Based on the following construction which statement below
must NOT be true?

Answer:

The probability that one red chip was selected is 0.0053.

Step-by-step explanation:

Let the random variable X be defined as the number of red chips selected.

It is provided that the selections of the n = 5 chips are done with replacement.

This implies that the probability of selecting a red chip remains same for each trial, i.e. p = 6/9 = 2/3.

The color of the chip selected at nth draw is independent of the other selections.

The random variable X thus follows a binomial distribution with parameters n = 5 and p = 2/3.

The probability mass function of X is:

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

Compute the probability that one red chip was selected as follows:

[tex]P(X=1)={5\choose 1}\ (\frac{2}{3})^{1}\ (1-\frac{2}{3})^{5-1}[/tex]

                [tex]=5\times\frac{2}{3}\times \frac{1}{625}\\\\=\farc{2}{375}\\\\=0.00533\\\\\approx 0.0053[/tex]

Thus, the probability that one red chip was selected is 0.0053.

Answer:

0.0412

Step-by-step explanation:

Total chips = 6 red + 3 black chips

Total chips=9

n=5

Probability of (Red chips ) can be determined by

=[tex]\frac{6}{9}[/tex]

=[tex]\frac{2}{3}[/tex]

=0.667

Now we used the binomial theorem

[tex]P(x) = C(n,x)*px*(1-p)(n-x).....Eq(1)\\ putting \ the \ given\ value \ in\ Eq(1)\ we \ get \\p(x=1) = C(5,1) * 0.667^1 * (1-0.667)^4[/tex]

This can give 0.0412

Answer:

6 pizzas

Step-by-step explanation:

At least 10 and fewer than 20 makes it 10-19

So,

10-19 => 6 pizzas

6 pizzas have at least 10 pieces of pepperoni but fewer than 20 pieces of pepperoni.

Answer:

It is only (5,24).

Step-by-step explanation:

You are correct.

Sometimes, check all options means there could be just one option.

Answer:

-3

Step-by-step explanation:

a-2+3=-2

-3 -3

a-2=-5

+2 +2

a=-3

// have a great day //

Answer:

a = -3

Step-by-step explanation:

a - 2 + 3 = -2

Add like terms.

a + 1 = -2

Subtract 1 on both sides.

a = -2 - 1

a = -3

The value of a in the equation is -3.

Answer:

[tex]-4x+28[/tex]

Step-by-step explanation:

[tex]18-2(x+x-5)[/tex]

[tex]18+(-2)(x)+(-2)(x)+(-2)(-5)[/tex]

[tex]18+-2x+-2x+10[/tex]

[tex]-2x-2x+10+18[/tex]

[tex]=-4x+28[/tex]

Answer:

x<16

Step-by-step explanation:

number n

eight less than four times a number ... 4 x n - 8

is less than 56 ... < 56

4 x n - 8 < 56

4 x n < 56 + 8

4 x n < 64/4

n < 64 / 4

n < 16

Answer:

Step-by-step explanation:

Let the number be x

Four times the number :  4x

Eight less than four times a number: 4x - 8

4x - 8 < 56

Now add 8 to both sides,

4x < 56+8

4x < 64

Divide both sides by 4,

x < 64/4

x < 16

Possible values of number = Value less than 16

Answer:

Due to the higher coefficient of variation, 2009's GMAT scores show a more dispersed distribution

Step-by-step explanation:

To verify how dispersed a distribution is, we find it's coefficient of variation.

Coefficient of variation:

Mean of [tex]\mu[/tex], standard deviation of [tex]\sigma[/tex]. The coefficient is:

[tex]CV = \frac{\sigma}{\mu}[/tex]

Which year's GMAT scores show a more dispersed distribution

Whichever year has the highest coefficient.

2009:

Mean of 500, standard deviation of 90. So

[tex]CV = \frac{90}{500} = 0.18[/tex]

2010:

Mean of 570, standard deviation of 85.5. So

[tex]CV = \frac{85.5}{570} = 0.15[/tex]

Due to the higher coefficient of variation, 2009's GMAT scores show a more dispersed distribution

2009's GMAT scores show a more dispersed distribution.

Given that in 2009: Mean = 500 and standard deviation = 90.

