of samples from a larger population at random but using a specific interval. to get the systematic sample the larger population is divided by the sample size.

from the information available in the report it is very evident that not all voters can be captured at once hence cluster sampling and systematic sampling would be employed .  

B) the company will randomly select precinct to increase the likelihood of the sample size representing the entire population very well

Answer:

x = -7.33        OR         x = [tex]\frac{-22}{3}[/tex]

y = 13

Step-by-step explanation:

→You can use the substitution method. First, make y by itself in (-2 + 2y = 24):

-2 + 2y = 24

2y = 26

y = 13

→Then, plug in 13 for y into the other equation:

3x + 2y = 4

3x + 2(13) = 4

3x + 26 = 4

3x = -22

x = -7.33        OR         x = [tex]\frac{-22}{3}[/tex]

Answer:

18×18×36

Step-by-step explanation:

According to the Question

108≥ 4h + w

Volume V is given by

V = wh^2

⇒V= (108-4h)h^2

⇒V= 108h^2 - 4h^3

Now differentiating and keeping = 0 we get

V' = 216h - 12h^2 = 0

h = 216/12 = 18

w = 108 - 4×18 = 36

V = 36×18^2 = 11664 from a box of 18×18×36.

Answer:

There were 30 people attending at the start of the concert

Step-by-step explanation:

The coefficient of the value raised to an exponent in these types of functions is always the "starting" value. In your case, '30' is the coefficient, so it is the starting value. FYI: 1.10 is the rate at which the people increase, t is time passed, 20 is a constant, and P is the total number of people after the time goes by.

Answer:

There were 30 people attending at the start of the concert.

Step-by-step explanation:

30 is the coefficient, so that's your starting point, basically.

Answer:

Lucas groups the polynomial (12x^3 + 8x) + (–6x^2 – 4) to factor → 2 (2 x - 1) (3 x^2 + 2)

Step-by-step explanation:

Factor the following:

12 x^3 - 6 x^2 + 8 x - 4

Hint: | Factor out the greatest common divisor of the coefficients of 12 x^3 - 6 x^2 + 8 x - 4.

Factor 2 out of 12 x^3 - 6 x^2 + 8 x - 4:

2 (6 x^3 - 3 x^2 + 4 x - 2)

Hint: | Factor pairs of terms in 6 x^3 - 3 x^2 + 4 x - 2 by grouping.

Factor terms by grouping. 6 x^3 - 3 x^2 + 4 x - 2 = (6 x^3 - 3 x^2) + (4 x - 2) = 3 x^2 (2 x - 1) + 2 (2 x - 1):

2 3 x^2 (2 x - 1) + 2 (2 x - 1)

Hint: | Factor common terms from 3 x^2 (2 x - 1) + 2 (2 x - 1).

Factor 2 x - 1 from 3 x^2 (2 x - 1) + 2 (2 x - 1):

Answer: 2 (2 x - 1) (3 x^2 + 2)

Answer:

Both students are correct because polynomials can be grouped in different ways to factor. Both ways result in a common binomial factor between the groups. Using the distributive property , this common binomial term can be factored out. Each grouping results in the same two binomial factors.

Step-by-step explanation:

this is the sample response provided by edge

Answer:

For k = 1:

=NEGBINOMDIST(0, 1, 0.666) = 0.6660

For k = 2:

=NEGBINOMDIST(1, 1, 0.666) = 0.2224

For k = 3:

=NEGBINOMDIST(2, 1, 0.666) = 0.0743

For k = 4:

=NEGBINOMDIST(3, 1, 0.666) = 0.0248

For k = 5:

=NEGBINOMDIST(4, 1, 0.666) = 0.0083

For k = 6:

=NEGBINOMDIST(5, 1, 0.666) = 0.0028

Step-by-step explanation:

The probability of obtaining a defective 10-year old widget is 66.6%

p = 66.6% = 0.666

The probability of obtaining a non-defective 10-year old widget is

q = 1 - 0.666 = 0.334

The random variable will be the number of items that must be tested before finding the first defective 10-year old widget.

