A survey of 25 randomly selected customers found the ages shown (in years). The mean is 32.64 years and the standard deviation is 9.39 years.

a) Construct a 80% confidence interval for the mean age of all customers, assuming that the assumptions and conditions for the interval have been met.

b) How large is the margin of error?


a) What is the confidence interval?


b) What is the margin of error?

The margin of error is

=================================================================

Explanation:

Imagine rotating the figure so that the triangular face is flat on the ground. This makes the triangular faces to be the floor and ceiling of this room.

The floor is a triangle with base 24 meters and height 7 meters. The floor area is base*height/2 = 24*7/2 = 84 square meters.

Multiply this floor area with the height of the room (22 m) to get the volume of the room.

volume = (floor area)*(height) = 84*22 = 1848 cubic meters

Answer:

i am not sure about your question but if it is 3 divided by y-3 =12 divide by y+3 you can use this

Step-by-step explanation:

3÷y-3=12÷y+3

cross multiply

12(y-3)=3(y+3)............brackets off

12y-36=3y+9..............group the same

12y-3y=9+36

9y=45.......duved by 9 both sides

y=5

Answer:

15.71 m

Step-by-step explanation:

C = πd

d= diameter

C = π (3.14) * 5

= about 15.71 m

A. 15.71 m

Answer:[tex]5\pi[/tex]

Step-by-step explanation:The circumference is pi times the diameter. If you want a proof you can find it online with a quick search. This applied here means that since the diameter is 5, the circumference is 5*pi or rather 5pi.

Answer:

x=5

Step-by-step explanation:

The two lines are the same length

2x+7 = 5x-8

15 = 3x

x = 5

Answer:

n² blocks are needed to build a staircase with n steps.

Step-by-step explanation:

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find how many terms are in [tex]\pmb{10y^2-3y+8}[/tex].

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

So let's compute the number of terms in this expression.

The first term is [tex]\pmb{10y^2}[/tex].

Is anything added or subtracted from 10y²?

Sure! [tex]\pmb{-3y}[/tex] is subtracted from 10y².

Also, 8 is added to -3y.

Thus, this expression has 3 terms.

Hope it helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

Answer:

56/64 simplified is 0.875 or 7/8 as a fraction

The graph of the two given system of inequalities y > 2x - 5

y < -3x is; Attached below

We are given two inequalities;

y > 2x - 5

y < -3x

The graph that represents the 2 inequalities has been attached and from the graph, we see that;

The solution of the system of inequalities is the shaded pink area between the two dotted lines.

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         There are three main ways of solving quadratic equations. The quadratic formula, factoring, and completing the square.

[1] using the quadratic formula

     When the equation is in the form of ax² + bx + c = 0.

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

Read more about the quadratic formula here:

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[2] factoring

Read more about how to solve with factoring here:

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[3] completing the square

     To start out with completing the square, make sure your constant is isolated on one side. The equation will be as ax² + bx = -c

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The answer of the following options are as 50, 64, 36, 40, 100, 9, 12, 12 100, 27, 150 42, 50 72, 28.3.

Suppose the fraction is proper (the numerator is smaller than the denominator).

Let it be

[tex]\dfrac{a}{b}[/tex]

Then, we can interpret it as:

a parts out of b parts of a thing.

[tex]1. \dfrac{2}{5} t = 20\\\\t = 20 \times \dfrac{5}{2}\\\\t= 50[/tex]

[tex]2. \frac{7}{8} p = 56\\\\p = 56 \times \frac{8}{7} \\\\ p= 64[/tex]

[tex]3. \frac{5}{6} x = 30 \\\\x = 30 \times \frac{6}{5} = 36[/tex]

[tex]4. \frac{1}{2} x = 20\\\\x = 20 \times 2 = 40[/tex]

[tex]5. \frac{3}{5} s = 60\\\\s = 60 \times \frac{5}{3} = 100[/tex]

