The sector of a circle with a 12-inch radius has a central angle measure of 60

What is the exact area of the sector in terms of pi

Answer:

a.)The total 4-letters passwords when repetition of letters is allowed are 456976

b.)The total 4-letters passwords when repetition of letters is not allowed are 358800

Step-by-step explanation:

Some situations of probability involve multiple events. When one of the events affects others, they are called dependent events. For example, when objects are chosen from a list or group and are not returned, the first choice reduces the options for future choices.

There are two ways to sort or combine results from dependent events. Permutations are groupings in which the order of objects matters. Combinations are groupings in which content matters but order does not.

How many 4-letter passwords can be made using the letters A throught Z if...

a)Repetition of letters is allowed?

There are only 26 possible values for each letter of the password (The English Alphabet consists of 26 letters). The total 4-letters passwords when repetition of letters is allowed are [tex]26^{4} =456976[/tex]

b) Repetition of letters is not allowed?

If repetition of  letters is not allowed, we can only choose 4 letters out of 26. Using the permutation equation [tex]nP_{k} =\frac{n!}{(n-k)!}[/tex]

The total 4-letters passwords when repetition of letters is not allowed are [tex]26P_{4} =\frac{26!}{(26-4)!}=26.25.24.23=358800[/tex]

.

When repetition of letters is allowed, there are 456,976 possible 4-letter passwords that can be made using the letters A through Z. When repetition of letters is not allowed, there are 358,800 possible passwords that can be made.

a) When repetition of letters is allowed, we have 26 choices for each of the 4 positions in the password. Therefore, the number of 4-letter passwords that can be made is 26 * 26 * 26 * 26 = 456,976.

b) When repetition of letters is not allowed, the number of choices for the first position is 26. For the second position, there are 25 choices left, since we can't repeat the letter used in the first position. Similarly, for the third position, there are 24 choices, and for the fourth position, there are 23 choices. Therefore, the number of 4-letter passwords that can be made without repetition is 26 * 25 * 24 * 23 = 358,800.

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Answer: OC

Step-by-step explanation: exact answer is 64.6

To estimate how many shoppers received free earbuds, 19% of 340 is calculated. The closest equivalent fraction to 19% is 20%, which means dividing 340 by 5, resulting in 68 shoppers receiving free earbuds, making option C correct.

The question revolves around the application of percentage calculations to a real-world scenario, where 340 shoppers at an electronics store are given various specials. To estimate how many shoppers received a free set of earbuds, we must calculate 19% of 340 shoppers.

Using equivalent fraction to estimate, 19% is close to 20%, and 20% of 340 can be found by dividing 340 by 5 (because 20% is the same as 1/5th).:

Therefore, about 68 shoppers received a free set of earbuds. This makes option C the correct choice. To note, we have not used the given table and information in the question as they do not relate to the calculation required for the current problem.

Answer: 100 cm = 1 m

Step-by-step explanation:

Like most metric measurements, 100 centimeters are equal to 1 meter.

Answer:

A. [tex]y-5=1.5(x-4)[/tex].

B. [tex]y=1.5x-1[/tex].

Step-by-step explanation:

The given line passes through (2,2) and (4,5).

The slope the given line can be found using the formula;

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{5-2}{4-2}[/tex]

This gives [tex]m=\frac{3}{2}=1.5[/tex].

The slope-intercept form is [tex]y-y_1=m(x-x_1)[/tex].

We substitute the second point to get:

[tex]y-5=1.5(x-4)[/tex].

We expand to get:

[tex]y-5=1.5x-6[/tex].

[tex]y=1.5x-6+5[/tex].

[tex]y=1.5x-1[/tex].

Answer:

The length of the largest table that can be brought in the house on a diagonal is [tex]9.5\ ft[/tex]

Step-by-step explanation:

we know that

Applying the Pythagoras Theorem

Find the length of the diagonal of the frame

[tex]d^{2} =3^{2} +8^{2} \\\\ d^{2}=90\\\\ d=\sqrt{90}\ ft\\\\ d=9.5\ ft[/tex]

Answer:

Step-by-step explanation:

Alright, lets get started.

