The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 10% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine. Assuming his suspicion that 10% of his customers buy a magazine is correct, what is the probability that exactly 5 out of the first 13 customers buy a magazine?

Answer:

\(\boxed {\boxed {\sf 682}}\)

Step-by-step explanation:

The nth term of an arithmetic sequence can be found using the following formula.

\(a_n=a+d(n-1)\)

where a is the first term, d is the common difference, and n is the term.

First, we should find the common difference.

We can do this by subtracting each term from the term following it. Basically, subtract the first term from the second term, the second from the third, and so on.

\(d= a_2-a_1\)

The second term is 25 and the first is 16.

\(d= 25-16\)

\(d=9\)

Now we know the common difference is 9. We also know the first term is 16 and we are looking for the 75th term.

\(d=9 \\a=16 \\n= 75\)

Substitute the values into the formula.

\(a_{75}=16+9(75-1)\)

Solve according the PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).

Solve the parentheses first.

\(a_{75}=16+9(74)\)

Multiply next.

\(a_{75}=16+666\)

Finally, add.

\(a_{75}=682\)

The 75th term in the sequence is 682.

The position of  √17 between 4 and 5, which is nearer 5, and the location of 6, which is between 2 and 3, which is nearer 2.

A visual representation of real numbers in a linear manner is a number line. It is a straight line that is divided into intervals or segments, each of which stands for a distinct real number value.

Number lines can be vertical or horizontally oriented, and they can also have a positive or negative orientation. Positive numbers often extend to the right or up, whereas negative numbers typically extend to the left or down. The origin of the number line, or zero, is typically situated in the middle of the line.

The number line is a crucial tool in mathematics since it offers a means of representing numerical relationships visually and carrying out fundamental arithmetic operations. For instance, positive and negative motions along a number line can be used to depict addition and subtraction, respectively, with positive movements denoting addition and negative movements denoting subtraction. On a number line, multiplication and division can alternatively be shown as repeated addition or subtraction.

If we have a number line with the proper markings, we may indicate where the square roots of 17 and 6 are located as follows:

To begin, determine the approximate square root values:

√17 is between 4 and 5, since 4² = 16 and 5² = 25.

√6 is between 2 and 3, since 2² = 4 and 3² = 9.

Place the number √17 closer to 5, between 4 and 5.

Place the number √6 between the numbers 2 and 3, closer to 2.

Since 6 and 17 are not integers and their values are not evenly spaced, it should be noted that their markings will not be evenly spaced on the number line.

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Number line attached below,

You have the following statement:

- 6 less than twice the difference of a number and 8 is equal to 14.

To determine the algebraic expression of the previous situation, you analize by parts the previous sentence.

- The difference of a number and 8: it can be taken as n - 8

- Twice the difference of a number and 8: 2(n - 8)

- 6 less than twice the difference of a number and height: 6 - 2(n - 8)

Thus, the algebraic equation is:

6 - 2(n - 8) = 14

The only automorphism of a well-ordered set is the identity.

To prove this statement, we need to show that any automorphism of a well-ordered set must be the identity function. An automorphism is a bijective function that preserves the order structure of the set.

Assume we have a well-ordered set (W, ≤), where W is the set and ≤ is the order relation.

Let f: W → W be an automorphism of the set.

We aim to prove that f is the identity function, i.e., f(x) = x for all x ∈ W.

Suppose, for contradiction, that there exists an element a ∈ W such that f(a) ≠ a.

Since f is a bijective function, there must exist some b ∈ W such that f(b) = a.

Since (W, ≤) is well-ordered, there is a least element c in the set {x ∈ W : f(x) ≠ x}.

Let d = f(c). Since f is an automorphism, f(c) ≠ c, and thus d ≠ c.

Since (W, ≤) is well-ordered, there is a least element e in the set {x ∈ W : f(x) = d}.

Consider the element f(e). Since f is a bijective function, there must exist some f^{-1}(f(e)) = e' ∈ W such that f(e') = f(e) = d.

