How many different sets of initials can be formed if every person has one surname (i.e., last name) and either one or two given names (i.e., a first name, or a first and middle name).

Answers

Answer 1

The different sets of initials can be formed if every person has one surname (i.e., last name) and either one or two given names (i.e., a first name, or a first and middle name) is 15600.

There are 26 possible letters, each set of initials would have 3 letters in it, order doesn't matter, i.e. ABC does not equal ACB. using permutation   26P3 = 5600.

A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters. Common mathematical problems involve choosing only several items from a set of items in a certain order.

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Related Questions

please help me out with this

Answers

Answer:

25

Step-by-step explanation:

sin © =36/(35+x)=21/35

36/(35+x)=21/35

x=(36*35/21)-35

x=25

Step-by-step explanation:

SOLUTION::

please watch the image for explanation

What is the Value of the expression? 2 (1/4)^2

Answers

Answer:

[tex]\frac{1}{8}[/tex]

Step-by-step explanation:

2 ( [tex]\frac{1}{4}[/tex] )²

= 2 × [tex]\frac{1}{16}[/tex] ← cancel 2 and 16 by 2

= 1 × [tex]\frac{1}{8}[/tex]

= [tex]\frac{1}{8}[/tex]

Solve each triangle. Round answers to the nearest tenth.

Answers

Step-by-step explanation:

1.) ˆ B = 7∘ ,  ˆ A = 28 ∘ ,  a = 27

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

2.) c ≈ 28.0

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

3.) The triangle has the following measures.

A  =  36 ˚

a  =  14  units

B  =  105 ˚  

b  =  23 units

C  =  39 ˚  

c  = 15  units

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

4.) a  ≅  15.0 units

B  =  145 ˚

b  ≅  22.9 units

prove that the value of each expression is divisible by the given number 8^10-2^27 is divisible by 14

Answers

Answer:

Proof below

Step-by-step explanation:

General Strategy:Find factors of divisorUse algebraic properties to reveal those factors in the given expression.

Divisibility

A number, p, is divisible by another number, d, if and only if there is some non-negative integer, n, such that n*d=p.

To prove that, 300 is divisible by 10 because, 30 is a non-negative integer, and 10*30=300.

Strategies for Divisibility by a composite number

Note that in the previous example, 10 is a composite number.  This means that both one 2 and one 5 (the full list of 10s factors) had to be factored out of the 300.

In the given problem, we are to prove that the number is divisible by 14.  Observe 14 is composite with factors of 2 and 7.

Properties of exponents

Since the expression is given with exponents, it will be helpful to recall a few exponent properties to algebraically manipulate the expression.

Recall the following property of exponents:

[tex]x^{a}*x^{b}=x^{(a+b)}[/tex]   [tex](x^{a})^{b}=x^{ab}[/tex]

Finding a factor of 14 in the given expression

Original expression...

[tex]8^{10}-2^{27}[/tex]

Recognizing 8 as a power of 2...

[tex](2^3)^{10}-2^{27}[/tex]

Simplifying and rewriting so that both terms are powers of 2...

[tex]2^{30}-2^{27}[/tex]

Observing that both terms have 27 twos as factors...

[tex]2^{27}*2^{3}-2^{27}[/tex]

Factoring out 27 twos...

[tex]2^{27}*(2^{3}-1)[/tex]

Simplifying the expression in the parenthesis:

[tex]2^{27}*(8-1)[/tex]

[tex]2^{27}*(7)[/tex]

Knowing that we also need a factor of 2, use properties of exponents, and associative property of multiplication...

[tex](2^{26}*2^1)*7[/tex]

[tex]2^{26}*(2^1*7)[/tex]

[tex]2^{26}*(2*7)[/tex]

[tex]2^{26}*14[/tex]

Since 2^26 is a non-negative integer, the original expression is divisible by 14.


Every year, the value of a surveying machine depreciates by 25 % of its value in the previous year.
If the value of the machine was $ 11 250 in 2012, find its value in 2010.