The height of the door is 8 feet.

The width of the door is 3 feet.

The largest size of the table that can be brought in this house from this given door is diagonally from this door.

So, lets find the diagonal of this door.

If we apply Pythagorean theorem ,

[tex]c^2=a^2+b^2[/tex]

[tex]c^2=3^2+8^2[/tex]

[tex]c^2=9+64=73[/tex]

taking square root on both sides

[tex]c=\sqrt{73}=8.5[/tex]

So, the maximum length of the table would be 8.5 feet.  :  Answer

Hope it will help :)

Answer:

Step-by-step explanation:

f(x) = x³ + 2x² + x

f(x) = x.(x² + 2x + 1)

f(x) = x.(x + 1)²

So, f(x) = 0 when x = 0 or when x = -1

But

f(x) = x.(x + 1)² = x.(x + 1).(x + 1)

So we have three roots, x = 0, x = -1 and x = -1, although two of them are equal.

So we have a multiple zero x = -1 with a multiplicity 2.

Alterativa A.

Answer:

A

Step-by-step explanation:

Answer:

[tex]\large\boxed{Q1:\ x=2\ or\ x=5}\\\boxed{Q2:\ x=1-\sqrt{21}\ or\ x=1+\sqrt{21}}[/tex]

Step-by-step explanation:

[tex]\text{Use the quadratic formula:}\\\\ax^2+bx+c=0\\\\\text{If}\ b^2-4ac<0,\ \text{then the equation has}\ \bold{no\ solution}\\\\\text{If}\ b^2-4ac=0,\ \text{then the equation has one solution}\ x=\dfrac{-b}{2a}\\\\\text{If}\ b^2-4ac>0,\ \text{then the equation has two solutions}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\==========================================[/tex]

[tex]\bold{Q1}\\\\x^2-7x+10=0\\\\a=1,\ b=-7,\ c=10\\\\b^2-4ac=(-7)^2-4(1)(10)=49-40=9>0\\\\\sqrt{b^2-4ac}=\sqrt9=3\\\\x_1=\dfrac{-(-7)-3}{2(1)}=\dfrac{7-3}{2}=\dfrac{4}{2}=2\\\\x_2=\dfrac{-(-7)+3}{2(1)}=\dfrac{7+3}{2}=\dfrac{10}{2}=5\\\\========================================[/tex]

[tex]\bold{Q2}\\x^2-2x=20\qquad\text{subtract 20 from both sides}\\\\x^2-2x-20=0\\\\a=1,\ b=-2,\ c=-20\\\\b^2-4ac=(-2)^2-4(1)(-20)=4+80=84>0\\\\\sqrt{b^2-4ac}=\sqrt{84}=\sqrt{4\cdot21}=\sqrt4\cdot\sqrt{21}=2\sqrt{21}\\\\x_1=\dfrac{-(-2)-2\sqrt{21}}{2(1)}=\dfrac{2-2\sqrt{21}}{2}=1-\sqrt{21}\\\\x_2=\dfrac{-(-2)+2\sqrt{21}}{2(1)}=\dfrac{2+2\sqrt{21}}{2}=1+\sqrt{21}[/tex]

Answer:

Step-by-step explanation:

x^2 - 7x + 10 = 0 can be factored as follows:  (x - 5)(x - 2).  Note that -5x -2x combine to -7x, the middle term of this quadratic, and that (-5)(-2) = +10, the constant term.  Setting each of these factors = to 0 separately, we get:

x = 5 and x = 2.

x^2 - 2x = 20 should be rewritten in standard form for a quadratic equation before you attempt to solve it:  x^2 - 2x - 20 = 0.  This quadratic is not so easily factored as was the previous one.  Let's use the quadratic formula:

      -b ± √(b²-4ac)

x = --------------------

             2a

Here, a = 1, b = -2 and c = -20, so the discriminant b²-4ac = (-2)^2 - 4(1)(-20), or 4 + 80, or 84.  84 has only one perfect square factor:  4·21.  Because the discriminant is +, we know that this equation has two real, unequal roots.