By the definition of automorphism, f(f^{-1}(y)) = y for all y ∈ W. Applying this property to e', we have f(f^{-1}(f(e'))) = f(e') = d.

However, f^{-1}(f(e')) = e' ≠ c, and thus f(e') ≠ d. This contradicts the fact that e is the least element in the set {x ∈ W : f(x) = d}.

Therefore, our assumption that there exists an element a such that f(a) ≠ a is false.

Since we assumed f(a) ≠ a for arbitrary a ∈ W, it follows that f(x) = x for all x ∈ W.

Hence, the only automorphism of a well-ordered set is the identity function.

Therefore, we have proven that the only automorphism of a well-ordered set is the identity function.

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Answer:

12%

Step-by-step explanation:

Let the rate of interest be R%
r = R% as decimal =R/100

Simple interest earned for 3 years at rate r on ₹15,000 = ₹5,400

The formula for interest earned is given by
I = Prt
where P is the principal amount (15,000)

r = annual interest rate as a decimal (to be determined)

t = number of years

Plugging in known values we get

5400 = 15000 x r x 3

         = 45000 x r

r = 5400/45000

r = 0.12

Rate of interest as a percentage = r x 100 = 0.12 x 100 = 12%

Step-by-step explanation:

OUT of  35 spins   4 + 15 + 3  = 22   were blue or green or purple

 22/35 probability  = 63%

Answer:

-3

Step-by-step explanation:

the graph is the coefficient so it is the number before x

Answer:

-3

Step-by-step explanation:

Slope describes the rate of change between the change in y and the change in x. What the equation tells us is that y decreases by 3 each time (aka. increasing by -3) when x increases by 1. This gives us a slope of -3.

Answer:

11

Step-by-step explanation:

f(x)=3x+8

f(1)=3(1)+8

f(1)=3+8

f(1)=11

Answer:

The anwser is 11

Step-by-step explanation:

You just replace x with 1, and solve, so it would be 3(1) + 8, which is 11.

Answer:

ਮੁਆਫ ਕਰਨਾ ਮੈਨੂੰ ਬਿੰਦੂ ਚਾਹੀਦੇ ਹਨ

Step-by-step explanation:

Answer:

9807654e6785e46754

Step-by-step explanation:

Answer:Sorry

Step-by-step explanation:

Hi would help but i dont know and im not in collage sorry.

The inequality that represents the interval shown on the number line is:

5 ≤ x ≤ 9

We want to use inequality notation to define the interval shown on the number line.

We can see that the first point is marked with a closed circle, at x = 5.

And then we have another closed circle at x = 9

The closed circles means that these points are solutions to the inequality, so we need to use the symbols:

≤ and ≥

Then we can write the inequality:

5 ≤ x ≤ 9

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Answer:

2^1* 3^7

Step-by-step explanation:

8^-1 * 3^3/ 2^-4 * 9^-2

Negative exponents move from the numerator to the denominator or from the denominator to the numerator

2^4*9^2* 3^3 /8^1  

Rewriting 9^2 as 3^2^2 = 3^4  and 8 = 2^3

2^4 * 3^3 * 3^4 / 2^3

2^4/ 2^3 = 2   and 3^3 * 3^4 = 3^(3+4) = 3^7

2* 3^7

Answer:

Step-by-step explanation:

\(\frac{8^{-1}*3^{3}}{2^{-4}*9^{-2}}=\frac{(2^{3})^{-1} * 3^{3}}{2^{-4}*(3^{2})^{-2}}\\\\=\frac{2^{3*-1}*3^{3}}{2^{-4}*3^{2*-2}}\\\\=\frac{2^{-3}*3^{3}}{2^{-4}*3^{-4}}\\\\=2^{-3+4}*3^{3+4}\\\\=2^{1}*3^{7}\\\\=2*3^{7}\)

Answer:

y = (-5/7)x - 16

Step-by-step explanation:

(y - 4)= -5/7(x + 28)

y - 4= -5/7x - 20

   +4             +4

------------------------

y = (-5/7)x - 16

I hope this helps!

