Write an expression for "the quotient of z and 4

Answer:

x = -1 and y = 1/2

Step-by-step explanation:

Let u = 1/x, and v = 1/y

Then the pair of equations

-3/x + 4/y = 11

1/x - 2/y = -5

Can be written as

-3u + 4v = 11 .................................(1)

u - 2v = -5......................................(2)

From (2)

u = 2v - 5 .......................................(3)

Substituting (3) into (1)

-3(2v - 5) + 4v = 11

-6v + 15 + 4v = 11

-6v + 4v = 11 - 15

-2v = -4

v = 4/2 = 2

Substituting this value of v in (3)

u = 2v - 5

u = 2(2) - 5

= 4 - 5

= -1

That is

u = -1, v = 2

Since u = 1/x, and v = 1/y, we have

1/x = -1

=> x = -1

And

1/y = 2

=> y = 1/2

Therefore

x = -1 and y = 1/2

Answer:

61.76 ft^2

Step-by-step explanation:

First find the area of the rectangle without the circle

A = l*w = 14*8 =112

Then find the area of the circle

The diameter is 8 so the radius is 8/2 =4

A = pi r^2 = 3.14 * 16 =50.24

The shaded region is the rectangle minus the circle

112-50.24 =61.76 ft^2

Answer:

  parallel lines both have slope 1/3; non-parallel lines both have length 5

Step-by-step explanation:

It generally works well to follow instructions.

A graph of the points shows you that the parallel sides are RA and PT. The difference between the end points of these segments are ...

  A - R = (6, 8) -(-3, 5) = (9, 3) = (Δx, Δy)

So, the slope of RA is Δy/Δx = 3/9 = 1/3

And the other difference and slope are ...

  P -T = (9, 4) -(-3, 0) = (12, 4)   ⇒   Δy/Δx = 4/12 = 1/3

The slope of RA is the same as the slope of PT, so those segments are parallel.

__

The length of segment TR can be found from the differences of the end point coordinates:

  R - T = (-3, 5) -(-3, 0) = (0, 5)

Since these points are on the same vertical line, this tells us the segment length is 5.

The other difference of coordinates is ...

  A - P = (6, 8) -(9, 4) = (-3, 4)

The distance formula tells us the length of AP is then ...

  AP = √((-3)² +4²) = √25 = 5

Non-parallel sides TR and AP have the same lengths, so the trapezoid is isosceles.

Answer:

Step-by-step explanation:

There's no plot, but I can give you this: Median is better with a large outlier, while mean is better for symmetry. Therefore, the correct answer would be either the first or fourth. Ofc, we can't see the plot so that's all I can give you.

Hope that helped,

-sirswagger21

Answer:both sides will be equal

Step-by-step explanation:

Answer:

[tex] E(X) =1 *\frac{1}{5} +2 *\frac{2}{5} +7*\frac{2}{5}= 3.8[/tex]

Now we can find the second moment with this formula:

[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i)[/tex]

And replacing we got:

[tex] E(X^2) =1^2 *\frac{1}{5} +2^2 *\frac{2}{5} +7^2*\frac{2}{5}= 21.4[/tex]

The variance would be given by:

[tex] Var(X) =E(X^2) -[E(X)]^2 = 21.4 -[3.8]^2 = 6.96[/tex]

And the deviation would be:

[tex] Sd(X) =\sqrt{6.96}= 2.638[/tex]

Step-by-step explanation:

For this case we have the following distribution given:

X      1      2      7

P(X) 1/5  2/5   2/5

We need to begin finding the mean with this formula:

[tex] E(X) = \sum_{i=1}^n X_i P(X_i)[/tex]

And replacing we got:

[tex] E(X) =1 *\frac{1}{5} +2 *\frac{2}{5} +7*\frac{2}{5}= 3.8[/tex]

Now we can find the second moment with this formula:

[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i)[/tex]

And replacing we got:

[tex] E(X^2) =1^2 *\frac{1}{5} +2^2 *\frac{2}{5} +7^2*\frac{2}{5}= 21.4[/tex]

The variance would be given by:

[tex] Var(X) =E(X^2) -[E(X)]^2 = 21.4 -[3.8]^2 = 6.96[/tex]

And the deviation would be:

[tex] Sd(X) =\sqrt{6.96}= 2.638[/tex]

Answer:

b

Step-by-step explanation:

Answer:

he

Step-by-step explanation:

hi

Answer:

1008

Step-by-step explanation:

to find the number of combinations, just multiply everything. you will get 1008 :)

Answer:

sorry'but I don't know the answer

Answer:

C.