In 2010: Mean = 570 and standard deviation = 85.5.

If the standard deviation is higher then the scores will be more dispersed.

Note that: 90 > 85.5. And 90 corresponds to 2009.

So, 2009's GMAT scores show a more dispersed distribution.

Learn more: https://brainly.com/question/11231804

Answer: 38 23/24

Step-by-step explanation:

Turn the mixed numbers into improper fractions

5 * 3 = 15

15 + 2 = 17

17/3

————————

6 * 8 = 48

48 + 7 = 55

55/8

————————

Now multiply the improper fractions

17/3 * 55/8

17 * 55 = 935

3 * 8 = 24

Divide 935 by 24 to get the answer as a mixed number.

935 / 24 = 38.95833

0.95833/1 = 23/24

935/24 as a mixed number is 38 23/24

Answer: 119 / 4

Step-by-step explanation:

5 2/3 x 6 7/8

= 17/3 x 6 x 7/8

= 17 x 2 x 7/8

= 17 x 2 x 7/8

= 17 x 7/4

= 119 / 4

Answer:

The 90% confidence interval for the mean production rate fro the new method is (75.9, 84.1).

Step-by-step explanation:

We have to calculate a 90% 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=80.

The sample size is N=18.

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{10}{\sqrt{18}}=\dfrac{10}{4.24}=2.36[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=18-1=17[/tex]

The t-value for a 90% confidence interval and 17 degrees of freedom is t=1.74.

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

[tex]MOE=t\cdot s_M=1.74 \cdot 2.36=4.1[/tex]

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

[tex]LL=M-t \cdot s_M = 80-4.1=75.9\\\\UL=M+t \cdot s_M = 80+4.1=84.1[/tex]

The 90% confidence interval for the mean production rate fro the new method is (75.9, 84.1).

Answer: 4,582,656

Step-by-step explanation:

A coin is tossed 4 times,

2^4 outcomes: 16

and then a standard six-sided die is rolled 3 times, 6^3

216 outcomes:

and finally, a group of two cards is drawn from a standard deck of 52 cards without replacements

It says a “group”, so, I guess the order doesn’t matter… So it is “52 choose 2”

52*51/ (2*1) = 26*51

how many different outcomes are possible?

16*216*26*51 = 4,582,656

Answer:

21

Step-by-step explanation:

1/5 of 30 is 6

10% of 30 is 3

3+6=9

30-9=21

which is 7/10

Answer:

Simon has 7/10 of the cakes left.

Answer:

a. The claim is that the amount of television watched per day last year by the average person differed from that in 2005.

b. The critical values are tc=-1.729 and tc=1.729.

The acceptance region is defined by -1.792<t<1.729. See the picture attached.

c. Test statistic t=0.18.

The null hypothesis failed to be rejected.

d. At a significance level of 10%, there is not enough evidence to support the claim that the amount of television watched per day last year by the average person differed from that in 2005.

e. The 95% confidence interval for the mean is (2.29, 7.23).

Step-by-step explanation:

We have a sample of size n=20, which has mean of 4.76 and standard deviation of 5.28.

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{20}(1+4.6+5.4+. . .+6.2)\\\\\\M=\dfrac{95.2}{20}\\\\\\M=4.76\\\\\\s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2\\\\\\s=\dfrac{1}{19}((1-4.76)^2+(4.6-4.76)^2+(5.4-4.76)^2+. . . +(6.2-4.76)^2)\\\\\\s=\dfrac{100.29}{19}\\\\\\s=5.28\\\\\\[/tex]

a. This is a hypothesis test for the population mean.

The claim is that the amount of television watched per day last year by the average person differed from that in 2005.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=4.55\\\\H_a:\mu\neq 4.55[/tex]

The significance level is 0.1.

The sample has a size n=20.

The sample mean is M=4.76.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=5.28.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{5.28}{\sqrt{20}}=1.181[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{4.76-4.55}{1.181}=\dfrac{0.21}{1.181}=0.18[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=20-1=19[/tex]

The critical value for a level of significance is α=0.10, a two tailed test and 19 degrees of freedom is tc=1.729.

The decision rule is that if the test statistic is above tc=1.729 or below tc=-1.729, the null hypothesis is rejected.

