Find and Interpret the mean absolute deviation of the data 5,8,8,10,13,14,16,22?

Answer:

[6, 8).

Step-by-step explanation:

When we are looking for the range of a function by just looking at the graph, we have to define from what point to what point the graph move vertically. On the other hand, if we were looking for the domain, we would state from where to where the graph moves horizontally.

In this case we have to analyze the graph vertically, since we are looking for the range of the function. Therefore, if we take a look at the line we can notice that it goes from y=6 to y=8. Therefore the range should be from 6 to 8.

Now, this result must be expressed in interval notation, meaning that we have to state whether the values of each end are contained or not by the function. The graph already tells us about it., because it marks it with the closed or open dots. In the case of the number 6, we have a closed dot, means that the function contains the number 6. For the other end we have an open dot, means that the function doesn't contain the number 8.

Applying internal notation, the range of this function is:

[6, 8).

Learn more about interval notation here:

1. https://web.nmsu.edu/~kberver/Unit1/Unit18.html#:~:text=An%20interval%20is%20closed%20if,used%20for%20an%20open%20endpoint.

2. https://brilliant.org/wiki/interval-notation/#:~:text=Interval%20notation%20is%20a%20way,inequality%20or%20system%20of%20inequalities.

Answer:

16

Step-by-step explanation:

just divide 528 by 33

Each person caught 5 fish.

Multiply 5 fish by total people.

5 x 9 = 45

Answer: 45 fish

Answer:

45 fish

Step-by-step explanation:

Given :

Solving :

a.) The value of pulses exported by US in billion would be=30 billion.

b.) The ratio of wheat export of UK to maize export of IND would be= 6:5

For question a.)

To calculate the pulses, the following steps should be taken as follows:

From the bar chart, the value of pulses in billions = 30 billions.

For question b.)

The ratio of wheat export at UK and maize export at IND would be calculated as follows:

The quantity of wheat export at UK = 24

The quantity of maize export at IND = 20

Therefore, the ratio of wheat to maize = 24:20= 6:5

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Answer:

D

Step-by-step explanation:

If you use pythagoroem theroem which is a^2 + b^2= c^2

you do 5 x 5= 25

12 x 12= 144

25+144= 169

169 square root = 13

the missing angle is 13

For this right triangle drawn on the coordinate plane, The calculation could be used to find the length of AC that will be (25+144)

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

It is given that the base, perpendicular, and hypotenuse of the right angle are as,

AB=12

BC=5

AC=?

Apply the Pythagoras theorem in ΔABC

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

h²=p²+b²

AC²=BC²+AB²

AC²=(5)²+(12)²

AC²=25+144

Thus, for this right triangle drawn on the coordinate plane, The calculation could be used to find the length of AC that will be (25+144)

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Answer:

9

Step-by-step explanation:

Y intercept when x = 0

Y = 9

where m is slope and b is y-intercept

Hence,

Here given equation: y = ½ x + 9

Identify,

slope: ½ and y-intercept: 9

Answer:

A. In vertex form, f(x) = 2(x - 2)² +1 and therefore has a minimum value of 1.

Step-by-step explanation:

Function is given as;

f(x) = 2x² - 8x + 9

From quadratic formula, we know that;

a = 2

b = -8

c = 9

Now, x-coordinate of the vertex is;

x = -b/2a

x = -(-8)/2(2)

x = 2

Let's find the y-coordinate;

f(2) = 2(2)² - 8(2) + 9

f(2) = 8 - 16 + 9

f(2) = 1

Thus, y-coordinate = 1

This means the vertex coordinate is (2, 1)

Now, vertex form of a quadratic equation is;

f(x) = a(x - h)² + k

Where, (h, k) is the coordinate of the vertex and a is the first term as earlier seen.

Thus;

f(x) = 2(x - 2)² + 1

Now, the leading coefficient is positive and so it means that the parabola will open upwards and thus, will have a minimum value of 1.

Answer:

C

Step-by-step explanation:

so we are given our equation in point-slope form; y-y1=m(x-x1). (x1,y1) is a point, where m is the slope.

Perpendicular lines have slopes that are negative and reciprocal; when you multiply them, they are equal to -1.

The slope of our line is 2.

To find the slope of the new line, use this equation:

2m=-1

divide by 2

m=-1/2

so the slope of our new line is -1/2

as said above, slope-point form is y-y1=m(x-x1)

we are given the point (-3,-5)

substitute our info into the equation:

y--5=-1/2(x--3)

or:

y+5= -1/2(x+3)

the answer is C

Hope this helps!