Step-by-step explanation:

1/2r = 2π/Cb

Answer:

80% confidence interval of the true average number of hours of TV watched per week is [8.28 hours, 11.02 hours].

Step-by-step explanation:

We are given that a college student is interested in investigating the TV-watching habits of her classmates and surveys 20 people on the number of hours they watch per week. The results are provided below;

Hours of TV per week (X): 6, 14, 13, 6, 16, 10, 19, 4, 5, 5, 18, 8, 7, 14, 8, 8, 9, 12, 6, 5.

Firstly, the Pivotal quantity for 80% confidence interval for the true average is given by;

                                P.Q. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean number of hours of TV watched per week = [tex]\frac{\sum X}{n}[/tex] = 9.65

            s = sample standard deviation = [tex]\sqrt{\frac{\sum (X -\bar X)^{2} }{n-1} }[/tex]  = 4.61

            n = sample of people = 20

           [tex]\mu[/tex] = true average number of hours of TV watched per week

Here for constructing 80% confidence interval we have used One-sample t-test statistics as we don't know about population standard deviation.

So, 80% confidence interval for the true average, [tex]\mu[/tex] is ;

P(-1.33 < [tex]t_1_9[/tex] < 1.33) = 0.80  {As the critical value of t at 19 degrees of

                                               freedom are -1.33 & 1.33 with P = 10%}  

P(-1.33 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 1.33) = 0.80

P( [tex]-1.33 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.33 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.80

P( [tex]\bar X-1.33 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.33 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.80

80% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.33 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+1.33 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                         = [ [tex]9.65-1.33 \times {\frac{4.61}{\sqrt{20} } }[/tex] , [tex]9.65+1.33 \times {\frac{4.61}{\sqrt{20} } }[/tex] ]

                                         = [8.28 hours, 11.02 hours]

Therefore, 80% confidence interval of the true average number of hours of TV watched per week is [8.28 hours, 11.02 hours].

if percent of 1 year was 5%:

meaning time between accidents must be atleast 1 week

The mean waiting time that exists between the accidents would be:

- 1 week

'Mean waiting time' is determined through the contemplated value of an odd(random/casual) variable.

Given that,

Probability(P) of no accident taking place in 1 year = 5%

Assuming T be the accidents' number that takes place during a year,

Since 5% is the probability or chance of no accident to take place,

The mean waiting time between accidents = 1 week at least via Poisson process.

Thus, 1 week would be the correct answer.

Learn more about 'Mean' here:

brainly.com/question/521501

Answer:

efdm3rndne

Step-by-step explanation:

nenejej4ree2wiwiwwi3ieiej

Answer:

-8/5

Step-by-step explanation:

x/3+1= 7/15

x/3= 7/15-1

x/3=  -8/15

x= - 8/5

Answer:

Log 110 = 2.041

Step-by-step explanation:

Log 110 can be simplified and reduced to

Log 110 = log (10*11)

Log 110 = log10 + log11

But log10 = 1

Log 11= unknown = x

10^x= 11

X= 1.0413926

Log 110 = 1+1.0413926

Log110 = 2.0413926

Log 110 = 2.041

Answer:

  24.2

Step-by-step explanation:

You are given the hypotenuse and angle, and you want to find the length of the adjacent side.

The mnemonic SOH CAH TOA reminds you that the relation between angle and sides is ...

  Cos = Adjacent/Hypotenuse

  cos(41°) = x/32

  x = 32·cos(41°)

  x ≈ 24.2

Answer:

-2 is an output of the function.

Step-by-step explanation:

The given table is as follows:

[tex]\left[\begin{array}{cc}{x}&f(x)\\-6&8\\7&3\\4&-5\\3&-2\\-5&12\end{array}\right][/tex]

Here, the values written on the left side of table i.e. values of [tex]x[/tex] are known as the domain values or input values to a function.

The values written on the right side of table i.e. values of [tex]f(x)[/tex] are known as the range values or output values of the function [tex]f(x)[/tex].

Let us consider the pairs of values:

(-6,8) then left side value is of [tex]x[/tex] and right side value is of [tex]f(x)[/tex]

i.e. when [tex]x=-6[/tex], the output value [tex]f(x) =8[/tex].

The same thing applies for all the pairs of values.

similarly for the pair (3,-2):

Left side value is of [tex]x[/tex] and right side value is of [tex]f(x)[/tex]

i.e. when [tex]x=3[/tex], the output value [tex]f(x) =-2[/tex].

