The lengths of nails produced in a factory are normally distributed with a mean of 5.02 centimeters and a standard deviation of 0.05 centimeters. Find the two lengths that separate the top 6% and the bottom 6%. These lengths could serve as limits used to identify which nails should be rejected. Round your answer to the nearest hundredth, if necessary.

Answer:an=20(-1/2)^n-1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

height = 5

Step-by-step explanation:

The volume of a prism is V = l*w*h

You are not given any information about the exact values of l and w.

You do know however that L and w when multiplied together = 20, so you can put that in for l*w. Then the formula becomes

V = 20*h

You are told that the volume is 100. Now the problem is simplified. You get

100 = 20 * h               Divide both sides by 20

100/20 = 20*h/20     Combine like terms.

5 = h

Answer:

the area of the circle is 102.11 square metres

Answer:

The probability that on a randomly selected day the statistics professor will have five messages is 0.1755.

Step-by-step explanation:

Let the random variable X represent the number of e-mail messages per day a statistics professor receives from students.

The random variable is approximated by the Poisson Distribution with parameter λ = 5.

The probability mass function of X is as follows:

[tex]P(X=x)=\frac{e^{-5}\cdot 5^{x}}{x!};\ x=0,1,2,3...[/tex]

Compute the probability that on a randomly selected day she will have five messages as follows:

[tex]P(X=5)=\frac{e^{-5}\cdot 5^{5}}{5!}[/tex]

               [tex]=\frac{0.006738\times 3125}{120}\\\\=0.17546875\\\\\approx 0.1755[/tex]

Thus, the probability that on a randomly selected day the statistics professor will have five messages is 0.1755.

Answer:

what method exactly r u using ????

Answer:

work is shown and pictured

Answer:

The correct answer is B (24 units)

Step-by-step explanation:

Answer:

Mathematics could make scientists to have a preliminary understanding of the dimensions, perimeters, areas and volumes of different craters on Mars.

Step-by-step explanation:

Martian Craters are series of craters formed on the surface of Mars. The study of a planets crater gives an understanding of the properties of matter that lies under the crater.

Mathematics can be applied to determine the dimensions, perimeter, area and volume of the features of a crater using appropriate conversions and theorems.

The Pi in the sky theorem can be applied to determine the area and perimeter, even volume of different craters on the Mars surface. Also, eingenfunction expansion theorem gives a preliminary knowledge of the craters.

By measurements and conversions processes, the features of Martian crater could be studied from images.

Answer:

18, 13

Step-by-step explanation:

x=4+1/2y

x+y=31

4+1/y+y=31

3/2y=27

y=18

x=31-18=13

Answer:

13 & 18

Step-by-step explanation:

Create the formulas:

0.5x+4=y

x+y=31

0.5x+4=y

Multiply both sides by 2

x+8=2y

x+y=31

Subtract 31 from both sides

x+y-31=0

Subtract y from both sides

x-31= -y

Multiply both sides by -1

-x+31=y

Multiply both sides by 2

-2x+62=2y

Combine equations:

-2x+62=x+8

Add 2x to both sides

62=3x+8

Subtract 8 from both sides

3x=54

Divide both sides by 3

x=18

0.5x+4=y

Subtract y from both sides

0.5x-y+4=0

Subtract 0.5x from both sides

-y+4= -0.5x

Multiply both sides by -1

y-4=0.5x

Multiply both sides by 2

2y-8=x

x+y=31

Subtract y from both sides

x= -y+31

Combine equations:

2y-8= -y+31

Add y to both sides

3y-8=31

Add 8 to both sides

3y=39

Divide both sides by 3

y=13

Answer:

32

Step-by-step explanation:

r:m

2:14

1:7

m=224

r=224 divided by 7

224/7=32

Edit: unless it is proportional to r^2 in which case it is a different answer

Answer:

m=504

Step-by-step explanation:

Answer:

For the given data, the mean is 50.8, the median is 51, and the mode is 52.

For the sample with this error, the mean is 48.7, the median is 51, and the mode is 52.

For the sample with this value removed, the mean is 43.2, the median is 50, and the mode is 52.

Step-by-step explanation:

We are given the following set of sample data below;

18, 26, 30, 42, 50, 52, 52, 76, 78, 84.