9514 1404 393

Answer:

Step-by-step explanation:

Consider the answer choices.

  3 & 5: product 15, sum 8 . . . . product > sum

  2 & 2: product 4, sum 4 . . . . product = sum (not >)

  1 & 4: product 4, sum 5 . . . . product < sum (not >)

Of the offered choices there are two counter examples:

  2 and 2

  1 and 4

_____

Additional comment

Chances are that the preferred answer is 1 and 4.

1 and <anything> will be a counterexample.

Answer:

Yes

Step-by-step explanation:

'

Yes, this F(x) is a polynomial function involving the first and null integer powers of x:  x^0 and x^1.

Answer: You didn't give answer choices but I think the answer would be (17, 73/3)

The restrictions on the width is that it must be between 14.1 yards and 17.3 yards

From the question, we have the following parameters that can be used in our computation:

Area = between 240 yd² and 360 yd²

Also, we have

Length = 1.2 times the width

This means that

l = 1.2w

The area is then calculated as

Area = lw

So, we have

Area = 1.2w²

This means that

240 < 1.2w² < 360

Divide through by 1.2

200 < w² < 300

Take the square roots

14.14 < w < 17.32

Approximate

14.1 < w < 17.3

Hence, the width must be between 14.1 yards and 17.3 yards

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Answer:

Step-by-step explanation:

I do know give me brainliest first

Answer:

24 gift bags

Step-by-step explanation:

Well first the question says to find the GCF and you find that by finding prime factors in each number. Then you would want to subtract 96-72 and get the answer of 24 so you would be able to make 24 gift bags. Hope this helps!!

May I have heart, 5 star, and brainliest please?

Answer:  geometric series

Step-by-step explanation:

If it is arithmetic, the difference from each term to the next will always be the same.

4096 - 1024 = 3072; 1024 - 256 = 768

3072 ≠ 768. so not arithmetic

If it is geometric, the ratio of each term to the next will always be the same.

4096/1024 = 4

1024/256 = 4

256/64 = 4

64/16 = 4

This is a geometric series. Each term (after the first) is (1/4) of the term before.

Hope this helps.

The inverse function of f(x) = 3x + 5 is given as follows:

C. p(x) = 1/3x - 5/3.

The function in the context of this problem is defined as follows:

f(x) = 3x + 5.

To obtain the inverse function, first we must exchange the variables x and y, hence:

y = 3x + 5

x = 3y + 5.

Now we must isolate the variable y, hence:

3y = x - 5

y = (x - 5)/3.

p(x) = 1/3x - 5/3.

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This question is of a topic called subset that is a part of set theory.

statement 1 is true. statement 2 is true. statement 3 is false, statement 4 is true.

I assume the questioner has the basic understanding of set theory and what subsets are.

Statement 1st "{1,2,3,4,5} ⊄ {1,2,4}" is true because here not every element of set {1,2,3,4,5} is an element of set {1,2,4}.

Statement 2nd "{11, 13, 15} ⊂ { 11, 12, 13, 14, 15, 16, ... }"  that is set {11, 13, 15} is a proper subset of set { 11, 12, 13, 14, 15, 16, ... } is true since every element of set {11, 13, 15} belongs to set { 11, 12, 13, 14, 15, 16, ... } also set

{11, 13, 15} is not equal to set  { 11, 12, 13, 14, 15, 16, ... }.

statement 3rd "∅ ⊈ {d, f, g, n}" is false since ∅ = null set is the subset of every set.

statement 4th "{21, 22, 23, 26, 29} ⊆ {21, 22, 23, 26, 29}" is true both sets have same elements therefore are subsets of each other and hence both are also equal to each other.

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Answer:

6

Step-by-step explanation:

h=3(12/6)

Answer:

13,074

Step-by-step explanation:

Jefferson has 3 times as many students as Washington. Multiply 4,358 times 3.

4358 x 3 = 13,074

The expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.

The standard deviation is a measurement of how widely apart a set of numbers or statistics are from their mean.