So, the answer is:

-2 is an output of the function.

Answer:

-2

Step-by-step explanation:

Answer:

Eve gets 1.47 and Amelie gets 0.81

Step-by-step explanation:

the ratio is 9 to 5 so we can say 9x + 5x=2.28

14x=2.28

x=0.16

so eve gets 9x = 9(2.28/14) = 1.47

and amelie gets 5x = 5(2.28/14) = 0.81

Answer:

a. All measures exist

b. The Mean and the mode

c. Positively skewed

d. The mean and the median

Step-by-step explanation:

a. The frequencies of the data are;

1       2

2      4

3       1

5       2

6       3

9        1

11        1

14        1

15       1

18       1

The formula for mode is given as follows;

The mean = 108/17 = 6.35

The median of 1 1 2 2 2 2 3 5 5 6 6 6 9 11 14 15 18 = (n + 1)/2th term = 9th term  

∴ The median = 5

The mode = 3×Median - 2 × Mean = 15 - 2 × 6.35 = 2.29

Hence all exist

The answer is none theses measures

b. Whereby 18 is replaced by 39 the mean will be then be

(108 + 39 - 18)/17 = 7.59

The median, which is the 9th term remain the same;

Hence only the mean and mode will be affected

c. Since more values are concentrated on the left side of the data distribution, the distribution is positively skewed

d. The largest measurement = 18 the 17th term

Removal will give

Mean = (108 - 18)/16 = 5.625 Mean changes

Median = (16 + 1)/2 th term = 8.5th term = 5 The median remains the same

The mode = 3(Mean - Median) changes

Therefore, the mean and the median will be changed.

Answer:

Option c

Step-by-step explanation:

The study is an observational study. An observational study is made when the researchers collect data based on what they see, hear or observe without any form of manipulation or treatment plan from the researchers. Thus, in this case, the study is an observational study because the study examines individuals in a sample, but does not try to influence the response variable/influence their responses.

Answer:

0.0062

Step-by-step explanation:

Find the standard error.

σ = 20 / √100

σ = 2

Find the z-score.

z = (x − μ) / σ

z = (70 − 65) / 2

z = 2.5

Find the probability.

P(Z > 2.5) = 1 − 0.9938

P(Z > 2.5) = 0.0062

Answer:

Step-by-step explanation:

the complex number and its conjugate

Answer:

(1+3i)(1-3i)

Step-by-step explanation:

Answer:

3+6i

Step-by-step explanation:

I did it

Answer:3+6i

Step-by-step explanation:

Answer:

[tex] P(A) = 0.21[/tex]

We want to find the probability that a randomly selected freshman from this college does not take an introductory statistics class, so then we can use the complement rule given by:

[tex] P(A') = 1-P(A)[/tex]

Where A is the event of interest (a freshman at a certain college takes an introductory statistics class) and A' the complement (a freshman at a certain college NOT takes an introductory statistics class) and then replacing we got:

[tex] P(A')=1-0.21= 0.79[/tex]

Step-by-step explanation:

For this problem we know that the probability that a freshman at a certain college takes an introductory statistics class is 0.21, let's define of interest as A and we can set the probability like this:

[tex] P(A) = 0.21[/tex]

We want to find the probability that a randomly selected freshman from this college does not take an introductory statistics class, so then we can use the complement rule given by:

[tex] P(A') = 1-P(A)[/tex]

Where A is the event of interest (a freshman at a certain college takes an introductory statistics class) and A' the complement (a freshman at a certain college NOT takes an introductory statistics class) and then replacing we got:

[tex] P(A')=1-0.21= 0.79[/tex]

Answer:

Option c

Step-by-step explanation:

This is an experiment because the researcher wants to test efficiency of the magnetic bracelets in the elimination of motion sickness i.e. whether they experienced motion sickness even after wearing the magnetic bracelets.

Answer: this is a guess but 7.69 percent chance that you will pick a blue candy

Step-by-step explanation:

Answer:

Choosing 1 blue and 1 green candy

Step-by-step explanation:

There are no red candies and there is only 1 blue candy.

Suppose 43% of the population has a retirement account. If a random sample of size 774 is selected, what is the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 3%?

Answer:

the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 3% is 0.9082

Step-by-step explanation:

Given that:

sample size n = 774

Let P be the population proportion for having a retirement account  = 0.43

Also

Let consider [tex]\hat p[/tex] be the sample proportion of having a retirement account.