The formula for calculating mean is given by;

         Mean  =  [tex]\frac{\text{Sum of all data values}}{\text{Total number of observations}}[/tex]

                     =  [tex]\frac{18+ 26+ 30+ 42+ 50+ 52+ 52+ 76+ 78+ 84}{10}[/tex]  

                     =  [tex]\frac{508}{10}[/tex]  =  50.8

For calculating median, we have to observe that the number of observations (n) in our data is even or odd, i.e;

                    Median  =  [tex](\frac{n+1}{2})^{th} \text{ obs.}[/tex]

                    Median  =  [tex]\frac{(\frac{n}{2})^{th}\text{ obs.} +(\frac{n}{2}+1)^{th}\text{ obs.} }{2}[/tex]

Now, here in our data the number of observations is even, i.e. n = 10.

So, Median  =  [tex]\frac{(\frac{n}{2})^{th}\text{ obs.} +(\frac{n}{2}+1)^{th}\text{ obs.} }{2}[/tex]

                    =  [tex]\frac{(\frac{10}{2})^{th}\text{ obs.} +(\frac{10}{2}+1)^{th}\text{ obs.} }{2}[/tex]

                    =  [tex]\frac{5^{th}\text{ obs.} +6^{th}\text{ obs.} }{2}[/tex]

                    =  [tex]\frac{50+52 }{2}[/tex]  =  51

A Mode is a value that appears the maximum number of times in our data.

In our data, the value 52 is appera]ing maximum number of times, i.e. 2 times which means that mode of our data is 52.

Now, suppose the value 76 in the data is mistakenly recorded as 55 instead of 76. For the sample with this error,

            New Mean  =   [tex]\frac{18+ 26+ 30+ 42+ 50+ 52+ 52+ 55+ 78+ 84}{10}[/tex]  

                                =  [tex]\frac{487}{10}[/tex]  =  48.7

Now, suppose the value 76 in the original sample is inadvertently removed from the sample. For the sample with this value removed,

            New Mean  =   [tex]\frac{18+ 26+ 30+ 42+ 50+ 52+ 52+ 78+ 84}{9}[/tex]  

                                =  [tex]\frac{432}{10}[/tex]  =  43.2

            So, Median  =  [tex](\frac{n+1}{2})^{th} \text{ obs.}[/tex]

                                 =  [tex](\frac{9+1}{2})^{th} \text{ obs.}[/tex]

                                 =  [tex]5^{th} \text{ obs.}[/tex] = 50

Answer:

[tex]C(t) =\dfrac{ r}{k} - \left (\dfrac{r-kC_{0}}{k} \right )e^{ -kt}[/tex]

[tex]C(t) =\dfrac{ r}{k}- e^{ -kt}[/tex]   ,thus, the  function is said to be an increasing function.

Step-by-step explanation:

Given that:

[tex]\dfrac{dC}{dt}= r-kC[/tex]

[tex]\dfrac{dC}{r-kC}= dt[/tex]

Taking integration on both sides ;

[tex]\int\limits\dfrac{dC}{r-kC}= \int\limits \ dt[/tex]

[tex]- \dfrac{1}{k}In (r-kC)= t +D[/tex]

[tex]In(r-kC) = -kt - kD \\ \\ r- kC = e^{-kt - kD} \\ \\ r- kC = e^{-kt} e^{ - kD} \\ \\r- kC = Ae^{-kt} \\ \\ kC = r - Ae^{-kt} \\ \\ C = \dfrac{r}{k} - \dfrac{A}{k}e ^{-kt} \\ \\[/tex]

[tex]C(t) =\frac{ r}{k} - \frac{A}{k}e^{ -kt}[/tex]

here;

A is an integration constant

In order to determine A, we have [tex]C(0) = C0[/tex]

[tex]C(0) =\frac{ r}{k} - \frac{A}{k}e^{0}[/tex]

[tex]C_0 =\frac{r}{k}- \frac{A}{k}[/tex]

[tex]C_{0} =\frac{ r-A}{k}[/tex]

[tex]kC_{0} =r-A[/tex]

[tex]A =r-kC_{0}[/tex]

Thus:

[tex]C(t) =\dfrac{ r}{k} - \left (\dfrac{r-kC_{0}}{k} \right )e^{ -kt}[/tex]

2. Assuming that C0 < r/k, find lim t→[infinity] C(t) and interpret your answer

[tex]C_{0} < \lim_{t \to \infty }C(t) \\ \\C_0 < \dfrac{r}{k} \\ \\kC_0 <r[/tex]

The equation for C(t) can  be rewritten as :

[tex]C(t) =\dfrac{ r}{k} - \left (\dfrac{r-kC_{0}}{k} \right )e^{ -kt}C(t) =\dfrac{ r}{k} - \left (+ve \right )e^{ -kt} \\ \\C(t) =\dfrac{ r}{k}- e^{ -kt}[/tex]

Thus;  the  function is said to be an increasing function.