The expected value for the amount of money made selling all of the candy in one bag can be found by;

Expected value = mean number of candy bars per bag x price per candy bar

Expected value = 12 x $1.25 = $15

Formula for the standard deviation of a product of random variables:

\(SD (XY) = \sqrt{((SD(X)^2)(E(Y^2)) + (SD(Y)^2)(E(X^2)) + 2(Cov(X,Y))(E(X))(E(Y)))}\)

where X and Y are random variables, SD is the standard deviation, and Cov is the covariance.

X is the number of candy bars in a bag, which has a mean of 12 and a standard deviation of 2. Y is the price per candy bar, which is a constant $1.25. So we have:

E(Y²) = $1.25² = $1.5625

E(X²) = (SD(X)²) + (E(X)²) = 2² + 12² = 148

Cov (X,Y) = 0 (because X and Y are independent)

Using these values, we can calculate the standard deviation for the amount of money made selling all of the candy in one bag:

\(SD = sqrt((2^{2} )(148) + (0)(12)(1.25)^{2} + 2(0)(2)(12)(1.25))\)

SD = √(592)

SD ≈ $24.33

Therefore, the expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.

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Answer:

\(f(2)=19\)

Step-by-step explanation:

\(f(x) =2(3^{x} )+1\)

\(f(2)= 2(3^{2})+1\)

\(f(2)= 2(9) +1\)

\(f(2)= 18+1\)

\(f(2)=19\)

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Answer:

Step-by-step explanation:

F(-2) = 13

Answer:

1. Not possible

2. Possible

3. Possible

4. Possible

Step-by-step explanation:

Answer the answer is b. 6 tickets cost $30

Step-by-step explanation:

Answer:

Felipa is correct

Step-by-step explanation:

carl

\(6-4(4-6x)+12x\\\\2(4-6x)+12x\) this is incorrect by PEMDAS  he should have multiplied the 4 by 4-6x and then add with 6

so Felipa is correct

Answer:

\(\frac{1}{3}\)

Step-by-step explanation:

Three feet make a yard, so 2 yards is 6 feet

\(\frac{2}{6}\)  If we divide the top (numerator) and the bottom (denominator) by 2 we get

\(\frac{2}{6}\) ÷ \(\frac{2}{2}\) = \(\frac{1}{3}\)

Answer:

Given equation:

\(10^{5x-2}=2^{8x-3}\)

Take natural logs of both sides:

\(\implies \ln 10^{5x-2}= \ln 2^{8x-3}\)

\(\textsf{Apply log Power law}: \quad \ln_ax^n=n\ln_ax\)

\(\implies (5x-2)\ln 10=(8x-3) \ln 2\)

Expand brackets:

\(\implies 5x\ln 10 - 2\ln 10=8x \ln 2 -3 \ln 2\)

Collect like terms:

\(\implies 5x\ln 10 - 8x \ln 2 =2\ln 10-3 \ln 2\)

Factor left sides:

\(\implies x(5\ln 10 - 8 \ln 2) =2\ln 10-3 \ln 2\)

\(\textsf{Apply log Power law}: \quad \ln_ax^n=n\ln_ax\)

\(\implies x(\ln 10^5 - \ln 2^8) =\ln 10^2- \ln 2^3\)

\(\textsf{Apply log Quotient law}: \quad \ln_a\frac{x}{y}=\ln_ax - \ln_ay\)

\(\implies x\left(\ln\left(\dfrac{10^5}{2^8}\right)\right) =\ln\left(\dfrac{10^2}{2^3}\right)\)

Simplify:

\(\implies x\left(\ln\left(\dfrac{3125}{8}\right)\right) =\ln\left(\dfrac{25}{2}\right)\)

\(\implies x=\dfrac{\ln\left(\dfrac{25}{2}\right)}{\ln\left(\dfrac{3125}{8}\right)}\)

\(\implies x=0.4232297737...\)

Answer:

-2

Step-by-step explanation:

The page numbers are 265 and 266.

An integer can be described as numbers that  has no decimal or fractional part , this can be negative and positive numbers as well as  zero.

let the Left page number be n

let the Right page number  to be (n + 1)

Then the equation become

\([n + (n + 1) = 511]\)

then 2n + 1 = 531

2n = 530

n = 265

Therefore the  page numbers are 265 and 266.

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Answer:

The dispersion among sample means is less than the dispersion among the sampled items themselves because:______

b. Very large values are averaged down

Step-by-step explanation:

The sample means represent average values obtained from both large and moderate values.  Through the process of averaging, the data values obtained as the sample means are much closer to the true values.  This is why the dispersions among the sampled items will be larger than the dispersions among the sample means.  Sample dispersions describe how spread out the data values are on the number line.

