A box contains 65 balls numbered from 1 to 65. If 11 balls are drawn with replacement, what is the probability that at least two of them have the same number?

The algebraic equation to represent the given situation is as follows,

y = 4 + 2x

What is an algebraic equation?

The term "algebraic equation" refers to a formulation of the equality of two expressions using the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extraction of a root on a set of variables.

An expression that includes variables, constants, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, etc.).

Forming the Algebraic Equation

Number of book present on the shelf initially = 4

It is given that 2 books are added per minute to the shelf.

If x is the number of minutes, then the books added will be 2x.

If y is the total number of books present on the shelf, then the algebraic equation is given as,

y = Number of books initially present on the shelf  + 2x

⇒ y = 4 + 2x

Thus, y = 4 + 2x is the required algebraic equation.

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The two digit number larger than 40 and lesser than 50, and the difference between the ones and tens digits gives the two digit number as 41

Let XY represent the two digit number;

From the question, we have the following inequalities and equations;

Therefore;

Which gives;

Y = 1

X = 4

Therefore;

The two digit number, XY = 41

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Answer:

y =x - 2

Step-by-step explanation:

If the slope of the line is  'm', then the slope of the perpendicular to the given line = [tex]\sf \dfrac{-1}{m}[/tex]     (opposite reciprocal)

    y = -x - 3

Compare with equation of line in slope y-intercept form: y = mx +b

 m = -1

[tex]\sf \text{Slope of the perpendicular line = $-(\dfrac{1}{-1})= 1$}[/tex]

This line passes through (2, 0);

Equation of the line in slope - point form:

        [tex]\sf y - y_1 = m(x - x_1)[/tex]

       y  - 0   = 1 (x - 2)

            y = x - 2

Answer:

x=9.73

Step-by-step explanation:

This is trigonometry work! :)

So cos46°=x/14

          x=14×cos46°

          x≈9.73

Hope this helps <3

The coordinate of the image of JKL when dilated by a factor of 5 with respect to the origin is J'(-15, 10), K'(15, 10) and L'(0, 20).

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.

Translation is the movement of a point either up, left, right or down in the coordinate plane.

Let us assume that triangle JKL has vertices at J(-3, 2), K(3, 2) and L(0, 4).

The coordinate of the image of JKL when dilated by a factor of 5 with respect to the origin is J'(-15, 10), K'(15, 10) and L'(0, 20).

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The recursive formula of h(n) is h(1) = 36 and h(n) = h(n -1) - 5

The function is given as:

h(n) = 41- 5n

Calculate h(1) and h(2)

h(1) = 41- 5(1)

h(1) = 36

h(2) = 41- 5(2)

h(2) = 31

Calculate the difference between h(1) and h(2)

d = 31 - 36

d = -5

This means that:

h(1) = 36 and h(n) = h(n -1) - 5

Hence, the recursive formula of h(n) is h(1) = 36 and h(n) = h(n -1) - 5

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Answer:

45

Step-by-step explanation:

small brain

When preparing a representative sample from a list of 200 customers who complained about errors in their statements, a systematic sample might select every tenth customer for review.

Systematic random sampling is known to be a form of a random sampling method that needs one to select samples using a system of intervals where one has ranges of numbered population.

Note that When preparing a representative sample from a list of 200 customers who complained about errors in their statements, a systematic sample might select every tenth customer for review.

See options below

a. stratified sample

b. comprehensive sample

c. random sample

d. Systematic sample

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Her annual salary after 8 years will be $57,600.

To find what is her annual salary, to the nearest $100, after 8 years of service:

Find 4% of 45,000

[tex]\frac{x}{45000} *100=4\\\frac{x}{450} =4\\x =1800[/tex]

So, 4% of $45,000 of $1800.

1st year = $45000

2nd year = 45000 + 1800 = $46800

3rd year = 46800 + 1800 = $48600

4th year = 48600 + 1800 = $50400

5th year = 50400 + 1800 = $52200

6th year = 52200 + 1800 = $54000

7th year = 54000 + 1800 = $55800

8th year = 55800 + 1800 = $57600

Therefore, her annual salary after 8 years will be $57,600.

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The salary of Sonya after 8 years will be $61,600 (nearest $100).

The interest on the a loan or deposit that is calculated using the both initial principal as well as the accrued interest from prior periods is known as compound interest (sometimes known as compounding interest).

Some features of compounding are-

Calculation for the amount after 8 years-

The principal amount is $45,000

Rate of interest is 4% per year.

Time duration is 8 years.

The formula for total amount after compounding is -

[tex]A=P\left(1+\frac{r}{n}\right)^{n t}[/tex]

A  = final amount

P  = initial principal balance

r  = interest rate

n  = number of times interest applied per time period.

t  = number of time periods elapsed.

As the rate of interest is applied only one in a year ; n = 1.

Substitute the values in the formula to get the value.

[tex]A=45,000\left(1+\frac{.04}{1}\right)^{8}\\A=45,000\left(1.04}\right)^{8}\\\\A=61585.60[/tex]

Therefore, the salary of Sonya will be $61600 (nearest $100) after 8 years.