They are:

       -(-2) ± √(4·21)         2 ± 2√21

x = ----------------------  =  ----------------- =   1 ± √21

             2(1)                            2

For this case we have by definition, that the volume of a cone is given by "

[tex]V = \frac {1} {3} \pi * r ^ 2 * h[/tex]

Where:

h: It's the height

r: It is the cone radius

They tell us as data that the volume is 8 [tex]\pi[/tex]and the height is 6 cm, we must find an expression that allows to clear the radius, then:[tex]8 \pi = \frac {1} {3} \pi * r ^ 2 * 6[/tex]

Answer:

Option D

Answer:

Step-by-step explanation:

Y=20. X=10. Y=5. X=2.5

X is half of Y so 20 is y

Answer:

20

Step-by-step explanation:

ANSWER

72km/h

EXPLANATION

The average speed of the car can be calculated using the formula:

Average Speed=total distance/ total time taken.

The car covers a distance of 108km in 1½ hours.

We substitute the values into the formula to obtain,

[tex]Average \: \: Speed= \frac{108}{1.5} [/tex]

[tex]Average \: \: Speed=72 {kmh}^{ - 1} [/tex]

Therefore the average speed of the journey is 72km/h

Answer:

It's the second one:

yes; 4+5=6

Step-by-step explanation:

ANSWER

The graph in option D.

EXPLANATION

The given function is:

[tex]y = 3 {x}^{2} - 12x + 10[/tex]

We complete the square to obtain:

[tex]y = 3( {x}^{2} - 4x) + 10[/tex]

[tex]y = 3( {x}^{2} - 4x + {( - 2)}^{2} ) + 10 - 3 {( - 2)}^{2}[/tex]

[tex]y = 3{( x- 2)}^{2}+ 10 - 12[/tex]

[tex]y = 3{( x- 2)}^{2} - 2[/tex]

The graph of this function opens upwards and has its vertex at (2,-2).

The y-intercept is 10.

From the options the graph that satisfies all these properties is D.

Answer: Second option.

Step-by-step explanation:

By the Right Triangle Altitude Theorem, we know that the altitude "h" (Observe the figure attached) is:

[tex]h=\sqrt{9*3}\\h=3\sqrt{3}[/tex]

Then, since we know the value of the altitude, we can calculate the value of "y" with the Pythagorean Theorem:

[tex]a=\sqrt{b^2+c^2}[/tex]

Where "a" is the   hypotenuse and "b" and "c" are the legs of the right triangle.

We can identify that:

[tex]a=y\\b=9\\c=h=3\sqrt{3}[/tex]

Then, substituting values, you get that "y" is:

[tex]y=\sqrt{9^2+(3\sqrt{3})^2}=6\sqrt{3}[/tex]

Answer:

[tex]6050(1+\frac{0.031}{12})^{3}(1+\frac{0.206}{12})^{9}[/tex]

Step-by-step explanation:

p = $6050

The card offered an introductory APR of 3.1% for the first 3 months

r = 3.1% or 0.031

t = 3

n = 12

So, compound interest formula for this period is :

[tex]6050(1+\frac{0.031}{12})^{3}[/tex]

And a standard APR of 20.6% thereafter,

r = 20.6% or 0.206

t = 9

n = 12

So, compound interest formula for this period is :

[tex]6050(1+\frac{0.206}{12})^{9}[/tex]

Now as the p is common, we can re write the expressions as :

[tex]6050(1+\frac{0.031}{12})^{3}(1+\frac{0.206}{12})^{9}[/tex]

Final answer:

The domain of the function g(x) = -[x] + 3 is all real numbers because the floor function is defined for all real numbers.

Explanation:

The given function is g(x) = -[x] + 3. To determine the domain of g(x), we look for the set of all input values (x) that the function can accept.

The square brackets around x indicate that we are dealing with the floor function, which takes a real number and rounds it down to the nearest integer.

Since the greatest integer function is defined for all real numbers, the only restriction we have is when the function involves division by zero.

Since the process of rounding down to the nearest integer is defined for all real numbers, the domain of g(x) is all real numbers, which is expressed as ∞ < x < ∞ or –∞ < x < ∞.

