the mean annual income for adult women in one city is $28,520 and the standard deviation of the incomes is $5000. the distribution of incomes is skewed to the right. suppose that we select samples of size 43. determine whether the sampling distribution for is normal (or approximately normal) and give its mean and standard deviation.

Answer:

[tex] \frac{1}{ \sqrt{10} } [/tex]

The values of x and y in the triangle are 15 and 88 degrees.

A triangle is a polygon with 3 sides. The sum of angles in a triangle is 180 degrees.

A triangle can be classified base on its sides and angles as equilateral triangle, isosceles triangle and scalene triangles.

An equilateral triangle has three of its sides and angles equal to each other.

An isosceles triangle has 2 sides and angles equal to each other.

A scalene triangle has no sides equal to each other.

Therefore,

The other triangle on the left side is an equilateral triangle.

Therefore, all it sides and angles are equal.

Hence, each angle of the triangle is 60 degrees.

A traversal line cut across the sides of the parallel lines of the triangles formed.

Therefore,

60° = 4x

x = 60 / 4

x = 15

Therefore,

60 + y + 32 = 180(sum of angles in a triangle)

y = 180 - 92

y = 88°

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Percentage spent on transportation is 12%

Percentage spent on Property tax is 11%

Percentage spent on utilities is 9%

Percentage spent on food is 20%

Percentage spent on mortgage payment is 30%

Percentage spent on entertainment is 8%

Percentage spent on miscellaneous is 10%

What are the percentages?

Percentage is the fraction of a number expressed as a number out of 100. In order to convert a number of fraction to percentage, multiiply by 100. The sign that is used to represent percentage is %.

Percentage spent on transportation = (576 / 4800) x 100 = 12%

Percentage spent on Property tax = (528 / 4800) x 100 = 11%

Percentage spent on utilities = (432 / 4800) x 100 = 9%

Percentage spent on food = (960 / 4800) x 100 = 20%

Percentage spent on mortgage payment = (1440 / 4800) x 100 = 30%

Percentage spent on entertainment = (384 / 4800) x 100 = 8%

Percentage spent on miscellaneous = (480 / 4800) x 100 = 10%

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The angle of labour, Conservative Lib Democrat Other is 138, 192, 24 and 6 degree respectively.

The table shows the votes of 900 people in the last elections.

Political Party    Frequency     Angle in

Labour                    345

Conservative          480

Lib Democrat           60

Other                        15

345 + 480 + 60 + 15 = 900

The total angle in a pie chart is 360

The angle for labour is = 360 (345 / 900) = 138 degree

The angle for Conservative is = 360 (480 / 900) = 192 degree

The angle for Lib democrate is = 360 (60 / 900) = 24 degree

The angle for others is = 360 (15 / 900) = 6 degree

Therefore, the angle of labour, Conservative Lib Democrat Other is 138, 192, 24 and 6 degree respectively.

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The categories of the functions are:

The category of the functions are given as

As a general rule, linear functions can take any of the following forms

Where the variables a, A, m, b, B, c and C are real numbers

Any equation that do not have the above form is considered a nonlinear function

Using the above forms as a guide, we have the linear equations to be

(16) y = 7 - x  (17) y = ∛8 - x (19) 2 + y = x + 4 (21) x -y = |-54|

All other equations are nonlinear equations

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Answer:

50 degrees

Step-by-step explanation:

Line CDF is 180 degrees

76 and 54 and some part of the 180 degrees

1. add 76+54 = 130

2. subtract 180-130 = 50

Answer:

10

Step-by-step explanation:

Right angles add up to 90

5x + 4x = 90

9x = 90  Divide both sides by 9

x = 10

Answer:

3x+6-14

Step-by-step explanation:

The coordinates of the triangle FGH after dilating by 1/2 is F'(-2, -5/2), G'(-3/2, -1), and H'(-1/2, -3/2)

From the question, the given parameters are the vertices of Triangle FGH

The vertices are represented as

F(-4, -5), G(-3, -2), and H(-1, -3).

Also, from the question, we have

The scale factor of dilation is

k = 1/2

The above implies that

k represents the scale factor of dilation

The coordinates after the dilation is calculated as

Image of dilation = Vertices of the triangle x Scale factor

Substitute the known values in the above equation

So, we have

Image of dilation = [F(-4, -5), G(-3, -2), and H(-1, -3)] x 1/2

Evaluate the products

So, we have

Image of dilation = F'(-2, -5/2), G'(-3/2, -1), and H'(-1/2, -3/2)

Hence, the image after the dilation is F'(-2, -5/2), G'(-3/2, -1), and H'(-1/2, -3/2)

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Answer:

Option 1. This is a vertical pair of angles because they are two nonadjacent (not next to each other) angles formed by intersecting lines. The sides of one angle are the opposite rays to the sides of the other angle. (Angle 5=Angle 7)

Option 2 and 4 are wrong as the angles are not created by a set of parallel lines and a transversal.