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The slope of a line that passes through the point (-3,0) and has a y-intercept of 12 is 4.

Using the point slope equation,

y = mx + b

where

Therefore, using (-3, 0)

0 = -3m + 12

-12 = -3m

divide both sides by -3

m = -12 / -3

m = 4

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No, just like the average (mean) it is a mathematical quantity that is determined by its mathematical definition and the everyday meaning of “expected” is only a descriptive hint toward what it represents.

What does the expected value of a random variable mean?

Is the expected value always equal to the mean?

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Answer:

[tex]\frac{1\cdot \left(4+\sqrt{3}\right)}{\left(4-\sqrt{3}\right)\left(4+\sqrt{3}\right)}\\[/tex]

[tex]1\cdot \left(4+\sqrt{3}\right)=4+\sqrt{3}[/tex]

[tex]\left(4-\sqrt{3}\right)\left(4+\sqrt{3}\right) = 13[/tex]

[tex]= \frac{4+\sqrt{3}}{13}[/tex]

x = 4

y = 3

z = 13

Answer:

x = 4, y = 3, z = 13

Step-by-step explanation:

Multiply the equation by the opposite of the denominator

[tex]\frac{(1)(4 + \sqrt{3}) }{(4-\sqrt{3})(4+\sqrt{3} ) } \\\\\frac{4 + \sqrt{3} }{16 - 4\sqrt{3} +4\sqrt{3} -3} \\\\= \frac{4+\sqrt{3} }{13}[/tex]

Answer:

Step-by-step explanation:

419-79= 340 assignments left to do

340/7days=48.57..... or about 46 assignments a day to finish them all in a week

(1 week= 7 days)

I don't know if you were serious but good luck with all the work if you are

Answer:

47 on 6 days and 48 on 1 day.

Step-by-step explanation:

Firstly you need to subtract 79 from 419. You will have 330 assignments left and the divide 330 by 7 since there are 7 days in a week and you get 47.142 and so if you double check by multiplying 47 times 7 it gives 329 so then you get 47 on 6 days and 48 on 1 day. Hope this helps!

Answer:

24,150km

Step-by-step explanation:

The plane travels 3450km in 1 hr, since we need the distance traveled in 7 hrs we need to multiply 3450 by 7.

distance in 7hrs: 3450*7 = 24,150km

Answer:

P = 16.4

Step-by-step explanation:

Given the equation PV = nRT and the values we know, we need to isolate P .

Thus, we have:

[tex]PV=nRT\\3P=2*0.0821*300\\P=49.26/3\\P=16.42=16.4[/tex]

Answer: Option 4

Step-by-step explanation:

[tex]m\angle 20=62^{\circ}[/tex] (linear pair)

[tex]m\angle 11=70^{\circ}[/tex] (angle sum in a triangle)

[tex]m\angle 12=110^{\circ}[/tex] (linear pair)

Rule 1:

1, 3, 7, 15, 31, 63, 127, 255, 511, 1023 etc

Rule 2:

40, 24, 16, 12, 10, 9, 8.5, 8.25, 8.125, 8.0625 etc

Hope this helps!

The first sequence is 1,3,7,15,31 and second sequence is 40,24,16,12,10.

Given that first rule is that multiply by 2 then add 1 starting from 1 and second rule is that divide by 2 then add 4 starting from 40.

We have to find the sequences for each rule.

We have to start from starting point and then apply the rule to find the sequence.

Sequence of rule 1:

Second term of sequence=2*1+1=3

Third term of the sequence=2*3+1=7

Fourth term of the sequence=2*7+1=15

Fifth term of the sequence=2*15+1=31.

Sequence will be 1,3,7,15,31.

Sequence of rule 2:

Second term of sequence=40/2+4=24

Third term of sequence=24/2+4=16

Fourth term of sequence=16/2+4=12

Fifth term of sequence=12/2+4=10

Sequence will be : 40,24,16,12,10.

Hence the first sequence is 1,3,7,15,31 and second sequence is 40,24,16,12,10.

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Answer:

Gradient (slope) is 5.

Step-by-step explanation:

To find the gradient (slope) of a curve graph at x = x₁ can be done by steps following:

First, derive the given function which is:

[tex]\displaystyle{y = (\sqrt{x}+3)(3\sqrt{x}-5)[/tex]

Differentiation can be done two ways - go ahead and expand the expression then derive it or you can use the product rule where it states that [tex]\displaystyle{y'=u'v+uv'}[/tex]

I'll be using product rule:

[tex]\displaystyle{y' = (\sqrt{x}+3)'(3\sqrt{x}-5)+(\sqrt{x}+3)(3\sqrt{x}-5)'}[/tex]

Note that the following process will require you to have knowledge of Power Rules:

[tex]\displaystyle{y = ax^n \to y' = nax^{n-1}}[/tex]

Hence:

