how many arrangements of the 26 different letters are there that (a) contain either the sequence ""the"" or the sequence ""aid""?

the largest positive integer n[tex]\leq[/tex]112 for which there is a unique integer k

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

Given inequality is

[tex]\frac{15}{8} < \frac{n+k}{k} < \frac{13}{7}[/tex]

[tex]\frac{8}{15} < \frac{n}{n+k} < \frac{7}{13}[/tex]

[tex]n\frac{6}{7} < k < n\frac{7}{8}[/tex]

[tex]n\frac{7}{8}-n\frac{6}{7}[/tex] > 2

n[tex]\leq[/tex]112

Hence, the largest positive integer n[tex]\leq[/tex]112 for which there is a unique integer k

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We fail to reject H0. So there is enough evidence to state that the hypothesis H1 has the risk to make an error equal to α.

The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A lower number deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

The standard deviation is positive, or greater than zero, whenever there are two uneven terms in the observations. The standard deviation is exactly zero if all of the observations are equally distributed. Thus, the standard deviation can never be negative or less than zero.

We have two hypotheses:

H0: μ= 120

H1: μ≠ 120

where μ is the mean weight and per apple the value of α is 0.05. If conditions are met we will run sample a.

random: 49 apples are randomly selected

normal: 49>=30 so CLF holds. Now,

formula of z-test for μ

Test statistic:  z-test=(¯x−μ)/( σ/√n)

We are given with:

n=49

¯x=122.5

σ=12

putting values in formula:

z-test=(122.5-120)/(12/√49)

=1.458

P-value: P(z>1.458)=normal df(1.458, ∞,1)

=0.0724

And it is a two tailed test so

=2(0.0724)

=0.1448

Since P-value> α ; (0.0724>0.05)

So, we fail to reject H0. We do not have convincing evidence that there is a difference in mean weight per apple. So here we would say that there is enough evidence to state that the hypothesis H1 has the risk to make an error equal to α.

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Answer:

Step-by-step explanation:

the longest sideis greater than others.

so the answer is

Answer:

Yes it can

Step-by-step explanation:

Three sides of any length will always form a triangle.

The option B "The trials are done without replacement" is not a requirement for constructing a confidence interval for estimating the population​ proportion.

In the given question we have to check which of the following is not a requirement for constructing a confidence interval for estimating the population​ proportion?

The given options are:

a. There are at least 5 successes and 5 failures.

b. The trials are done without replacement.

c. The sample is a simple random sample.

d. There is fixed number of trials.

As we know that, an estimate's level of uncertainty is described by a confidence interval, which is a range of numbers.

As given that we have to find which of the following is not a requirement for constructing a confidence interval for estimating the population​ proportion. So for constructing a confidence interval for estimating the population​ proportion, we can find the trials without replacement.

So the option B "The trials are done without replacement" is correct.

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Answer:

see pic

Step-by-step explanation:

see pic

The correct option is the third one, the function is neither odd nor even.

A function y = f(x) is an odd function if for all values of x in its domain:

f(x) = f(-x)

The graph of these functions have an axis of symmetry at the y-axis.

And it is an odd function is for all values of x in its domain:

f(x) = -f(x)

These functions "invert" at the y-axis,

Now let's look at the graph.

When x = 5, we can see that:

f(x) = 9

And when x = -5, the function is:

f(-5) = -0.5

Neither of the conditions is meet.

Then the function is neither odd nor even.

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As each trial has a 0.375 probability, the probability for three successes is 0.05273 and for six successes is 0.00278.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, if we are unclear of how an event will turn out. Statistics is the study of occurrences subject to probability. The number of possible outcomes is divided by the total number of possible outcomes to determine probability. Odds are not the same as probability. Odds are calculated by dividing the probability of a given event by the probability that it won't. By dividing the number of preferable outcomes by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained.

Here,

The probability of success in each trial=3/8

For 3 success,

P(3)=(3/8)³

=0.05273

For 6 success,

P(6)=(3/8)⁶

=0.00278

The probability for 3 success is 0.05273 and for 6 success is 0.00278 as for each trial, the probability is 0.375.

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The regression model that would offer the better fit is one with a smaller standard error of the estimation and a given elements coefficient of determination when two regression models used on the same data set have had the same dependent variables but a variable figure of explanatory factors.

The coefficient of determination is most frequently used to determine how well a regression model fits observed data. For instance, data fitting the regression model 60% of the time is indicated by a determination coefficient of 60%. In general, a greater coefficient denotes a better model fit.