Option 3 is wrong as the angles are not adjacent.

Option 5 is wrong as the angles do not have a sum of 90°.

Answer:

[tex]x=\frac{vw}{k-y}[/tex]

Step-by-step explanation:

Answer: b (-1,1)

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

Substitute x with 2 and y with 2

2 = 2 * 2 + a

2 = 4 + a

subtract 4 on both sides

2  = 4 + a

-4    -4

-2 = a

Answer:

Step-by-step explanation:

since they are verticle angles:

8x+7=9x-4

subtract 8x and add 4

x=11

Answer:

(4, 1 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) , then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = C (1, 9 ) and (x₂, y₂ ) = D (7, - 7 ) , then

midpoint = ( [tex]\frac{1+7}{2}[/tex] , [tex]\frac{9-7}{2}[/tex] ) = ( [tex]\frac{8}{2}[/tex] , [tex]\frac{2}{2}[/tex] ) = (4, 1 )

Answer:

Step-by-step explanation:

12 times 2 =24 60 into 10 so i think it will be 6

Answer:

A' = (6, 3)

B' = (1, 1)

C' = (8, 7)

Step-by-step explanation:

Vertices of triangle ABC:

Given mapping rule:

(x, y) → (x + 4, y + 6)

This notation tells you that the x-coordinate is translated 4 units to the right, and the y-coordinate is translated 6 units up.

Substitute the coordinates of each point into the mapping rule to find the vertices of triangle A'B'C':

⇒ A' = (2 + 4, -3 + 6) = (6, 3)

⇒ B' = (-3 + 4, -5 + 6) = (1, 1)

⇒ C' = (4 + 4, 1 + 6) = (8, 7)

The probability that exactly 10 customers will use the atm during the next noon lunch hour is 0.0948

From the question, we have the following parameters:

Average number of customers = 12

Number of customers = 10

The above parameters means that:

x = 10

λ = 12

The probability of a Poisson distribution is represented as

P(x) = λˣe⁻λ/x!

This gives

P(x = 12) = 10¹² * e⁻¹⁰/12!

Evaluate

P(x = 12) = 10¹² * e⁻¹⁰/479001600

Solving further, we have

P(x = 12) = 0.0948

Hence, the probability is 0.0948

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Answer:

a) 132 g oat cereal, 132 g pretzels, 66 g nuts

b) 84 g oat cereal, 84 g pretzels, 42 g nuts

c) 200 g oat cereal, 200 g pretzels, 100 g nuts

d) 300 g oat cereal, 300 g pretzels, 150 g nuts

Step-by-step explanation:

a) 330 = 5x

x=66

132 oat cereal

132 pretzels

66 nuts

(And repeat for all masses)

:] Tell me if this is incorrect!

(Brainliest would help a lot lol)

Answer:

1. 1.4, 1 5/8, 12/5, 8/8

2. 0.88

3. 1/4 and 8/8

4. 12/5 and 2/100

5. 1 5/8 and 1.625

6. 1 1/2

The values of u and v that makes △QRS and △IKJ congruent triangles are u = 7 and v = 3

The triangles are given as

△QRS and △IKJ

The statement △QRS≅△IKJ means that

The triangles △QRS and △IKJ are congruent triangles

This means that the corresponding sides are congruent

So, we have the following equations:

v + u + 15 = 10u - 15v

-4u + 2v + 99 = 7v + 8u

Evaluate the like terms

So, we have

9u - 16v = 15

12u + 5v = 99

Make u the subject in 12u + 5v = 99

So, we have

u = (-5v + 99)/12

Substitute u = (-5v + 99)/12 in 9u - 16v = 15

9(-5v + 99)/12 - 16v = 15

So, we have

9(-5v + 99) - 192v = 180

Open brackets

-45v + 891 - 192v = 180

Evaluate the like terms

-237v = -711

Divide by -237

v = 3

Substitute v = 3 in u = (-5v + 99)/12

u = (-5 x 3 + 99)/12

Evaluate

u = 7

Hence, the values are u = 7 and v = 3

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Solution:

The confidence interval is expressed as

where

Given a 99% confidence interval for a sample size of 891 with a mean of 20.8 and a standard deviation of 17.6, this implies that

By substituting these values into the above equation, we have

Hence, we have

The statement mentions that the pool started empty, which implies that the graph must start at the point (0,0).