[tex]6. \frac{1}{3} t = 3 \\\\t = 3\times 3 = 9[/tex]

[tex]7. \frac{3}{4} x = 9\\\\x = 12[/tex]

[tex]8. \frac{11}{12} x = 11\\\\x = 11 \times 12/11 = 12[/tex]

[tex]9. \frac{8}{10} t = 80\\\\t = 80 \times 10/8 = 100[/tex]

[tex]10. \frac{p}{3} = 9 \\\\p = 9 \times 3 = 27[/tex]

[tex]11. \frac{n}{5} = 30\\\\n = 30 \times 5 = 150[/tex]

[tex]12. \frac{6a}{7} = 36 \\\\a = 36 \times 7/6 = 42[/tex]

[tex]13. \frac{1}{2} t + 3 = 28\\\\t = (28 - 3)2 = 50[/tex]

[tex]14. \frac{1}{6} r = 12\\\\r = 12\times 6 = 72[/tex]

[tex]15. \frac{11}{12} b = 32\\ \\b = 32 \times 11/12 = 29.33[/tex]

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Answer:

Its a for me

Step-by-step explanation:

trust me fuys

Complete the square:

x² - 4x + 6 = 0

x² - 4x = -6

x² - 4x + 4 = -6 + 4

(x - 2)² = -2

But the left side is positive for any real number x, so there are no real solutions.

If you're solving over the complex numbers, we can go on to say

x - 2 = ± √(-2)

x - 2 = ± 2i

x = 2 ± 2i

where i = √(-1).

Answer:

12345678910

Step-by-step explanation:

TANQR

The standard notation of 7,250,000 is [tex]7.25 \times 10^6[/tex]

The standard notation of 0.000045 is [tex]4.5 \times 10^{-5}[/tex]

It is the way of writing a large number between 1 to 10 with a power of 10.

We have,

7,250,000

To write this number in standard notation, we can use powers of 10.

We start by counting the number of digits to the left of the decimal point.

In this case, there are 7 digits to the left of the decimal point.

We can then express this number in scientific notation as:

[tex]7.25 \times 10^6[/tex]

This means that we have 7.25 times 10 raised to the power of 6.

Now,

0.000045

To write this number in standard notation, we can again use powers of 10. We start by counting the number of digits to the right of the decimal point. In this case, there are 5 digits to the right of the decimal point.

We can then express this number in scientific notation as:

[tex]4.5 \times 10^{-5}[/tex]

This means that we have 4.5 times 10 raised to the power of -5.

Thus,

The standard notation of 7,250,000 is [tex]7.25 \times 10^6[/tex]

The standard notation of 0.000045 is [tex]4.5 \times 10^{-5}[/tex]

Learn more about scientific notation here:

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The complete question.

Write this number in standard notation.

7,250,000

0.000045

Answer:

V = 1607.7 in^3

V = 0.94 ft^3

Step-by-step explanation:

To find the volume of a traffic cone, use the formula for the volume of a cone: (1/3)*π*h*r^2

h = height

r = radius of cone

Step 1: determine variables and units

2 feet = 24 inches

diameter = 2 * radius

radius = (1/2) * diameter = (1/2)*16 in = 8 inches

Step 2: determine volume

V = (1/3)*π*h*r^2

V = (1/3)*3.14*24*(8)^2

V = 1607.7 in^3

Optional step 3: determine volume in ft^3

h = 2 ft

r = 0.67 ft

V = (1/3)*π*h*r^2 = (1/3)*3.14*2*(0.67)^2

V = 0.94 ft^3

Answer:

[tex]x=\dfrac{2}{3},-\dfrac{3}{2}[/tex]

Step-by-step explanation:

Given equation:

[tex]6x^2+5x-6=0[/tex]

First, factor the left side of the given equation.