Answer:  \(y =-\frac{5}{7}x -16\)

Step-by-step explanation:

The slope-intercept form is y = mx + b, where m is the slope, and b is the y-intercept.

\((y-4)= -\frac{5}{7} (x+28)\)

\(y -4=(-\frac{5}{7})(x) + (-\frac{5}{7})(28)\)

\(y -4=-\frac{5}{7}x + (-20)\)

\(y -4=-\frac{5}{7}x -20\)      Add 4 on both sides.

\(y =-\frac{5}{7}x -16\)

Considering the definition of distance between two points, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.

The distance between two points is equal to the length of the segment that joins them. Therefore, to determine the distance between two different points, you must calculate the squares of the differences between their coordinates and then find the root of the sum of said squares.

In other words, the distance between two points in space is the magnitude of the vector formed by said points.

So, given the coordinates of two distinct points (x1, y1) and (x2, y2), the distance between two points is the square root of the sum of the squares of the difference of the coordinates of the points:

distance= \(\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\)

In this case, you know:

Replacing in the definition of distance:

distance= \(\sqrt{(5-(-2))^{2} +(-4-1)^{2} }\)

distance= \(\sqrt{(5+2)^{2} +(-5)^{2} }\)

distance= \(\sqrt{7^{2} +(-5)^{2} }\)

distance= \(\sqrt{49+25 }\)

distance= √74= 8.6023

Finally, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.

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Answer:

B

Step-by-step explanation:

EDGEN

Answer:

B. About 52.1 percent of the variation in number of bite-sized pretzels grabbed with the dominant hand is accounted for by the linear relationship formed with handspan.

Step-by-step explanation:

Answer:

f(3x)= 3x+5/6x+2

substitute the value of X in the given question.

if u want simplified form then u can try rationalising.

f(3x)= 3x+5/6x+2 hope helped thanks for points

Answer:

\(54\pi \: {cm}^{2} \)

Step-by-step explanation:

Given:

A cone

l = 15 cm

r (radius) = 3 cm

Find: A (surface area) - ?

\(a(surface) = \pi {r}^{2} + \pi \times r \times l\)

\(a(surface) = \pi \times {3}^{2} + \pi \times 3 \times 15 = 9\pi + 45\pi = 54\pi \: {cm}^{2} \)

Answer: \(6.67m^3\)

Step-by-step explanation:

For hemisphere...

diameter (d1) = 3m

radius (r1) = (3/2)m

The total volume of the hemisphere

\(v1=\frac{2}{3} \pi (r1)^3\)

\(=\frac{2}{3} \pi (\frac{3}{2} )^3\)

\(=\frac{9}{4} \pi\)

-----------------------------------------------------------------------

For smaller cylinder

diameter (d2) = 0.75

radius (r2) = 0.75/2m

height (h2) = 0.80m

Volume of smaller cylinder

(V2) = \(\frac{1}{3} \pi (r2)^2h2\)

\(=\frac{1}{3} \pi (\frac{0.75}{2} )^2*0.80\)

\(=\frac{3}{80} \pi\)

------------------------------------------------------------------------

For bigger cylinder

Volume of bigger cylinder =

\(V3=\frac{1}{3} \pi (\frac{1.25}{2} )^2*0.70\)

\(=\frac{35}{384} \pi\)

-----------------------------------------------------------------------

Volume of water =  \((v1 - v2 - v3) =\frac{9}{4} \pi -\frac{3}{80} \pi -\frac{35}{384} \pi = 6.67 m^3\)

The school is about 14.95 meters tall, and the mirror is 8.25 meters from the school.

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let Ф represent the angle Elijah makes with the ground, hence:

tanФ = 1.45/0.8

Ф = 61.11°

The angle of elevation to the building is 61.11°. Let h represent the height of the building.

tan(61.11°) = h/8.25

h = 14.95

The school is about 14.95 meters tall, and the mirror is 8.25 meters from the school.

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The measure of angle is θ cannot determine the statements that are true about its reference angle.

There are two issues with the given statement.

First, it does not specify the measure of angle θ.

Second, the statement cos(0)=-3/10 is not related to the reference angle of θ.