The geometric distribution is given by

[tex]$P(X = k) = p \times q^{k - 1}$[/tex]

Solving manually:

For k = 1:

[tex]P(X = 1) = 0.666 \times 0.334^{1 - 1} = 0.666 \times 0.334^{0} = 0.666[/tex]

For k = 2:

[tex]P(X = 2) = 0.666 \times 0.334^{2 - 1} = 0.666 \times 0.334^{1} = 0.2224[/tex]

For k = 3:

[tex]P(X = 3) = 0.666 \times 0.334^{3 - 1} = 0.666 \times 0.334^{2} = 0.0743[/tex]

For k = 4:

[tex]P(X = 4) = 0.666 \times 0.334^{4 - 1} = 0.666 \times 0.334^{3} = 0.0248[/tex]

For k = 5:

[tex]P(X = 5) = 0.666 \times 0.334^{5 - 1} = 0.666 \times 0.334^{4} = 0.0083[/tex]

For k = 6:

[tex]P(X = 6) = 0.666 \times 0.334^{6 - 1} = 0.666 \times 0.334^{5} = 0.0028[/tex]

Using Excel function:

NEGBINOMDIST(number_f, number_s, probability_s)

Where

number_f = k - 1 failures

number_s = no. of successes

probability_s = the probability of success

For the geometric distribution, let number_s = 1

For k = 1:

=NEGBINOMDIST(0, 1, 0.666) = 0.6660

For k = 2:

=NEGBINOMDIST(1, 1, 0.666) = 0.2224

For k = 3:

=NEGBINOMDIST(2, 1, 0.666) = 0.0743

For k = 4:

=NEGBINOMDIST(3, 1, 0.666) = 0.0248

For k = 5:

=NEGBINOMDIST(4, 1, 0.666) = 0.0083

For k = 6:

=NEGBINOMDIST(5, 1, 0.666) = 0.0028

As you can notice solving manually and using Excel yields the same results.

Answer:

127.5

Step-by-step explanation:

Multiply 170 by 0.75

127.5

Answer:

3 divided by 4 = 0.75 = 3/4

0.75 x 170 = 127.5

or

170/1 x 3/4 = 510/4 = 127 1/2

1/2 = 0.5 = 1 divided by 2

127 + 0.5 = 127.5

127.5 is the answer

Hope this helps

Step-by-step explanation:

Answer:

Coefficient of variation (weight) = 15%

Coefficient of variation (volume) = 25%

Step-by-step explanation:

Let's begin by listing out the given information:

Population = 200, Average weight = 26 lb,

standard deviation (weight) = 3.9 lb,

Average volume = 8.8 ft³,

standard deviation (volume) = 2.2 ft³

Based on the data given, the manager will have to make a deduction by comparing the relative scatter of both variables due to the different units of measuring weight (pounds) and volume (cubic feet).

To compare the variation of the weight and volume, we use the coefficient of variation given by the formula:

Coefficient of Variation = (Standard deviation ÷ Mean) * 100%

⇒ [tex]C_{v}[/tex] = (σ ÷ μ) * 100%

For weight

σ = 3.9 lb, μ = 26 lb

[tex]C_{v}[/tex] (weight) = (3.9 ÷ 26.0) * 100% = 15%

[tex]C_{v}[/tex] (weight) = 15%

For volume

σ = 2.2 ft³, μ = 8.8 ft³

[tex]C_{v}[/tex] (volume) = (2.2 ÷ 8.8) * 100% = 25%

[tex]C_{v}[/tex] (volume) = 25%

∴ the relative variation of the volume of the package is greater than that of the weight of the package

Answer:

7/10 or 70% left

Step-by-step explanation:

total cakes=  30

Gave to Sali

Gave to Jane

Cakes left:

Cakes left fraction:

Answer:

7/10

Step-by-step explanation:

Cakes Simon gave to Sali = 30*1/5

= 6

Cakes Simon Gave to Jane = 30 * 1/10

= 3

Cakes left = 30 - (6-3)

= 21

21 cakes were left, so in terms of a fraction, it'd be 21/30, which can be reduced to 7/10

Hope this helps!

Answer:

[tex]x=2+\sqrt{11},\:x=2-\sqrt{11}[/tex]

Step-by-step explanation:

[tex]x^2-4x-7=0\\\mathrm{Solve\:with\:the\:quadratic\:formula}\\Quadratic\:Equation\:Formula\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\mathrm{For\:}\quad a=1,\:b=-4,\:c=-7:\quad x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}\\x=\frac{-\left(-4\right)+\sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}:\quad 2+\sqrt{11}[/tex]

[tex]x=\frac{-\left(-4\right)-\sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}:\quad 2-\sqrt{11}\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=2+\sqrt{11},\:x=2-\sqrt{11}[/tex]

Answer:

George is 43.20 ft East of his starting point.