The degree of deviation around the mean increases with the coefficient of variation. Typically, a percentage is used to indicate it. Without units, it enables comparison of value distributions whose measurement scales are incomparable.

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the probability that she will correctly answer

A) 10 questions = 0

b) 9 questions =  0.00003

c) 8  questions =  0.00039

d) 7 questions =0.00309

e) 6 questions = 0.01622

f) 5 questions = 0.0584

Here  the total number of  question is 5+3+2= 10, and every question has four possible answers, for this problem, we will be  using the binomial distribution, the formula  is :

[tex]C_{n,k}[/tex][tex]p^{k}[/tex][tex]q^{n-k}[/tex] ,here C is the  combination,  p is the probability of success and q is the probability of having the success

for the given situation :

the p = 1/ 4 whereas, q=3/4

here n =10

now  for different values of  k  which is  the number of successes,  we substitute the know values in the formula, and we get

P(k=10) = 0

P(k=9) = 0.00003

P(k=8) = 0.00039

(P=7)= 0.00309

(P=6)=0.01622

(P=5)= 0.0584

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The slope of two perpendicular lines is the negative inverse of each other thus the equation of the perpendicular line will be y = (-2/5)x + c.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

As per the given line,

5x-2y=12

2y = 5x - 12

y = (5/2)x - 6

The slope of the above line is 5/2

Since the slope of two perpendicular lines is the negative inverse of each other.

Thus,slope of line = -1/(5/2) = -2/5

So equation will be y = (-2/5)x + c

Hence"The slope of two perpendicular lines is the negative inverse of each other thus the equation of the perpendicular line will be y = (-2/5)x + c".

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answer:

provided in the explanation.

step-by-step explanation:

the graph would contain the points (0,0), (1,10), (2,20), etc. the slope is 10, which represents the number of coordinate video games practiced in x number of hours. the representation for the slope depends on whether coordinate video game or hours practiced is on the x or y axis. hope that helps!

The distance between the two elevation is 30 metres. Therefore, Steve is correct.

A hiker is hiking at an elevation located 18 meters above sea level. Simultaneously a diver is diving at a location that is 12 meters below sea level.  

The distance between the two elevation can be calculated as follows:

Jessica said the answer is 6 meters. Steve said the answer is 30 meters.

Let's find who is correct.

The hiker is 18 metres above sea level . The diver is 12 meters below sea level. For the diver to get to sea level he will travel 12 meters. For the diver to get to the hiker position he will travel extra 18 metres.

Therefore, the distance in elevation is 12 + 18 = 30 metres. Hence, Steve is correct.

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The probability they will get a full scholarship and an internship Is 0.2

What is Probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty, probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.

However, if two coins are tossed, four outcomes might occur: (H, H), (H, T), (T, H), and (T, T).

For instance, when we flip a coin, there are just two potential results: Head OR Tail (H, T).

Given that these two events are independent. Hence,

P(Full scholarship and an internship)

= P(Full scholarship) * P(Internship)

= 0.50 * 0.40

= 0.20

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Jane makes sure that the (B) coffee is brewed simultaneously in each pot as part of her experimental study.

Experimental investigations involve introducing an intervention and observing its results.

Typically, volunteers in experimental research are grouped randomly, or by chance.

In experimental research, the dependent and independent variables are compared to examine how they relate to one another.

A link between a certain feature of an item and the variable under investigation is either accepted or denied following the conclusion of an experimental research study.

Laboratory experiments are the most fundamental type of experimental study, albeit they can take on several forms depending on the research topic.

Laboratory experiments are the most fundamental type of experimental study, albeit they can take on several forms depending on the research topic.

So, in the given situation, Jeane makes sure that the coffee is brewed simultaneously in all of the pots.

Therefore, Jane makes sure that (B) coffee is brewed simultaneously in each pot as part of her experimental study.

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Complete question;
Jenae noticed that many of her co-workers would opt for the coffee that appeared to be most recently brewed, regardless of the flavor of the coffee offered. This leads her to believe that what she was witnessing was not really representative of everyone's true flavor preferences. She adapted her experimental study accordingly. Select one control in Jenae's experimental study:

a. Jeane places condiments at random places throughout the kitchen.

b. Jeane makes sure that the coffee in different pots is brewed at the same time.

c. Jeane uses different locations in the kitchen for the coffee pots.

d. Jeane monitors the habit of co-workers who do not drink coffee.