Answer: see below

Step-by-step explanation:

To find a coterminal angle, add or subtract 360° to the given angle as many times as needed to get a positive or negative angle.

I should mention that there are an infinite number of answers!

4) 400°

I can subtract 360° to get a positive angle of 40°

I can subtract another 360° to get a negative angle of -320°

5) -360°

I can subtract 360° to get a negative angle of -720°

I can add 360° twice to get a positive angle of 360°

6) -1010°

I can add 360° to get a negative angle of -650°

I can add 360° another 3 times to get a positive angle of 720°

7) 567°

I can subtract 360° to get a positive angle of 207°

I can subtract another 360° to get a negative angle of -153°

8) -164°

I can subtract 360° to get a negative angle of -524°

I can add 360° to get a positive angle of 194°

9) 358°

I can subtract 360° to get a negative angle of -2°

I can add 360° to get a positive angle of 718°

Answer:

Step-by-step explanation:

(x + k) is a factor of f(x)

x+k=0 => x= -k;    -k is a root of f(x)

=> f(-k)=0

[tex](x + k) is a factor of f(x)x+k=0 = > x= -k; -k is a root of f(x)= > f(-k)=0[/tex]

So the correct option is B.fl-k)=0.

The cube root function is f(x)=3√x f ( x ) = x 3 . A radical function is a function that is defined by a radical expression. The following are examples of rational functions: f(x)=√2x4−5 f ( x ) = 2 x 4 − 5 ; g(x)=3√4x−7 g ( x ) = 4 x − 7 3 ; h(x)=7√−8x2+4 h ( x ) = − 8 x 2 + 4 7 .

The root function is used to find a single solution to a single function with a single unknown. In later sections, we will discuss finding all the solutions to a polynomial function. We will also discuss solving multiple equations with multiple unknowns. For now, we will focus on using the root function.

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Answer:

E) 0.99

Step-by-step explanation:

100 recruits x 0.4 chance of retiring as police officer = 40 officers

probability of being married at time of retirement = (1 - 0.25) x 40 = 30 officers

each new recruit will result in either 0, 1 or 2 new pensions

mean = µ = E(Xi) = (0 x 0.6) + (1 x 0.1) + (2 x 0.3) = 0.7

σ²  = (0² x 0.6) + (1² x 0.1) + (2² x 0.3) - µ² = 0 + 0.1 + 1.2 - 0.49 = 0.81

in order for the total number of pensions (X) that the city has to provide:

the normal distribution of the pension funds = 100 new recruits x 0.7 = 70 pension funds

the standard deviation = σ = √100 x √σ² = √100 x √0.81 = 10 x 0.9 = 9

P(X ≤ 90) = P [(X - 70)/9] ≤ [(90 - 70)/9] =  P [(X - 70)/9] ≤ 2.22

z value for 2.22 = 0.9868 ≈ 0.99

Answer:

plot a point at 6 up from (0,0) and then go down one and over three places then plot another point- and so on - and so on

Step-by-step explanation:

To graph the line using the slope and intercept, first understand what the slope and intercept mean:

Slope is how steep or flat the line appears on the graph.

The y-intercept is the point at which the line hits the y-axis. In this equation, the line hits the y-axis at positive 6, which means that the point is (0, 6).

You can use a method called "rise over run" to graph. The slope is negative one over three, so the line will "rise" negative one units after "running" three units.

So, for every one unit down, the line will travel three units to the right.

Graph this from the point (0, 6), your y-intercept, and plot the points according to the slope:

Answer:The point from which circle is drawn is called center of circle.

Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thnk me...

Answer:

c. 7.25

Step-by-step explanation:

Given the following information from an experiment:

[tex]\left\begin{array}{ccc}&$Sample Size&$Sample Mean \\$Treatment 1&5&4\\$Treatment 2&10&8\\$Treatment 3&5&9\end{array}\right[/tex]

Total Sample Size =5+10+5=20

Therefore, the overall mean

[tex]=\dfrac{(5 \times 4)+ (10 \times 8) + (5 \times 9)}{20} \\=\dfrac{145}{20}\\\\=7.25[/tex]

Answer:

30%

Step-by-step explanation:

fat ÷ total

15 ÷ 50

.3

30%

Answer:

30%

Step-by-step explanation:

To find the percent from fat, take the calories from fat and divide by the total

15/50

.3

Multiply by 100%

30%

Answer:

The answer would be 1,853,614,297

Answer:

  44x +56y = 95

Step-by-step explanation:

To write the equation of the perpendicular bisector, we need to know the midpoint and we need to know the differences of the coordinates.