As the test statistic t=0.18 is within the critical values and lies in the acceptance region, the null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the amount of television watched per day last year by the average person differed from that in 2005.

We have to 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=4.76.

The sample size is N=20.

The standard error is s_M=1.181

The degrees of freedom for this sample size are df=19.

The t-value for a 95% confidence interval and 19 degrees of freedom is t=2.093.

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

[tex]MOE=t\cdot s_M=2.093 \cdot 1.181=2.47[/tex]

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

[tex]LL=M-t \cdot s_M = 4.76-2.47=2.29\\\\UL=M+t \cdot s_M = 4.76+2.47=7.23[/tex]

The 95% confidence interval for the mean is (2.29, 7.23).

Answer:

14.4 units

Step-by-step explanation:

In Trigonometry

[tex]\cos \theta =\frac{Adjacent}{Hypotenuse}\\[/tex]

In Triangle DEF,

[tex]\cos F =\dfrac{EF}{DF}\\\cos 26^\circ =\dfrac{EF}{16}\\EF=16 \times \cos 26^\circ\\=14.4$ units (correct to the nearest tenth).[/tex]

Answer:

[tex] P(X>8)[/tex]

And for this case we can use the cumulative distribution function given by:

[tex] F(x) = 1- e^{-\lambda x}[/tex]

And if we use this formula we got:

[tex] P(X>8)= 1- P(X \leq 8) = 1-F(8) = 1- (1- e^{-\frac{1}{8.9} *8})=e^{-\frac{1}{8.9} *8}= 0.4070[/tex]

Step-by-step explanation:

For this case we can define the random variable of interest as: "The life of an electric component " and we know the distribution for X given by:

[tex]X \sim exp (\lambda =\frac{1}{8.9}) [/tex]

And we want to find the following probability:

[tex] P(X>8)[/tex]

And for this case we can use the cumulative distribution function given by:

[tex] F(x) = 1- e^{-\lambda x}[/tex]

And if we use this formula we got:

[tex] P(X>8)= 1- P(X \leq 8) = 1-F(8) = 1- (1- e^{-\frac{1}{8.9} *8})=e^{-\frac{1}{8.9} *8}= 0.4070[/tex]

Answer: Working together, they can complete the task in 7 hours and 12 minutes.

Step-by-step explanation:

Ok, Briana needs 12 hours to complete the task.

Then we can find the ratio of work over time as:

1 task/12hours = 1/12 task per hour.

This means that she can complete 1/12 of the task per hour.

Henry needs 18 hours to complete the task, then his ratio is:

1 task/18 hours = 1/18 task per hour.

This means that he can complete 1/18 of the task in one hour.

If they work together, then the ratios can be added:

R = 1/12 + 1/18 = 18/(12*18) + 12/(18*12) = 30/216

we can reduce it to:

R = 15/108 = 5/36

So, working together, in one hour they can complete 5/36 of the task, now we can find the number of hours needed to complete the task as:

(5/36)*x = 1 task

x = 36/5 hours = 7.2 hours

knowing that an hour is 60 minutes, then 0.2 of an hour is 60*0.2 = 12 minutes.

then x = 7 hours and 12 minutes.

Answer:

Step-by-step explanation:

[tex](\sqrt{b^{2}})^{3}=b^{3}\\\\[/tex]

or If it is

[tex]\sqrt[3]{b^{2}} =(b^{2})^{\frac{1}{3}}=b^{2*\frac{1}{3}}=b^{\frac{2}{3}}[/tex]

Answer:

Step-by-step explanation:

The vertical asymptotes of the rational expression are the places where the denominator is zero:

  x^2 -16 = 0

  (x -4)(x +4) = 0 . . . . . true for x=4, x=-4

  x = 4, x = -4 are the equations of the vertical asymptotes

__

The zeros of a rational expression are the places where the numerator is zero:

  4x = 0

  x = 0 . . . . . . divide by 4

Answer:

The solution for this is:

y = (0.6 * x) + 1.25

Hope it helps! :)

Answer:

Having 3.2 liters of water for 3 hours of hiking

Step-by-step explanation:

If x represents the number of hours and y represents the number of liters of water, then we can plug the possible solutions into our inequality to see which solution(s) work.