To factor a quadratic in the form [tex]ax^2+bx+c[/tex] find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:

[tex]\implies ac=6\cdot-6=-36[/tex]

[tex]\implies b=5[/tex]

So the two numbers are: 9 and -4

Rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies 6x^2+9x-4x-6=0[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies 3x(2x+3)-2(2x+3)=0[/tex]

Factor out the common term [tex](2x+3)[/tex]:

[tex]\implies (3x-2)(2x+3)=0[/tex]

To solve for x:

[tex]\begin{aligned}\implies (3x-2) & =0 & \implies (2x+3) & = 0\\3x & = 2 & 2x & = -3\\x & = \dfrac{2}{3} & x & = -\dfrac{3}{2}\end{aligned}[/tex]

Therefore:

[tex]x=\dfrac{2}{3},-\dfrac{3}{2}[/tex]

[tex]\displaystyle\\|\Omega|=\binom{72}{4}=\dfrac{72!}{4!68!}=\dfrac{69\cdot70\cdot71\cdot72}{2\cdot3\cdot4}=1028790\\|A|=\binom{46}{4}=\dfrac{46!}{4!42!}=\dfrac{43\cdot44\cdot45\cdot46}{2\cdot3\cdot4}=163185\\\\P(A)=\dfrac{163185}{1028790}=\dfrac{473}{2982}\approx0.1586[/tex]

Answer:

whats nine + 10

Step-by-step explanation:

21

pencil is .10

pen is .90

Step-by-step explanation:

x = pencil y = pen

3x + y = 1.20

7x + 2y = 2.50

try make x or y cancelable

-2 times (3x + y = 1.20) = -6x - 2y = - 2.40

7x + 2y = 2.50

-6x - 2y = - 2.40

x = .10

plug .10 back into one of the equations

3(.10) + y = 1.20

.30 + y = 1.20

y = .90

Answer: The correct answer is A.

Step-by-step explanation: A line with a positive slope always increases and goes up.

Answer:

Hi,

Step-by-step explanation:

sin(a-b)=sin(a) cos(b)+ cos(a) sin(b)

a=45° and b=30°

[tex]sin(45^o-30^o)=sin(45^o)*cos(30^o)+cos(45^o)*sin(30^o)\\\\=\dfrac{\sqrt{2}}{2}* \dfrac{\sqrt{3}}{2}+\dfrac{\sqrt{2}}{2}*\dfrac{1}{2}\\\\\\\boxed{sin(15^o)=\dfrac{\sqrt{2}}{4}*(1+\sqrt{3} )}\\[/tex]

The two points are (-4, -2) and (4, 5) and the equation of the line is 8y = 7x + 12 passing through the two points.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

We have a quadrilateral ABCD which is reflected over a line and formed a mirror image A'B'C'D' of the quadrilateral.

From the graph:

The two points are (-4, -2) and (4, 5)

The line equation passing through two points:

[y - 5] = (5+2)/(4+4)[x - 4]

y - 5 = 7/8[x - 4]

8y - 40 = 7x - 28

8y = 7x + 12

Thus, the two points are (-4, -2) and (4, 5) and the equation of the line is 8y = 7x + 12 passing through the two points.

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Answer:

a = 63

b = 117

c = 63

Step-by-step explanation:

The sum of interior angles in a triangle is = 180

so the measure of a:

85 + 32 + a = 180 add like terms

117 + a = 180 subtract 117 from both sides

a = 63

a and be are supplementary angles so their sum is equal to 180

180 - 63 = 117 is the b's value

since a and c are on a pair of parallel lines, their value must be equal therefore the value of c is also 63

The value of x is 7 and the measure of ∠1 is 99

The given parameters are:

The sum of angles in a triangle is 180.

So, we have:

5x + 19 + 8x - 11 + 11x + 4 = 180

Evaluate the like terms

24x = 168

Divide both sides by 24

x = 7

Hence, the value of x is 7

The angles on a straight line add up to 180.