The midpoint is the average of the coordinate values:

  ((-2.5, -2) +(3, 5))/2 = (0.5, 3)/2 = (0.25, 1.5) = (h, k)

The differences of the coordinates are ...

  (3, 5) -(-2.5, -2) = (3 -(-2.5), 5 -(-2)) = (5.5, 7) = (Δx, Δy)

Then the perpendicular bisector equation can be written ...

  Δx(x -h) +Δy(y -k) = 0

  5.5(x -0.25) +7(y -1.5) = 0

  5.5x -1.375 +7y -10.5 = 0

Multiplying by 8 and subtracting the constant, we get ...

  44x +56y = 95 . . . . equation of the perpendicular bisector

Answer: 4 / 663

Step-by-step explanation:

There are 4 queens in a deck of 52 cards.

Probability = 4/52 = 1/13

There are 4 sevens

Probability = 4/51

Total probability = 1/13 x 4/51 = 4 / 663

The probability of drawing a queen first and a seven-second is 3/613.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

There are 4 queens in a standard deck, and once one queen is drawn, there are 51 cards left, including 3 sevens.

So, the probability of drawing a queen first is 4/52 or 1/13, and the probability of drawing a seven-second is 3/51.

By the multiplication rule of probability, multiply the probabilities of each event occurring:

P(Queen and Seven) = P(Queen) × P(Seven after Queen)

P(Queen and Seven) = (1/13) × (3/51)

P(Queen and Seven) = 3/613

Thus, the probability of drawing a queen first and a seven-second is 3/613.

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Answer:

a) P(6) = 0.0097

b) P(More than 3) = 0.1611

Step-by-step explanation:

For each question, there are only two possible outcomes. Either it is guessed correctly, or it is not. Questions are independent of each other. 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.

A student takes a multiple-choice test that has 11 questions.

This means that [tex]n = 11[/tex]

Each question has five choices.

This means that [tex]p = \frac{1}{5} = 0.2[/tex]

(a) Find P (6)

This is P(X = 6).

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

[tex]P(X = 6) = C_{11,6}.(0.2)^{6}.(0.8)^{5} = 0.0097[/tex]

P(6) = 0.0097

(b) Find P (More than 3).

Either P is 3 or less, or it is more than three. The sum of the probabilities of these outcomes is 1. So

[tex]P(X \leq 3) + P(X > 3) = 1[/tex]

We want P(X > 3). So

[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]

In which

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

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

[tex]P(X = 0) = C_{11,0}.(0.2)^{0}.(0.8)^{11} = 0.0859[/tex]

[tex]P(X = 1) = C_{11,1}.(0.2)^{1}.(0.8)^{10} = 0.2362[/tex]

[tex]P(X = 2) = C_{11,2}.(0.2)^{2}.(0.8)^{9} = 0.2953[/tex]

[tex]P(X = 3) = C_{11,3}.(0.2)^{3}.(0.8)^{8} = 0.2215[/tex]

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0859 + 0.2362 + 0.2953 + 0.2215 = 0.8389[/tex]

Then

[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.8389 = 0.1611[/tex]

P(More than 3) = 0.1611

Answer:

1/18

Step-by-step explanation:

First you would add 1/2 and 1/2 to get 1 then you would divide it by 18 to get 1/18

Answer:

1/18

Step-by-step explanation:

plz mark me brainliest.