Answer: 0.16

Step-by-step explanation:

7% people would indicate perceived pain relief after taking the two pain relievers.

The difference between an estimated value and the true value of a parameter or, sometimes, of a value to be predicted is an error of estimation.

Given that,In a study comparing the perceived effects of two painkillers, 200 randomly chosen persons were given the first one, and 93% reported noticeably lessening of their pain.

96% of the 450 people who received the other painkiller reported feeling noticeably relieved.We have to estimate the percentage of adults overall who would say they felt their pain was relieved after taking each painkiller.

Give the estimate 95% confidence interval.

We know that

,p=(186+432)/(200+450)p=0.95

We getL.B= 0.93-0.96+0.96√0.95(1-0.95)(1/200+1/450)

L.B= 0.07

U.B = 0.93-0.96+0.96√0.95(1-0.95)(1/200+1/450)

U.B = 0.01

Bound of error = 096√0.95(1-0.95)(1/200+1/450)  = 0.04

∴ 7% percentage of adults overall who would say they felt their pain was relieved after taking each painkiller.

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The equation of the line that passes through the points (7, -8) and (-4, 6) in point slope form is y - 6 = -14/11(x + 4)

The coordinates of the first point = (7, -8)

The coordinates of the second point = (-4, 6)

The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

The slope of the line = (6-(8) / (-4-7)

= 6+8 / -4-7

= 14 / -11

= - 14/11

Point slope form is

[tex]y-y_1=m(x-x_1)[/tex]

Substitute the value in the equation

y - 6 = -14/11(x - (-4))

y - 6 = -14/11(x + 4)

Therefore, the equation of the line is y - 6 = -14/11(x + 4)

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The value of integers m and n is 17 and 32 respectively.

Here, we are given that in a five-team tournament, each team plays one game with every other team.

Chance of winning = 50% or 1/2

We need to find the probability that at least one team wins all games or at least one team loses all games. We can use complementary counting to do so.

Each team will play 4 matches.

Probability that there is one team which wins all games = [tex]5*1/2^{4}[/tex]

= 5/16

Similarly, the probability that there is one team which loses all games = 5/16

The probability that one team wins all games and another team loses all games = [tex][5(1/2)^{4} ][4(1/2^{3})][/tex]

= (5/16)(4/8)

= 5/32

Now, 5/16 + 5/16 - 5/32 = 15/32

Since this is the complement of the probability we want, we subtract it from 1 to get (1- 15/32) = 17/32

Thus, the value of integers m and n is 17 and 32 respectively.

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Answer: 40

Step-by-step explanation:

P = a+b+c = 10+17+13 = 40

The number of sweets each friend gets = 6

The number of sweets s that each friend gets = the number of sweets in a box n ÷ number of friends f the sweets are shared between

s = n ÷ f

s = n/ f

if there are 48 sweets and 8 friends.

That is,

n = 48 sweets

f = 8 friends

Find s,

s = n/ f

= 48 / 8

= 6

s = 6 sweets

The number of sweets each friend gets = 6

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The volume of the rectangular solid with the given measures is equal to 972 cubic inches.

As given in the question,

Measures of edges of rectangular solid is given by :

1.5 feet by 1 1/2 feet by 3 inches

Conversion of feet to inches:

1 feet  = 12 inches

Let length = 1.5 feet

                 = 1.5 × 12

                 = 18inches

Width = 1 1/2 feet

          = ( 3/2 ) × 12

          = 18 inches

Height = 3 inches

Volume of the rectangular solid

= length ×width ×height

= 18 × 18 × 3

= 972 cubic inches

Therefore, the volume of the rectangular solid is equal to 972cubic inches.

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The minimum cost is 12.

The Vector r(u, v) with the domain D does not define a smooth parametrized surface.

Vector: Vectors are quantities that can be identified by magnitude and direction. Examples are velocity and acceleration.