Answer:

\(h(x)=\frac{1}{2}x -\frac{1}{2} .\)

Step-by-step explanation:

if the initial function is f(x)=2x+1, then

x=2*h(x)+1;

2h(x)=x-1;

\(h(x)=\frac{x}{2} -\frac{1}{2}.\)

PS. change design according the local requirements.

Answer:

\(y^{-1} =\frac{1}{2} x-\frac{1}{2}\)

Step-by-step explanation:

To find the inverse, you want to swap the inputs with the outputs, which is why you have the swapped domain and range between a function and its range.

So, given f(x)=2x+1, its inverse would give,

x=2y+1.

Solve for y,

2y=x-1 -> y=(x-1)/2 -> y=\(\frac{1}{2} x-\frac{1}{2}\)

Therefore, \(y^{-1} =\frac{1}{2} x-\frac{1}{2}\)

Answer:

(A)

Step-by-step explanation:

The survey follows of women's height a normal distribution.

The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.

The new height requirements would be 57.7 to 68.6 inches

The given parameters are:

\mathbf{\mu = 63.5}μ=63.5 --- mean

\mathbf{\sigma = 2.5}σ=2.5 --- standard deviation

(a) Percentage of women between 58 and 80 inches

This means that: x = 58 and x = 80

When x = 58, the z-score is:

\mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

This gives

\mathbf{z_1= \frac{58 - 63.5}{2.5}}z

1

=

2.5

58−63.5

\mathbf{z_1= \frac{-5.5}{2.5}}z

1

=

2.5

−5.5

\mathbf{z_1= -2.2}z

1

=−2.2

When x = 80, the z-score is:

\mathbf{z_2= \frac{80 - 63.5}{2.5}}z

2

=

2.5

80−63.5

\mathbf{z_2= \frac{16.5}{2.5}}z

2

=

2.5

16.5

\mathbf{z_2= 6.6}z

2

=6.6

So, the percentage of women is:

\mathbf{p = P(z < z_2) - P(z < z_1)}p=P(z<z

2

)−P(z<z

1

)

Substitute known values

\mathbf{p = P(z < 6.6) - P(z < -2.2)}p=P(z<6.6)−P(z<−2.2)

Using the p-value table, we have:

\mathbf{p = 0.9999982 - 0.0139034}p=0.9999982−0.0139034

\mathbf{p = 0.9860948}p=0.9860948

Express as percentage

\mathbf{p = 0.9860948 \times 100\%}p=0.9860948×100%

\mathbf{p = 98.60948\%}p=98.60948%

Approximate

\mathbf{p = 98.61\%}p=98.61%

This means that:

The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.

So, many women (outside this range) would be denied the opportunity, because they are either too short or too tall.

(b) Change of requirement

Shortest = 1%

Tallest = 2%

If the tallest is 2%, then the upper end of the shortest range is 98% (i.e. 100% - 2%).

So, we have:

Shortest = 1% to 98%

This means that:

The p values are: 1% to 98%

Using the z-score table

When p = 1%, z = -2.32635

When p = 98%, z = 2.05375

Next, we calculate the x values from \mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

Substitute \mathbf{z = -2.32635}z=−2.32635

\mathbf{-2.32635 = \frac{x - 63.5}{2.5}}−2.32635=

2.5

x−63.5

Multiply through by 2.5

\mathbf{-2.32635 \times 2.5= x - 63.5}−2.32635×2.5=x−63.5

Make x the subject

\mathbf{x = -2.32635 \times 2.5 + 63.5}x=−2.32635×2.5+63.5

\mathbf{x = 57.684125}x=57.684125

Approximate

\mathbf{x = 57.7}x=57.7

Similarly, substitute \mathbf{z = 2.05375}z=2.05375 in \mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

\mathbf{2.05375= \frac{x - 63.5}{2.5}}2.05375=

2.5

x−63.5

Multiply through by 2.5

\mathbf{2.05375\times 2.5= x - 63.5}2.05375×2.5=x−63.5

Make x the subject

\mathbf{x= 2.05375\times 2.5 + 63.5}x=2.05375×2.5+63.5

\mathbf{x= 68.634375}x=68.634375

Approximate

\mathbf{x= 68.6}x=68.6

Hence, the new height requirements would be 57.7 to 68.6 inches