A survey found that the American family generates an average of 17.2 pounds of glass garbage each year. Assume the standard deviation of the distribution is 2.5 pounds. Find the probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds. Assume that the sample is taken from a large population and the correction factor can be ignored. Round your final
answer to four decimal places and intermediate z-value calculations to two decimal places

Answer:

i hope this helpes

Step-by-step explanation:

a) A group of 16 pays $40 + ($2 x (16 - 10)) = $40 + $6 = $46.

b) The cost function can be represented as C(x) = 40 + 2(x - 10) for x > 10 and C(x) = 40 for x <= 10, where x is the number of people in the group and C(x) is the cost for the group.

c) The domain of the cost function is all non-negative real numbers less than or equal to 50 (0 <= x <= 50), since the maximum group size is 50. The range of the cost function is all non-negative real numbers greater than or equal to 40 (C(x) >= 40), since the minimum charge for a group is $40.

Answer:

a) $52

b) C(x) = 40 + 2x, if x > 10 and x ≤ 50

C(x) = 40, if x ≤ 10

c) Domain = {x ≥ 1 and x ≤ 50}

Range = { from 40 to 140}

Answer: 16

Step-by-step explanation:

To get from 3 to 12, you multiply by 4

To get from 5 to 20, you multiply by 4

So you just multiply 4 by 4 to get x

Answer:

x = 16

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{x}{4}[/tex] = [tex]\frac{20}{5}[/tex] = 4 ( multiply both sides by 4 to clear the fraction )

x = 16

Answer:

Then the two numbers are -11 and -6.

Step-by-step explanation:

-11+-6= -17

They are -11 and -6.

-11 + -6 = -17  

-11 x -6 = 66.

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The statement that A triangular prism contains two parallel hexagonal faces is False

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

A triangular prism contains two parallel hexagonal faces.

As a general rule, the parallel faces in a triangular prism are triangles

This is so because a triangular prism is a 3-dimensional object with a triangular base and three rectangular sides.

The two parallel faces of a triangular prism are congruent triangles, not hexagons.

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The function that is represented by the graph is y = ∛(x + 3) + 3.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The general form of a cube root function is -

y = a∛(x - h) + k and the parent graph is y = ∛x.

So the parent function is found.

The coordinate point for the parent function is -

(-1,-1) , (0,0) and (1,1).

In the graph it can be seen that the coordinate points are -

(-4,2), (-3,3) and (-2,4)

So the graph is first moved 3 units up and then moved three units left.

So, the coordinated become - (x + (-3) , y + 3)

So, the function that represents the graph is -

y = ∛(x + 3) + 3

Therefore, the function is y = ∛(x + 3) + 3.

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Answer: 3/5

The total number of slices is 10, and the number of yellow or red slices is 2 yellow slices + 4 red slices = 6 slices.

So, the probability of the dial stopping on a yellow or red slice is 6 slices / 10 total slices = 3/5.

This is the final answer, and it is already in its simplest form.

A baker had 24 cupcakes and wanted to divide them equally among 8 friends. How many cupcakes would each friend receive?

The problem can be represented by 8/3 ÷ 4, where 8 represents the number of friends, 3 represents the number of cupcakes each friend should receive, and 4 represents the number of groups the cupcakes should be divided into.

The division makes sense because first, we need to find out how many cupcakes each friend should receive, which is 24 ÷ 8 = 3. Then, we divide the number of cupcakes each friend should receive by the number of groups to find out how many cupcakes each group should receive, which is 3 ÷ 4 = 0.75 cupcakes per group.

The value -2 is the rate of change of the linear equation.

A general linear equation is:

y = a*x + b

Where a is the rate of change and b is the y-intercept.

The rate of change tells us how the variable y changes when the variable x changes.

In this case we have:

y=-2x+10

So the "-2" is the rate of change, it tells us that each time that x increases 1 unit, the value of y decreases by 2 units.