Given that:

Vector r(u, v) = (cos(u), sin(v), 1), D = {(u, v)

Vector [tex]r_{u}[/tex] = (-sinU, 0,0)

Vector [tex]r_{V}[/tex] = (0, cosv,0)

Vector [tex]r_{u}[/tex] x Vector [tex]r_{V}[/tex] =

[tex]\left[\begin{array}{ccc}i&j&k\\-sinU&0&0\\0&cosv&0\end{array}\right][/tex]

Solving the vector multiplication. We get,

Vector [tex]r_{u}[/tex] x Vector [tex]r_{V}[/tex] = 0 x i - j x 0 + (cosv x - sinU)

Vector [tex]r_{u}[/tex] x Vector [tex]r_{V}[/tex] = 0 - sinUcosv

Vector [tex]r_{u}[/tex] x Vector [tex]r_{V}[/tex] =  - sinUcosv

Vector [tex]r_{u}[/tex] x Vector [tex]r_{V}[/tex] = (0, 0,- sinUcosv)

The Vector r(u, v) with the domain D does not define a smooth parametrized surface.

Vector [tex]r_{u}[/tex] x Vector [tex]r_{V}[/tex] = (0, 0,- sinUcosv) therefore has some value.

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Answer: 8.123 is a decimal

Step-by-step explanation:

A decimal is a whole number and a fractional part

there is a decimal point

Answer:

I guess it's 77 although I'm not in high school

Tom Pedalled his bike at a pace of 6 km/h and ran at a speed of 3 km/h.

Given,

Tom went on a bike ride;

Distance covered = 6 miles

Speed of bike = x

Speed of jogging = x - 3

Jogging is one hour more than bike ride

That is,

(6/x - 3) - (6/x) = 1

6 (x - x + 3 / x(x - 3)) = 1

18 / x² - 3x = 1

x² - 3x = 18

x² - 3x - 18 = 0

x² - 6x + 3x - 18 = 0

x(x - 6) + 3(x - 6) = 0

(x + 3) (x - 6) = 0

x = 6

That is,

Tom travelled at a speed of 6 km/hr with bike and 3 km/hr by jogging.

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The Taylor series expansion of f of x is given by 11e to the fourth power + 22e to the fourth power times x minus two plus 22e to the fourth power multiplied by x minus two all squared, where f of x is equal to 11e to the power of two x in rising powers of x minus two.

An infinite sum of words that are expressed in terms of a function's derivatives at a single point is known as the Taylor series or Taylor expansion of a function in mathematics.

Near this point, the function and the sum of its Taylor series are equivalent for the majority of common functions.

For Brook Taylor, who introduced the Taylor series in 1715, they are named after him. When 0 is the point at which the derivatives are taken into account, a Taylor series is also known as a Maclaurin series in honor of Colin Maclaurin, who made great use of this unique situation of Taylor series in the middle of the 18th century.

The nth Taylor polynomial of a Taylor series is a polynomial of degree n that is created by the partial sum of the first n + 1 terms of a Taylor series.

Hence, The Taylor series expansion of f of x is given by 11e to the fourth power + 22e to the fourth power times x minus two plus 22e to the fourth power multiplied by x minus two all squared, where f of x is equal to 11e to the power of two x in rising powers of x minus two.

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The probability that a single randomly selected value is more than 987 dollars is 0.5664

We know that probability is defined as the ratio of number of favorable outcomes to the total number of outcomes.

We know very well that z-value is calculate by the formula

z = (X-μ) / σ/√n

where z is the z-value,

X is randomly selected value,

μ is standard mean

σ is standard deviation and

n is the sample size.

For, X=987

=>z = (987-1037) / (243/√69)

=>z= -50 / (243 / 8.33)

=>z = -50 / (29.171)

=>z= -1.714

Now, we need to find the probability of A>987,so,we need to find what is the probability of A<=987.

P(X>987)= 1-P(X≤987)

=>P(X>987)=1-P(z<(-1.714))

Using the z-table ,we get that P(z<(-1.714))=0.43353

Therefore, P(X>987)=1-0.43353=0.5664

Hence, required probability is 0.5664

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(Complete question) is:

CNNBC recently reported that the mean annual cost of auto insurance is 1037 dollars. Assume the standard deviation is 243 dollars. You take a simple random sample of 69 auto insurance policies. (Do not use tables unless directed to do so.)

Find the probability that a single randomly selected value is more than 987 dollars. P(Â > 987).Enter your answers as numbers accurate to 4 decimal places.

The value of the variable 'p' for the given inequality is found as p > -1/5.

For the stated question-

-5p -1 > -10p - 2

Solve the inequality as

Add 1 both sides.

-5p -1 + 1 > -10p - 2 + 1

-5p  > -10p - 1

Add 10p both sides.

-5p  + 10p > -10p - 1 + 10p

5p > -1

Divide both sides by 5

p > -1/5

Thus, the value of the variable 'p' for the given inequality is found as p > -1/5.

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