Answer: The area is  [tex]320m^2[/tex]

Step-by-step explanation:

The formula for calculate the area of a rectangle is:

[tex]A=lw[/tex]

Where "l" is lenght and "w" is the width.

We know the width and the perimeter, then we can solve for the lenght from the following formula, which is used to calculate the perimeter of a rectangle:

[tex]P=2l+2w[/tex]

Then:

[tex]72m=2l+2(16m)\\72m-32m=2l\\\l=\frac{40}{2}\\\\l=20m[/tex]

Substituting values into the formula [tex]A=lw[/tex], we get that the area of the rectangle is:

[tex]A=(16m)(20m)[/tex]

[tex]A=320m^2[/tex]

Answer:

The area of rectangle = 320 m²

Step-by-step explanation:

Points to remember

Area of rectangle = lb

l - length and b - width

It is given that, perimeter of rectangle is 72 m. And width of rectangle = 16 m

To find the value of length

Perimeter = 2(l + b)

72 = 2(l + 16)

36 = l + 16

l = 36 - 16 = 20

To find the area of rectangle

Area = lb

 = 20 * 16

 = 320 m²

Therefore area of rectangle = 320 m²

Step-by-step explanation:

Formula:

d×3.14=C

or

r×3.14×2=C

d=diameter

r=radius

Answer:

x<3/-2

Step-by-step explanation:

4x>6x+3

4x-6x>3

-2x>3

x<3/-2

Also help me with my question just click on my name and see my questions

Answer:

D:The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

hope this helps you

(ps.please make me  brainlyest)

Step-by-step explanation:

i just took the test on E2020 & got 100%

d) The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

Number of tree purchased                            Total Cost ($)

                1                                                                 60

                2                                                                120

                3                                                                180

                4                                                                240

                5                                                                290

For the linear function rate of change is constant.

Now, between 2 and 3 trees rate of change is given by

[tex]=\frac{180-120}{3-2} \\\\=60\\[/tex]

Now, between 3 and 5 trees rate of change is given by

[tex]=\frac{200- 180}{5-3} \\\\=55[/tex]

This is clearly that the rate of change isn't constant. Therefore, the function is non-linear.

so,

d) The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

Learn more about linear function here

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Answer:

242 mm²

Step-by-step explanation:

Given 2 similar figures with

ratio of sides = a : b, then

ratio of areas = a² : b² and

ratio of volumes = a³ : b³

Here the ratio of volumes = 27 : 1331, hence

ratio of sides = [tex]\sqrt[3]{27}[/tex] : [tex]\sqrt[3]{1331}[/tex] = 3 : 11, thus

ratio of areas = 3² : 11² = 9 : 121

let x be the surface area of the larger figure then by proportion

[tex]\frac{18}{9}[/tex] = [tex]\frac{x}{121}[/tex] ( cross- multiply )

9x = 18 × 121 ( divide both sides by 9 )

x = [tex]\frac{18(121)}{9}[/tex] = 2 × 121 = 242

The surface area of the larger figure is 242 mm²

Answer:

see explanation

Step-by-step explanation:

Given

f(x) = x² - p(x + 1) - c

     = x² - px - p - c ← in standard form

with a = 1, b = - p and c = - p - c

Given that α and β are the zeros of f(x), then

α + β = - [tex]\frac{b}{a}[/tex] and αβ = [tex]\frac{c}{a}[/tex], thus

α + β = - [tex]\frac{-p}{1}[/tex] = p , and

αβ = [tex]\frac{-p-c}1}[/tex] = - p - c

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

(α + 1)(β + 1) ← expand factors

= αβ +α + β + 1 ← substitute values from above

= - p - c + p + 1

= - c + 1 = 1 - c ← as required

Final answer:

By applying Vieta's formulas to the given polynomial, we can determine that the product (α + 1)(β + 1) equals 1 - c.

Explanation:

Given the polynomial f(x) = x2 - p(x + 1) - c, whose zeroes are alpha (α) and beta (β), we can use the relationship between the coefficients of a polynomial and its zeroes to find the value of (α + 1)(β + 1). According to Vieta's formulas for a second-degree polynomial ax2 + bx + c = 0, the sum of its roots (-b/a) is equal to α + β, and the product of its roots (c/a) equals αβ.