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Answer:

u ≥ 2

Step-by-step explanation:

2u-5>7 :

Add 5 to both sides:

2u = 7 + 5

2u > 12

Divide by 2:

u > 6

-3u ≤ -6

Multiply both sides by -1, inequality reverses
-3u(-1) ≥ -6(-1)

3u ≥ 6

Divide by 3:

u ≥ 2

Since  u > 6  is a subset of u ≥ 2, the interval for both inequalities is

u ≥ 2

Answer:

E

Step-by-step explanation:

just looking for the ration if scale factor is 2

multiply it and fimd the ans

The explicit rule for the nth term of the geometric sequence: 3, 18, 108, 648, 3,888, … is aₙ = 3( 6ⁿ⁻¹ )

The geometric sequence is expressed as aₙ = a₁ × rⁿ⁻¹

Given the set of numbers in the question;

3, 18, 108, 648, 3,888, …

The first term a₁ = 3

Next, we determine the common ratio r.

Divide a term by the previous term gives the common ratio.

Common ratio r = 18/3

Common ratio r = 6

Now, plug in the values of first and common ratio into the above formula to determine the nth term.

aₙ = a₁ × rⁿ⁻¹

aₙ = 3 × 6ⁿ⁻¹

aₙ = 3( 6ⁿ⁻¹ )

Therefore, the nth term of the sequence is aₙ = 3( 6ⁿ⁻¹ ).

Option D) aₙ = 3( 6ⁿ⁻¹ ) is the correct answer.

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Step-by-step explanation:

well, you have it further up :

P(A) = 17x = 17 × 1/32 = 17/32 = 0.53125

Step-by-step explanation:

Cross multiply to solve for "a":

6 * a = 8 * 8

Simplify the right side:

6 * a = 64

Divide both sides by 6 to isolate "a":

a = 64 / 6

Simplify:

a = 10.67

Therefore , the solution of the given problem of trigonometry comes out to be the five functions value are written above Cosθ = 3/5.

Relationships between cubic splines and trigonometry When the professions of mathematicians were united, it is thought that the field was founded during the third millennium BC. Precise mathematical methods can be used to solve a wide range of geometric issues or to determine the outcomes of calculations that use them. The study of the six fundamental trigonometric operations is known as trigonometry.

Here,

Given :

There are in 3 quadrant :

=> Sinθ = -4/5

=> Cosθ = √1 - Sin²θ

=>  Cosθ  = √1 - 16/25

=> Cosθ = 3/5

=>Tan θ = -4/5 / 3/5

=> Tan θ  = -4/3

=>Cot θ = -3/4

and

Cosec θ = -5/4

Sec  θ = 5/3

Therefore , the solution of the given problem of trigonometry comes out to be the five functions value are written above Cosθ = 3/5.

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Answer:

Expression for number of girls:

2b + 15

Equation for number of boys and girls:

b + (2b + 15) = 84

Number of boys

23

Number of girls

61

Step-by-step explanation:

b = number of boys

g = number of girls

b + g = 84

g = 2b+15

b + (2b + 15) = 84

3b + 15 = 84

3b = 69

b = 23

b + g = 84

23 + g = 84

g = 61

Answer:

$2970.42

Step-by-step explanation:

Take $71,290 and divide it by 12 then you get $5,940.83 then divide that by 2 and your answer is $2,970.42

The solution for the system of linear equations is given by ( 2,3) with cost of one ice cream cone as $2 and cost of one ice cream sandwich as $3.

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here: The system of linear equations are 2x+y=8

and x+y=5

Solving the system of linear equations by the method of elimination we get

2x+y=8

2x+2y=10

__________

  -y=-2

Thus y=2 and x=8-2 / 2

                         =3

Hence, The solution for the system of linear equations is given by ( 2,3)

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[tex]\cfrac{x^2 - 49}{x+2}\div \cfrac{x^2-14x+49}{3x+6}\implies \cfrac{x^2 - 49}{x+2}\cdot \cfrac{3x+6}{x^2-14x+49}[/tex]

[tex]\cfrac{\stackrel{\textit{difference of squares}}{x^2 - 7^2}}{x+2}\cdot \cfrac{3(x+2)}{(x-7)(x-7)}\implies \cfrac{~~\begin{matrix} (x-7) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(x+7)}{~~\begin{matrix} x+2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{3~~\begin{matrix} (x+2) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{(x-7)~~\begin{matrix} (x-7) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} \\\\\\ \cfrac{x+7}{1}\cdot \cfrac{3}{x-7}\implies \cfrac{3(x+7)}{x-7}[/tex]

The surface area of the sphere is 1519.8 yd².