Then, the pool slowly filled, so the amount of water in the pool remained constant when Janie turned off the water and went for a walk.

Finally, thanks to a truck in the neighborhood the pool filled up quickly, and when it was filled the amount of water remained constant.

Therefore, the graph that best represents this situation is the one shown in option B.

Answer:

x=50

Step-by-step explanation:

5(2-x)-10=25-2(3x+40)

Distribute:

10-5x-10=25-6x-80

Combine like terms

-5x-10=-6x-55

Put x to one side

x-10=-55

Make x by itself

x=-55

Answer:  x=−55

Step-by-step explanation:

Solve the equation step-by-step:

5(2−x)−10=25−2(3x+40)

Simplify both sides:

5(2−x)−10=25−2(3x+40)

Distribute:

(5)(2)+(5)(−x)+−10=25+(−2)(3x)+(−2)(40)

10+−5x+−10=25+−6x+−80

Combine Like Terms:

(−5x)+(10+−10)=(−6x)+(25+−80)

−5x=−6x+−55

−5x=−6x−55

Add 6x to both sides.

−5x+6x=−6x−55+6x

x=−55

Answer:

his age would be 72.

300-84=216

216÷3 is 72

The system of equations that could be used to determine the number of drinks and the number of tacos that Jordan bought are 2.5x + 2y = 26 and y = x + 4.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

Let's assume that number of drinks that Jordan and his children bought is x while the number of tacos is y.

The cost of drinks = 2.50x

Cost of tacos = 2y

Total cost 2.5x + 2y

2.5x + 2y = 26

Given that,

He bought 4 more tacos than drinks.

Therefore,

y = x + 4.

Hence "The system of equations that could be used to determine the number of drinks and the number of tacos that Jordan bought are 2.5x + 2y = 26 and y = x + 4".

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The midpoint between the given figures are -2.5 and 5.5 respectively.

A midpoint is defined as that particular point that divides two separate figures into two equal halves or the centre of two endpoints on a number line.

That is;

point a + point b/2

The figures given are :

Point a = -3

Point b = -2

= -3 + -2/ 2

= -5/2

= -2.5

For points 4 and 7 ;

= 4 + 7 / 2

= 11/2

= 5.5

Therefore, the middle or midpoint of -3 and -2 is -2.5 and the midpoint for 4 and 7 is 5.5.

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The quadratic function of h (x) in vertex form will be as h(x) = (x + 2)² − 3

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Given that the values of x and h (x) for the quadratic function is given by;

x = -3, -2, -1, 0, 1, 2, 3,

h (x) = -2, -3, -2, 1, 6, 13, 22

Consider the quadratic function as;

h (x) = ax² + bx + c

Now Substitute x = -3 and h (x) = -2 in quadratic function we get;

h (x) = ax² + bx + c

- 2 = a × (-3)² + b × -3 + c

- 2 = 9a - 3b + c

And, Plug x = -2 and h (x) = -3 in function we get;

h (x) = ax² + bx + c

- 3 = a × (-2)² + b × -2 + c

- 3 = 4a - 2b + c

And, plug x = -1 and h (x) = -2 in function we get;

h (x) = ax² + bx + c

- 2 = a × (-1)² + b × -1 + c

- 2 = a - b + c

After solving we get:

a = 1 , b = 4 and c = 1

Then

h (x) = ax² + bx + c

h (x) = 1 × x² + 4x + 1

h (x) = x² + 4x + 1

h (x) = x² + 4x + 4 - 4 + 1

h (x) = (x + 2)² - 3

Hence, The quadratic function of h (x) in vertex form will be as h(x) = (x + 2)² − 3

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When writing a repeating decimal as fraction , the fraction do not always have only 9’s or 9’s and 0’s as digits in the denominator .

Repeating Decimal is a decimal in which after certain point a particular digit  or sequence of digit repeats itself infinitely  .

For Example : 0.66666666...    

When in a fraction the numerator is divided by the denominator , it is not at all necessary that the denominator will always have 9’s or 9’s and 0’s .

We can understand more with the help of an example .

example : 1/3 = 0.3333... is a repeating decimal , which does not have a 9 , 0 in the denominator .

(ii) 5/3 = 1.666666.... is a repeating decimal , which does not have a 9 , 0 in the denominator .

Therefore , When writing a repeating decimal as fraction , the fraction do not always have only 9’s or 9’s and 0’s as digits in the denominator .

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