Step-by-step explanation:

Let Paula's speed be x ft/s

George's speed = 9 ft/s

Note that speed = (distance)/(time)

Distance = (speed) × (time)

George takes 50 s to run a lap of the track at a speed of y ft/s

Meaning that the length of the circular track = y × 50 = 50y ft

George and Paula meet 14 seconds after the start of the run.

Distance covered by George in 14 seconds = 9 × 14 = 126 ft

Distance covered by Paula in 14 seconds = y × 14 = 14y ft

But the sum of the distance covered by both runners in the 14 s before they first meet each other is equal to the length of the circular track

That is,

126 + 14y = 50y

50y - 14y = 126

36y = 126

y = (126/36) = 3.5 ft/s.

Hence, Paula's speed = 3.5 ft/s

Length of the circular track = 50y = 50 × 3.5 = 175 ft

So, in 4 minutes (240 s), with George running at 9 ft/s, he would have ran a total distance of

9 × 240 = 2160 ft.

2160 ft around a circular track of length 175 ft, means that George would have ran a total number of laps (2160/175) = 12.343 laps.

Breaking this into 12 laps and 0.343 of a lap from the starting point. 0.343 of a lap = 0.343 × 175 = 60 ft

So, 60 ft along a circular track subtends an angle θ at the centre of the circle.

Length of an arc = (θ/360°) × 2πr

2πr = total length of the circular track = 175

r = (175/2π) = 27.85 ft

Length of an arc = (θ/360) × 2πr

60 = (θ/360°) × 175

(θ/360°) = (60/175) = 0.343

θ = 0.343 × 360° = 123.45°

The image of this incomplete lap is shown in the attached image,

The distance of George from his starting point along the centre of the circular track = (r + a)

But, a can be obtained using trigonometric relations.

Cos 56.55° = (a/r) = (a/27.85)

a = 27.85 cos 56.55° = 15.35 ft

r + a = 27.85 + 15.35 = 43.20 ft.

Hence, George is 43.20 ft East of his starting point.

Hope this Helps!!!

Answer:

The best estimate of the mean of the population is 50,000 miles, which is the sample mean.

To make a better inference, we know that the 95% confidence interval for the mean is (49,306; 50,694).

Step-by-step explanation:

The unbiased point estimation for the population mean tread life is the sample mean (50,000 miles), as it is the only information we have.

Although, knowing the standard deviation, we can calculate a confidence interval to make a stronger inference.

We calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=50000.

The sample size is N=100.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3500}{\sqrt{100}}=\dfrac{3500}{10}=350[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=100-1=99[/tex]

The t-value for a 95% confidence interval and 99 degrees of freedom is t=1.98.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=1.98 \cdot 350=694.48[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 50000-694.48=49306\\\\UL=M+t \cdot s_M = 50000+694.48=50694[/tex]

The 95% confidence interval for the mean is (49306, 50694).

Answer:

Read below.

Step-by-step explanation:

Questions are underlined

Answers are bolded

Which of the following statements is true?

If two polygons are similar then the corresponding sides are proportional and the corresponding angles are proportional.

If two polygons are similar, then the corresponding sides are proportional and  the corresponding angles are congruent.

If two polygons are similar, then the corresponding sides are congruent and the corresponding angles are proportional.

None of the choices are correct.

Which of the following sides are corresponding if ΔABC is similar to ΔMNL?

AC and ML, BC and NL, AB and MN is the correct answer but the answer choices are:

AB and MN, BC and NL, AC and ML

AC and MN, BC and NL, AB and ML

AB and ML, BC and NL, AC and MN

None of the choices are correct.

Answer:

$ 1,060.00

Step-by-step explanation:

A = $ 1,060.00

A = P + I where

P (principal) = $ 1,000.00

I (interest) = $ 60.00

Compound Interest Equation

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

Where:

A = Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

R = Annual Nominal Interest Rate in percent

r = Annual Nominal Interest Rate as a decimal

r = R/100

t = Time Involved in years, 0.5 years is calculated as 6 months, etc.

n = number of compounding periods per unit t; at the END of each period

Answer:

  θ = ±2π/3 +2kπ . . . . . for any integer k

Step-by-step explanation:

  2·cos(θ) +1 = 0

  cos(θ) = -1/2 . . . . . subtract 1, divide by 2

The cosine function has the value -1/2 for θ = ±2π/3 and any integer multiple of 2π added to that.

  θ = ±2π/3 +2kπ . . . . . for any integer k