Three-dimensional shapes or solids are the names given to 3D shapes in geometry. Three separate dimensions, such as length, width, and height, are used to describe 3D shapes. The lack of thickness or depth in 2D shapes is the only distinction between them and 3D ones.

Given a sphere

diameter = 22 yards

radius = d/2 = 22/2

radius = 11 yards

the surface area of the sphere = 4πr²

S = 4πr²

S = 4(3.14)11²

S = 1519.76 yd²

S = 1519.8 yd²

Hence option A is correct

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Answer: no solution

Step-by-step explanation:

Answer: x = 14; y = 74; Isosceles and Acute

Step-by-step explanation: 3(x+7) = 3x + 21

Isosceles triangles have congruent base angles making 63 = 3x +21

Solve for x.

All angles of a triangle add up to 180 making y = 180 - 63 - 63.

Isosceles because two sides are congruent. And acute because all angles are under 90.

The error in River's analysis is that it is known if LM and MJ are perpendicular to KL and KJ.

What is error analysis?

Error analysis is a technique used to track out errors in learner language, ascertain whether they are systematic, and (if possible) provide an explanation for why they occurred.

It is given that -

Line segment KM is the bisector of ∠LKJ.

Also, line segment LM = MJ.

According to the angle bisector theorem if a line is a bisector of an angle then the corresponding sides of the angle should be perpendicular to the third side which is getting bisected.

Although it is given that  LM = MJ, but it is not known that if LM and MJ are   perpendicular to the sides of ∠LKJ.

Therefore, River cannot conclude that KM is the bisector of ∠LKJ.

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The probability that a student studied for exactly 4 hours rounded to the nearest hundredth is C. 0.26.

The concept that will be used here is probability. From the question the first column of a table serves as the amount of hours a student spent studying math,  while the  second column can be seen as the total number of pupils.

We can see from the second column's total  which is  35. We can see that just only 9 of them spent 5 hours  in the process of going over their arithmetic.

Then the likelihood that a student studied for four hours  can be known which can be calculated as :

= [9/35]

= 0.257 or 26%.

Therefore, option C is correct.

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The ratio of the sides = 7: 3

The ratio of perimeter = 7: 3

The ratio of the areas = 49: 9

Area of green polygon = 23

The polygons which are in the same shape but different in size are known as similar polygons. For similar polygons, the ratio of sides is known as the scale factor which is equal to the ratio of perimeters. Here the ratio of the areas is the squares of the scale factor.

Note:

Here we have two polygons

Side of the yellow polygon = 7 units

By the given formulas,

Perimeter of polygon = 6(7) = 42 units

Area of the polygon = 127 units²

Side of the green polygon = 3 units

Perimeter of polygon = 6(3) = 18 units

Area of Polygon = (3√3)/2 × (3)² = 23.383 ≅ 23

The ratio of the sides of polygons yellow to green = 7: 3

The ratio of perimeter = 42: 18 = 7: 3

The ratio of the areas = (7/3)² = 49/9

=> 49: 9

Therefore,

The ratio of the sides = 7: 3

The ratio of perimeter = 7: 3

The ratio of the areas = 49: 9

Area of green polygon = 23  

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A scale factor consists of two or more shapes who look the same but have different scales or measures. A scale factor of 2 means that the new triangle is two times the size of the original.

If we look at shape x, we can see it has a base of 4, and a height of 3. If we also know that a scale factor of two means that the new shape will be twice as large, we can use an equation that looks like this:

(Base/height × scale factor = new base length)

Now that we have these numbers, we can take them and see which shape matches the new length.

Shape D has a base of 8 and a height of 6, meaning that it has a scale factor 2 compared to shape x.

Therefore Shape D is the answer.

The similarity statement is competed as follows

The proportion is completed as below

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

Examining the figure shows that pair of equivalent sides are

KL / KJ and ML / KL

LJ / MJ and KJ / LJ

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