For this specific polynomial, a = 1, b = -p, and c = -c. Thus, we have:

α + β = p

αβ = -c

Now, let's calculate (α + 1)(β + 1):

(α + 1)(β + 1) = αβ + α + β + 1 = (-c) + (p - 1) + 1 = 1 - c

No, if you were to have three right angles, the fourth angle would also have to be a right angle. As a result, it would make the shape either a square or a rectangle.

Answer:

Average = 1

Step-by-step explanation:

Let us define the average first:

Average is calculated by adding up all the values and then dividing the sum by total number of values.

The formula for average may be written as:

[tex]Average = \frac{Sum}{count}[/tex]

In the following case,

Sum of numbers = -3-2+2+2+6 = 5

Count = 5

So,

Average = 5/5

=> Average = 1

Answer:

the answer is 1

Step-by-step explanation:

Sum of numbers = -3-2+2+2+6 = 5

Count = 5

So,  

Average = 5/5

=> Average = 1

Final Velocity = Initial Velocity + (Acceleration * time)

Final Velocity = ?

Initial Velocity = 3

Acceleration = 1.5

Time = 7

Plug in and solve

3+(1.5*7)

3+10.5

Velocity = 13.5m/s

Answer:

Area: 135 ft^2

Perimeter: 50 ft

Step-by-step explanation:

area:

take the rectanle so length 12 x 9 = 108 so that is the length of the rectangle and now we need to find that of the triangle left over

subract 18 - 12 = 6 so that is the base of the trianle and we know the side length is 9 so plus it in A = (9)(6)/2

A = 54/2

A = 27

add 27 + 108 to get the total area

135

perimeter:

18 + 9 + 11 + 12 = 50

For this case we have that by definition, the perimeter of the trapezoid is given by the sum of its sides:

[tex]p = 9 + 18 + 11 + 12\\p = 50[/tex]

So, the perimeter is 50ft

On the other hand, the area is given by:

[tex]A = \frac {1} {2} (b_ {1} + b_ {2}) * h[/tex]

Where:

[tex]b_ {1}:[/tex] It is the largest base

[tex]b_ {2}:[/tex] It is the minor base

h: It's the height

Substituting the values:

[tex]A = \frac {1} {2} (18 + 12) * 9\\A = \frac {1} {2} (30) * 9\\A = \frac {1} {2} (270)\\A = 135[/tex]

So, the area of the trapezoid is [tex]135 \ ft ^ 2[/tex]

Answer:

the perimeter is 50ft

the area of the trapezoid is [tex]135 \ ft ^ 2[/tex]

The slope is 7/4 and the intercept is -10

For this case we must divide the following expression:

[tex]\frac {\frac {14x ^ 2} {15}} {7x}[/tex]

And in this way we get the amount of money that each person will receive.

Then applying double C we have:

[tex]\frac {14x ^ 2} {15 * 7x} =\\\frac {14x ^ 2} {105x} =\\0.133x[/tex]

Thus, each person has 0.133x of money!

Answer:

0.133x

The answer is:

The correct option is:

A) $74.55

To calculate how much does Sonya pay for the four pairs altogether, we need to calculate the original price after the 50% discount and the taxes.

Calculating we have:

[tex]PriceAfterDiscount=35*50(percent)=35*\frac{50}{100}\\\\35*\frac{50}{100}=35*0.5=17.5[/tex]

We have that before the tax, the price of the shoes was $17.5, then, calculating the price after the taxes, we have:

[tex]AfterTaxes=17.5(1+6.5(percent))=17.5(1+\frac{6.5(percent)}{100})\\\\AfterTaxes=17.5(1+\frac{6.5(percent)}{100})=17.5*(1+0.065)\\\\AfterTaxes=17.5*(1+0.065)=17.5*1.065=18.637[/tex]

So, we have that the price after discount and the taxes is $18.637 per each pair of shoes.

Hence, the price for the four pairs of shoes will be:

[tex]TotalPrice=4*18.637=74.548=74.55[/tex]

Have a nice day!