Answer:

Step-by-step explanation:

a) image attached

b) Lets do the analysis in R , the complete R snippet is as follows

x<- c(89,177,189,354,362,442,965)

y<- c(.4,.6,.48,.66,.61,.69,.99)

# scatterplot

plot(x,y, col="red",pch=16)

# model

fit <- lm(y~x)

summary(fit)

#equation is

#y = 0.4041 + 0.0006211*X

# beta coeffiecients are

fit$coefficients

coef(summary(fit))[, "Std. Error"]

# confidence interval of slope

confint(fit, 'x', level=0.95)

The results are

> summary(fit)

Call:

lm(formula = y ~ x)

Residuals:

1 2 3 4 5 6 7

-0.05940 0.08595 -0.04151 0.03602 -0.01895 0.01136 -0.01346

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 4.041e-01 3.459e-02 11.684 8.07e-05 ***

x 6.211e-04 7.579e-05 8.195 0.00044 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.05405 on 5 degrees of freedom

Multiple R-squared: 0.9307,   Adjusted R-squared: 0.9168 # model is able to capture 93% of the variation of the data

F-statistic: 67.15 on 1 and 5 DF, p-value: 0.0004403 , p value is less than 0.05 , hence model as a whole is significant

> fit$coefficients

(Intercept) x

0.4041237853 0.0006210758

> coef(summary(fit))[, "Std. Error"]

(Intercept) x

3.458905e-02 7.579156e-05

> confint(fit, 'x', level=0.95)

2.5 % 97.5 %

x 0.0004262474 0.0008159042

c)

> x=c(89,177,189,354,362,442,965)

> y=c(0.40,0.60,0.48,0.66,0.61,0.69,0.99)

>

> ### linear model

> model=lm(y~x)

> summary(model)

Call:

lm(formula = y ~ x)

Residuals:

1 2 3 4 5 6 7

-0.05940 0.08595 -0.04151 0.03602 -0.01895 0.01136 -0.01346

Coefficients:

Estimate Std. Error t value Pr(>|t|)    

(Intercept) 4.041e-01 3.459e-02 11.684 8.07e-05 ***

x 6.211e-04 7.579e-05 8.195 0.00044 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.05405 on 5 degrees of freedom

Multiple R-squared: 0.9307, Adjusted R-squared: 0.9168

F-statistic: 67.15 on 1 and 5 DF, p-value: 0.0004403

s_e is the Residual standard error from the model and its estimated value is 0.05405. s_e is the standard deviation of the model.  

d) 95% confidence interval

> confint(model, confidence=0.95)

2.5 % 97.5 %

(Intercept) 0.3152097913 0.4930377793

x 0.0004262474 0.0008159042

Comment: The estimated confidence interval of slope of x does not include zero. Hence, x has the significant effect on y at 0.05 level of significance.

 e)

> predict(model, newdata=data.frame(x=250), interval="confidence", level=0.95)

fit lwr upr

1 0.5593927 0.5020485 0.616737

f)

> predict.lm(model, newdata=data.frame(x=250), interval="prediction", level=0.95)

fit lwr upr

1 0.5593927 0.4090954 0.7096901

Answer:

2 2/3

Step-by-step explanation:

Answer:

r = - [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

The common ratio r is the ratio between consecutive terms in the sequence.

r = [tex]\frac{48}{-96}[/tex] = [tex]\frac{-24}{48}[/tex] = [tex]\frac{12}{-24}[/tex] = [tex]\frac{-6}{12}[/tex] = - [tex]\frac{1}{2}[/tex]

Answer:

-1/2 or b on edge

Step-by-step explanation:

Answer:

51.56% probability that the mean weight of the sample of cows would differ from the population mean by greater than 11lbs if 49 cows are sampled at random from the herd

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 3181, \sigma = 119, n = 49, s = \frac{119}{\sqrt{49}} = 17[/tex]

What is the probability that the mean weight of the sample of cows would differ from the population mean by greater than 11lbs if 49 cows are sampled at random from the herd

Lower than 3181 - 11 = 3170 lbs or greater than 3181 + 11 = 3192 lbs. Since the normal distribution is symmetric, these probabilities are equal. So i will find one of them, and multiply by 2.

Probability of mean weight lower than 3170 lbs:

This is 1 subtracted by the pvalue of Z when X = 3170. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{3170 - 3181}{17}[/tex]

[tex]Z = -0.65[/tex]

[tex]Z = -0.65[/tex] has a pvalue of 0.2578

2*0.2578 = 0.5156

51.56% probability that the mean weight of the sample of cows would differ from the population mean by greater than 11lbs if 49 cows are sampled at random from the herd

Answer: 720 ft

Step-by-step explanation: He rides 720 feet.

if 120 feet are in 10 seconds then;

60 seconds are 60/10*120=720 feet

Answer:

720

Step-by-step explanation:

120/10 to find his feet per second which is 12 feet per second

12*60

since there are 60 seconds in a minute

= 720

Answer:

multiples of 12

Step-by-step explanation: when looking at the GCF, the answer is 12