The reference angle of θ is the acute angle between the terminal side of θ and the x-axis.

It is always positive and its measure is between 0 and 90 degrees or between 0 and π/2 radians.

The measure of the reference angle of θ is denoted by θ'.

To determine the reference angle of θ, we need to know the quadrant in which θ lies.

The reference angle of θ in standard position is the acute angle between the terminal side of θ and the x-axis.

If θ is in the first quadrant, then θ' = θ.

If θ is in the second quadrant, then θ' = π - θ.

If θ is in the third quadrant, then θ' = θ - π.

If θ is in the fourth quadrant, then θ' = 2π - θ.

The measure of angle θ, we can determine its reference angle using the above rules.

The statement cos(0)=-3/10 is not related to the reference angle of θ.

It is the value of the cosine function at 0 radians or 0 degrees.

This value does not correspond to any angle that has a reference angle.

The measure of angle θ cannot determine the statements that are true about its reference angle.

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The value of the expression is 16x(x+1) / 10x² -14x -12

In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

The given expression is

16/(x-2)  ÷ 4/(x+1) + 6/x

Simplify this to have

16 / (x-2) ÷ (10x + 6) / (x+1)(x)

this implies that 16/(x-2) * (x+1)(x)/(10x +6)

16(x² + x)/(x-2)(10x+6)

Therefore the value of the expression is

16x(x+1) / 10x² -14x -12

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The key features of the given quadratic functions are listed below.

In Mathematics and Geometry, the graph of any quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0) i.e 3 > 0.

For the quadratic function y = 3x² - 5, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, -5).

Domain: [-∞, ∞]

Range: [-5, ∞]

For the quadratic function y = -2x² + 12x - 15, the key features are as follows;

Axis of symmetry: x = 3.

Vertex: (3, 3).

Domain: [-∞, ∞]

Range: [-∞, 3]

For the quadratic function y = -x² + 1, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, 1).

Domain: [-∞, ∞]

Range: [-∞, 1]

For the quadratic function y = 2x² - 16x + 30, the key features are as follows;

Axis of symmetry: x = 4.

Vertex: (4, -2).

Domain: [-∞, ∞]

Range: [-2, ∞]

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Step-by-step explanation:

The side lengths of the kite are marked

TOTAL perimeter will be  25 + 25 + 35 + 35  = 120 cm

Answer:

XY: 15.23

Step-by-step explanation:

Smartness

The distance between the endpoints of line segment XY will be 15.2 units.

It is the measure of distance between the two points and is known as length. The length is measured in meters generally.

Let one point be (x, y) and another point be (h, k).

Then the distance between the points will be

D² = (x - h)² + (y - k)²

The endpoints of line segment XY are given below.

X(-9, 2) and Y(5, -4)

The distance between the endpoints of line segment XY will be given as,

D² = (x - h)² + (y - k)²

D² = (5 + 9)² + (-4 - 2)²

D² = (14)² + (-6)²

D² = 196 + 36

D² = 232

D = √232

D = 15.2 units

The distance between the endpoints of line section XY will be 15.2 units.

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Answer:

68

Step-by-step explanation:

15% of 80 is 12 so you subtract 12 from 80 and thats 68.

Answer: B) dot plot with 2 dots over 75, 7 dots over 76, 3 dots over 77, 3 dots over 78, 1 dot over 79

Step-by-step explanation: took the test, hope this helps c:

Answer:

1/12, 30/360 and 30°

Explanation:

the fraction turns through 1/12 of the circle, as shown in the diagram.

1/12 = 30/360, because 360 ÷ 12 × 1 = 30.

thus, the measure of the angle is 30°.

i hope this helps! :D do comment if you have any questions.

The correct answer is A: 600 <= money <= 2822.4.

This represents the range of possible values that Pankaj's accumulated money could fall into, given the specified conditions of the 3% interest rate compounded weekly for a maximum of 2 years. The lower bound, 600, represents the initial deposit amount, while the upper bound, 2822.4, represents the maximum amount of money Pankaj could earn after 2 years, assuming that interest is compounded every week.