[tex]\displaystyle{y'=\dfrac{1}{2\sqrt{x}}(3\sqrt{x}-5) + (\sqrt{x}+3)\dfrac{3}{2\sqrt{x}}[/tex]

Now we know the derivative. Next, we find the slope at x = 1 which you substitute x = 1 in derived function:

[tex]\displaystyle{y'(1)=\dfrac{1}{2\sqrt{1}}(3\sqrt{1}-5) + (\sqrt{1}+3)\dfrac{3}{2\sqrt{1}}}\\\\\displaystyle{y'(1)=\dfrac{1}{2}(3-5) + (1+3)\dfrac{3}{2}}\\\\\displaystyle{y'(1)=\dfrac{1}{2}(-2) + (4)\dfrac{3}{2}}\\\\\displaystyle{y'(1)=-1 + 2(3)}\\\\\displaystyle{y'(1)=-1 + 6}\\\\\displaystyle{y'(1)=5}[/tex]

Finally, we have found the slope or gradient at x = 1 which is 5.

Please let me know if you have any questions!

Answer:

23/24

Step-by-step explanation:

Let's convert all the fractions to a common denominator

(-12/24 - 3/24) + (18/24 + 20/24)

Combine like terms and you get 23/24

Answer:

17,576,000

Step-by-step explanation:

3 digits followed by 3 letters

Draw an underline character for each position with multiplication signs in between them.

_ × _ × _ × _ × _ × _

Now fill in each blank with the number of characters that can be used in that position. The first three blanks are used with digits, 0 through 9. There are 10 digits 0 through 9.

10 × 10 × 10 × _ × _ × _

For the last three blanks, each one gets a letter from A through Z. There are 26 letters to choose from fore each of the last three blanks.

10 × 10 × 10 × 26 × 26 × 26 = 17,576,000

Answer:

13.4 or √180

Step-by-step explanation:

Pythagorean theorem states

a² + b² = c²

C^2 is the longest side. The corner of the right angle points to it. The other sides are your a and b squared. They are called the legs or Opposite and Adjacent sides.

Answer: S ≈ 48.2°

Step-by-step explanation:

   We can use trigonometry functions to solve.

   Looking at angle S, t = 18 is the hypotenuse and r = 12 is the adjacent side. This means we can use the cosine function.

   [tex]\displaystyle cos(S) = \frac{\text{adjacent side}}{\text{hypotenuse }}=\frac{12}{18}[/tex]

  [tex]\displaystyle cos^{-1} (cos(S)) = (\frac{\text{adjacent side}}{\text{hypotenuse }}=\frac{12}{18})cos^{-1}[/tex]

  [tex]S = 48.189685...\\S \;$\approx$\; 48.2^{\circ}[/tex]

The large rectangle is 8/3 times bigger than the small rectangle.

Area of large rectangle will be:

= 4x(2x - 2)

= 8x² - 8x

Area of small rectangle will be:

= (3x - 3)x

= 3x² - 3x

The ratio will be:

= 8x² - 8x/3x² - 3x

= 8(x² - x)/3(x² - x)

= 8/3

The large rectangle is 8/3 times bigger than the small rectangle.

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Answer:

A

Step-by-step explanation:

point H is the point of intersection of the perpendicular bisectors of the triangle's sides and is the circumcentre.

Answer:

A. Circumcenter

Step-by-step explanation:

this is the point that has the same distance from all 3 vertexes.

being on the median line of DE, every point of that line has the same distance to D and E.

being also on the median line of FE means it has the same distance from F and E as every other point on that line.

and the same for DF.

H as the crossing point of all 3 median lines is the only point that has the same distance to D, E and F.

so, H is the center of a circle that goes through all 3 points.

Answer:

15:02 or 3:02 pm

Answer:

[tex]13.35 + 1.27 = 14.62 \\ \\1 hr = 60min \\ 62 min- 60min =2min \\ 14hr + 1hr = 15hr \\ \\it \: ends \: at \: 15.02[/tex]

Service organizations are ideally suited for activity-based costing because virtually all of the costs for a service company are indirect and appear to be fixed.

Activity-based costing is a method of assigning overhead and indirect costs such as salaries and utilities to products and services.

The ABC system of cost accounting is based on activities that are considered any event, unit of work, or task with a specific goal.

Here, activity-based costing has been used in manufacturing products but can also be applied to service industries, or businesses that provide a service instead of a product.

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Answer:

90

Step-by-step explanation:

Why cant people just answer questions without guessing or answer them correctly.

Answer:

y = -4x^2 - 3x + 4

x = 5

y = -4(5)^2 - 3(5) + 4

y = -4(25) - 15 + 4

y = -100 - 15 + 4

y = -114

Step-by-step explanation:

The number of lines that the points can make is; 21 lines

We are given that;

- There are 7 points on a Plane

- No 3 points on the plane are on the same line

Thus;

No 3 points are collinear and as such the number of lines that the points can make is found from the combination  formula;

C(7,2);

C(7,2) = 7!/(7 - 2)!*2!

= (7 × 6)/(2 × 1)

= 42/2

=21

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