However; as n is > 30 ; we can say:

[tex]\mathbf{\mu_{\hat p} = 0.43}[/tex]  ;  

 [tex]\mathbf{\sigma_{\hat p^2} = \dfrac{p(1-p)}{n}}[/tex]  

⇒   [tex]\mathbf{\sigma_{\hat p^2} = \dfrac{0.43(1-0.43)}{774}}[/tex]

⇒ [tex]\mathbf{\sigma_{\hat p^2} = \dfrac{0.43(0.57)}{774}}[/tex]

So; we need  P( the sample proportion will differ from 'p' by less than 3% i.e 0.03)

[tex]=P(| \hat p- p|< 0.03)[/tex]

[tex]=P(| \hat p- \mu _p|< 0.03)[/tex]

[tex]= P ( |\dfrac{\hat P - \mu_p}{\sigma_{\hat p}}|< \dfrac{0.03}{\sqrt{ \dfrac{0.43*0.57}{774} }})[/tex]

[tex]= P(|Z|<1.6859)\ \ \ \ [Z=(\dfrac{\hat P - \mu_{\hat P}}{\sigma_{\hat P}}) \sim N(0,1)][/tex]

[tex]= P(-1.6859 <Z<1.6859) \\ \\ = \Phi(1.6859)- \Phi (-1.6859) \\ \\ = \Phi (1.6859) - (1- \Phi(1.6859) \\ \\ = 2 \Phi (1.6859)-1[/tex]

From Normal Cumulative Distribution Function Table

[tex]= 2*0.9541 -1[/tex]

= 1.9082 - 1

= 0.9082

Thus; the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 3% is 0.9082

Answer:

The correct option is;

The accident rate is a linear model function of t. After t = 7, the slope changes, with the two lines intersecting at t = 7

Step-by-step explanation:

The given parameters are;

Accident rate data = y₁, y₂, y₃, y₄, y₅, y₆, y₇, y₈, y₉, y₁₀, y₁₁, y₁₂

Time at which data was recorded = t₁, t₂, t₃, t₄, t₅, t₆, t₇, t₈, t₉, t₁₀, t₁₁, t₁₂

Accident rate equation is a linear model given as follows;

y = X·B + E

Where:

y = Accident rate

X = Slope of linear model

B = Year

E = y intercept of model

At the end of the 6th year, a change in a regulation that affects safety, hence accident rate occurred given as follows;

Before the change in safety regulations occurred for year t < 7 y₁ = X₁B + E₁

After the change in safety regulations occurred for year t < 7 y₂ = X₂B + E₂

Therefore the slope changes from X₁ to X₂ after t = 7 with the second linear model starting from the end of the first linear model making the two lines intersect at t = 7 (the beginning of year 7)

Hence the correct option is that "The accident rate is a linear model function of t. After t = 7, the slope changes, with the two lines intersecting at t = 7."

Answer: axiom

Step-by-step explanation:

[tex]answer \\ g(x) = |x - 2| + 1 \\ here \: f(x) = |x| \\ if \: we \: want \: to \: shift \: this \: function \: 2 \: \\ unit \: right \: then \: make \: transformation \\ \: of \: x \: by \: (x - 2) \\ and \: if \: we \: want \: to \: make \: function \: \\ goes \: up \: with \: 1 \: unit \: then \: transformation \\ is \: f(x) \: by \: f(x) + 1 \\ now \\ g(x) = |x - 2| + 1 \\ hope \: it \: helps[/tex]

Answer:

Step-by-step explanation:

In this scenario, cost depends on mileage. Thus cost is the dependent variable.

As a general rule, if you have the form ...

  a = (some expression involving b)

you will find that "a" is the dependent variable, and "b" is the independent variable.

This problem statement gives you ...

  c = (an expression involving m)

"c" is the dependent variable; "m" is the independent variable.

The independent variable is m and the  dependent variable is c.

The dependent variable is the outcome or result that is affected by the independent variable. The independent variable is the factor that is changed or manipulated in order to observe the effect on the dependent variable.

Given that, the cost to rent a moving truck is a flat fee of $25 plus $0.60 per mile.

The equation c = 25 + 0.6m models the cost, c, in dollars for the number of miles, m, traveled in the truck.

In the given equation c = 25 + 0.6m, c is the dependent variable and the m is the independent variable.

Therefore, the independent variable is m and the  dependent variable is c.

Learn more about the independent variable here:

brainly.com/question/29430246.

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