The first option is having 3 liters of water for 3.5 hours of hiking. We will plug 3 in for y and 3.5 in for x:

y > 0.6x + 1.25

3 > 0.6(3.5) + 1.25

3 > 3.35

But since 3 is not greater than 3.35, this does not work.

The next option is having 2 liters of water for 2.5 hours of hiking:

2 > 0.6(2.5) + 1.25

2 > 2.75

But 2 is not greater than 2.75, so this does not work.

Option c is having 2.3 liters of water for 2 hours of hiking:

2.3 > 0.6(2) + 1.25

2.3 > 2.45

Since 2.3 is not greater than 2.45, this solution does not work.

The last option is having 3.2 liters of water for 3 hours of hiking:

3.2 > 0.6(3) + 1.25

3.2 > 3.05

3.2 IS greater than 3.05, so this solution works!

Answer:

Area = 108 cm^2

Perimeter = 44 cm

Step-by-step explanation:

Area, -->

24 + 30 + 24 + 30 -->

24(2) + 30(2)

48 + 60 = 108 cm^2

108 = area

10 + 12 + 10 + 12, -->

10(2) + 12(2) = 44 cm

44 = perim.

Hope this helps!

Answer:

Step-by-step explanation:

Draw the diagram.

This time put in the only one line for the height. That is only 1 height is 8 cm. That's it.

The base is 6 +  6 = 12 cm.

The slanted line is 10 cm

That's all your diagram should show. It is much clearer without all the clutter.

Now you are ready to do the calculations.

Area

The Area = the base * height.

base = 12

height = 8

Area = 12 * 8 = 96

Perimeter.

In a parallelagram the opposite sides are equal to one another.

One set of sides = 10 + 10 = 20

The other set = 12 + 12 = 24

Both sets = 20 + 24

Both sets = 44

Answer

Area = 96

Perimeter = 44

Answer:

About 11.77 centimeters

Step-by-step explanation:

By law of sines:

[tex]\dfrac{50}{\sin 62}=\dfrac{x}{\sin 12} \\\\\\x=\dfrac{50}{\sin 62}\cdot \sin 12\approx 11.77cm[/tex]

Hope this helps!

Answer:

n=N-1

Step-by-step explanation:

You can start by imagining this scenario on a small scale, say 5 squares.

Assuming it starts on the first square, the grasshopper can cover the full 5 squares in 2 ways; either it can jump one square at a time, or it can jump all the way to the end and then backtrack. If it jumps one square at a time, it will take 4 hops to cover all 5 squares. If it jumps two squares at a time and then backtracks, it will take 2 jumps to cover the full 5 squares and then 2 to cover the 2 it missed, which is also 4. It will always be one less than the total amount of squares, since it begins on the first square and must touch the rest exactly once. Therefore, the smallest amount n is N-1. Hope this helps!

The smallest value of n is N-1.

Square is a quadrilateral of equal length of sides and each angle of 90°.

Here given that there are 1×N squares i.e. N numbers of squares in one row.

The grasshopper can jump either one square or two squares to land on the next square.

Let's assume the scenario of 5 squares present in a row.

Let the grasshopper starts from the first square,

so the grasshopper can cover the full 5 squares in 2 methods;

one method is that it will jump one square at a time and reach at last square.

another method is it will jump all the squares to the finish and then backtrace.

If the grasshopper jumps one square at a time, it will take 4 jumps to cover all 5 squares.

Similarly, If a grasshopper jumps two squares at a time and then backtrace, it will take 2 jumps to reach the 5th square and then it will jump 1 square and then 2 squares to cover the 2 squares it missed, for which the number jump is also 4.

From the above it is clear that the number of jumps will always be one less than the total number of squares if the grasshopper begins from the first square and touch every square exactly once.

Therefore, the smallest value of n is N-1.

Learn more about squares

here: https://brainly.com/question/1538726

#SPJ2

Answer:

The population mean load failures for the three etch times are all equal

Step-by-step explanation:

For an ANOVA F test, the null hypothesis always assumes that mean which is also the average value of the dependent variable which is continuously are the same/ there is no difference in the means. The alternative is to test against the null and it is always the opposite of the null hypothesis.

Answer:

Approximately 0% probability that the average price for 15 gas stations is over $4.99.