This means that:

∠1 + ∠QNM = 180

Subtract ∠QNM from both sides

∠1 = 180 - ∠QNM

Substitute ∠QNM = 11x + 4

∠1 = 180 - 11x - 4

Substitute x = 7

∠1 = 180 - 11 * 7- 4

Evaluate

∠1 = 99

Hence, the measure of ∠1 is 99

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The statement f⁻¹(x) has a y-intercept of (0, –36) and f⁻¹(x) has a range of all real numbers options third and fifth are correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The question is: Consider the function f(x) = (-2/3)x - 24  Which conclusions can be drawn about f⁻¹(x) Select two options:

f⁻¹(x) has a slope of -2/3

f⁻¹(x) has a restricted domain.

f⁻¹(x) has a y-intercept of (0, –36).

f⁻¹(x) has an x-intercept of (–36, 0).

f⁻¹(x) has a range of all real numbers.

f(x) = (-2/3)x - 24

To find the inverse of a function:

interchange the x and y

x = (-2/3)y - 24

y = (-3/2)(x + 24)

y = (-3/2)x - 36

The slope of a function f⁻¹(x) is -3/2

From the graph, we can see the y-intercept is (0, -36) and the range will be all real numbers.

Thus, the statement f⁻¹(x) has a y-intercept of (0, –36) and f⁻¹(x) has a range of all real numbers options third and fifth are correct.

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Answer:

D and  E

Step-by-step explanation:

did the test

Answer:

D)

Step-by-step explanation:

[tex]\sf f(x) = \sqrt{x+1}\\\\\\g(x) = 7x\\\\ g(f(x)) = g(\sqrt{x+1}) = 7*\sqrt{x+1}[/tex]

Answer:

i think the answer is 25q - 5 / 4

Answer:

A) x = 113°

Explanation:

Given three sides: 6.4 cm, 5.8 cm, 10.2 cm

Use the cosine rule:

c² = a² + b² - 2ab cos(C)

Insert/put variables:

[tex]\rightarrow \sf 10.2^2 = 5.8^2 + 6.4^2 - 2(5.8)(6.4) cos(x)[/tex]

[tex]\rightarrow \sf -74.24 cos(x) = 10.2^2 - 5.8^2 - 6.4^2[/tex]

[tex]\sf \rightarrow -74.24 cos(x) = 29.44[/tex]

[tex]\rightarrow \sf cos(x) = \dfrac{29.44}{-74.24}[/tex]

[tex]\rightarrow \sf x = cos^{-1}(-\dfrac{23}{58})[/tex]   = 113.36°  ≈ 113°  (rounded to nearest degree)

Answer:

r = - 18/5

I hope this helps! ^^

( This problem has 13 steps, so it would take a lot of time to type them in ^^)

Answer:

1) Ans; C .

2) Ans; D.

3) Ans; A.

4) Ans; C.

a) A × B is the Cartesian product of A and B, given by the set

A × B = {(a, b) | a ∈ A and b ∈ B}

Then for A = {4, 6, 8} and {4, 5, 6}, we have the product

A × B = {(4, 4), (4, 5), (4, 6), (6, 4), (6, 5), (6, 6), (8, 4), (8, 5), (8, 6)}

b) The power set of a set X is the set containing all subsets of X. I'm not sure what you're asking to find the power set of, though. Hopefully it's not of A × B, since that would contain 2⁹ = 512 elements...

Instead I'll assume you mean a simpler set, such as A ∩ B. The intersection of A and B is

A ∩ B = {4, 6, 8} ∩ {4, 5, 6} = {4, 6}

and has only 2 elements, so its power set has 2² = 4 elements (much more manageable!) and is the set

Pow(A ∩ B) = {{}, {4}, {6}, {4, 6}}

Answer:

5.6 is the mean

Step-by-step explanation:

add up everything and then divide it over how many numbers are in the set to find the mean.

give brainliest, please!
hope this helps :)