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 = 4.74, \sigma = 0.16, n = 16, s = \frac{0.16}{\sqrt{16}} = 0.04[/tex]

What is the approximate probability that the average price for 15 gas stations is over $4.99?

This is 1 subtracted by the pvalue of Z when X = 4.99. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{4.99 - 4.74}{0.04}[/tex]

[tex]Z = 6.25[/tex]

[tex]Z = 6.25[/tex] has a pvalue very close to 1.

1 - 1 = 0

Approximately 0% probability that the average price for 15 gas stations is over $4.99.

Answer:

Triangular Prism

volume 748

Answer:

Option (D)

Step-by-step explanation:

Formula for the area of a triangle is,

Area of a triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

For the given triangle ABC,

Area of ΔABC = [tex]\frac{1}{2}(\text{AB})(\text{CD})[/tex]

Length of AB = [tex](y_2-y_1)[/tex]

Length of CD = [tex](x_3-x_1)[/tex]

Now area of the triangle ABC = [tex]\frac{1}{2}(y_2-y_1)(x_3-x_1)[/tex]

Therefore, Option (D) will be the answer.

Answer:

The value of [tex]x_{1}[/tex] is given by [tex]\frac{10}{3}[/tex]. Hence, the answer is A.

Step-by-step explanation:

This exercise represents a case where the Newton-Raphson method is used, whose formula is used for differentiable function of the form [tex]f(x) = 0[/tex]. The expression is now described:

[tex]x_{n+1} = x_{n} - \frac{f(x_{n})}{f'(x_{n})}}[/tex]

Where:

[tex]x_{n}[/tex] - Current approximation.

[tex]x_{n+1}[/tex] - New approximation.

[tex]f(x_{n})[/tex] - Function evaluated in current approximation.

[tex]f'(x_{n})[/tex] - First derivative of the function evaluated in current approximation.

If [tex]f(x) = x^{2} - 4[/tex], then [tex]f'(x) = 2\cdot x[/tex]. Now, given that [tex]x_{0} = 6[/tex], the function and first derivative evaluated in [tex]x_{o}[/tex] are:

[tex]f(x_{o}) = 6^{2} - 4[/tex]

[tex]f(x_{o}) = 32[/tex]

[tex]f'(x_{o})= 2 \cdot 6[/tex]

[tex]f'(x_{o}) = 12[/tex]

[tex]x_{1} = x_{o} - \frac{f(x_{o})}{f'(x_{o})}[/tex]

[tex]x_{1} = 6 - \frac{32}{12}[/tex]

[tex]x_{1} = 6 - \frac{8}{3}[/tex]

[tex]x_{1} = \frac{18-8}{3}[/tex]

[tex]x_{1} = \frac{10}{3}[/tex]

The value of [tex]x_{1}[/tex] is given by [tex]\frac{10}{3}[/tex]. Hence, the answer is A.

Answer:

0 miles

Step-by-step explanation:

The computation of the minimum possible number of miles traveled by  automobile is shown below:

As we can see that in the given histogram it does not represent any normal value i.e it is not evenly distributed moreover, the normal distribution is symmetric that contains evenly distribution data

But this histogram shows the asymmetric normal distribution that does not have evenly distribution data

Therefore the correct answer is 0 miles

Answer:

2,500

That is your correct answer.

Answer:

The answer is -4.

Step-by-step explanation:

You should get this answer if you do 3 - 7.

Answer:

18 pounds of cashews are needed.

Step-by-step explanation:

Given;

A manager bought 12 pounds of peanuts for $30.

Price of peanut per pound P = $30/12 = $2.5

Price of cashew per pound C = $5

Price of mixed nut per pound M = $4

Let x represent the proportion of peanut in the mixed nut.

The proportion of cashew will then be y = (1-x), so;

xP + (1-x)C = M

Substituting the values;

x(2.5) + (1-x)5 = 4

2.5x + 5 -5x = 4

2.5x - 5x = 4 -5

-2.5x = -1

x = 1/2.5 = 0.4

Proportion of cashew is;

y = 1-x = 1-0.4 = 0.6

For 12 pounds of peanut the corresponding pounds of cashew needed is;

A = 12/x × y

A = 12/0.4 × 0.6 = 18 pounds

18 pounds of cashews are needed.