Answers

Answer:

$17578.13

Step-by-step explanation:

join my stream for an explanation

(ChildOfHermes)

please mark brainliest

im only streaming for 15.5 hours

Please answer with everything needed i appreciate everyones help:00

Answers

Answer:

y = 5

Step-by-step explanation:

Step-by-step explanation:

the slope of a line is the ratio "y coordinate change / x coordinate change" when going from one point on the line to another.

when the slope is 0, it means the y coordinate change is 0 for all points. that means y is a constant. and the line is a horizontal line.

to go through (-2, 5) this constant y has to be the y value of the point.

so,

y = 5

that's it. that is the whole equation for that line, because the slope m is 0. what remains is the y-axis intercept (y = 5).

NEED HELP
pls & thank you

Answers

We have proven that BC = DE using the Segment addition postulate

Segment addition postulate

The segment addition postulate states that given two points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC

The reasons for the proof are given below:

Statement                                Reason

BD = BC + CD                          Segment addition postulate

CE = CD + DE                           Segment addition postulate

BD = CE                                    Given

BC + CD = CD + DE                  Substitution property

BC = DE                                   Subtraction property

Hence, we have proven that BC = DE using the Segment addition postulate

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For the following exercises, solve each inequality and write the solution in interval notation.
32. | x − 4 | ≥ 8

Answers

Answer:

The solution of the given set in interval form is [tex]$(-\infty,-4] \cup[12, \infty)$[/tex].

Step-by-step explanation:

It is given in the question an inequality as [tex]$|x-4| \geq 8$[/tex].

It is required to determine the solution of the inequality.

To determine the solution of the inequality, solve the inequality [tex]$x-4 \geq 8$[/tex] and, [tex]$x-4 \leq-8$[/tex]

Step 1 of 2

Solve the inequality [tex]$x-4 \geq 8$[/tex]

[tex]$$\begin{aligned}&x-4 \geq 8 \\&x-4+4 \geq 8+4 \\&x \geq 12\end{aligned}$$[/tex]

Solve the inequality [tex]$x-4 \leq-8$[/tex].

[tex]$$\begin{aligned}&x-4 \leq-8 \\&x-4+4 \leq-8+4 \\&x \leq-4\end{aligned}$$[/tex]

Step 2 of 2

The common solution from the above two solutions is x less than -4 and [tex]$x \geq 12$[/tex].

The solution set in terms of interval is [tex]$(-\infty,-4] \cup[12, \infty)$[/tex].

Can someone help with these geometry questions? It’s question 2, 3, 4 & 5, I gotta have answers fast pls :(

Answers

Answer:

Hey! I am gona help you.

BC ≅ EF

DE ≅ AB

Angle C ≅ Angle F

Angle D ≅ Angle A

Hope it might help!

Note -

2,3 can't be solved as there is no figure given here.

A new computer loses 1/3 of its value every year. Which graph- a, b, c, or d – could represent the relationship between the year and the computers value? Justify your choice.

Answers

The graph which represents the relationship between the year and the computers value is; Choice A.

Which graph represents the relationship?

According to the task content, it follows that the computer loses 1/3 of its value every year. Hence, it follows that the value of the computer each year is 2/3 of its previous value.

Hence, the relationship can best be modelled by an exponential function, a decay function to be more specific and can best be represented by Choice A.

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xan any one help please​

Answers

Answer:

Sophie.

Step-by-step explanation:

15. 30 in Italian minus 15 in German.

what is the slope for (3, 8) and (2, 6). ?

Answers

Answer:

m = 2

Step-by-step explanation:

[tex]m = \frac{rise}{run} =\frac{y_{2}-y_1}{x_2-x_1}[/tex]

[tex]=\frac{6 - 8}{2 - 3} \\= \frac{-2}{-1}\\ = 2[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{The formula for finding the slope:}[/tex]

[tex]\mathbf{\dfrac{y_2 - y_1}{x_2 - x_1} = slope}[/tex]

[tex]\huge\textbf{Some people understand formula like:}[/tex]

[tex]\mathbf{\dfrac{rise}{run} = slope}[/tex]

[tex]\huge\textbf{Breaking down the question:}[/tex]

[tex]\mathbf{y_2 \rightarrow \boxed{\textbf{6}}}[/tex]

[tex]\mathbf{y_1 \rightarrow \boxed{\textbf{8}}}[/tex]

[tex]\mathbf{x_2 \rightarrow \boxed{\textbf{2}}}[/tex]

[tex]\mathbf{x_1 \rightarrow \boxed{\textbf{3}}}[/tex]

[tex]\huge\textbf{What your equation should look like:}[/tex]

[tex]\mathbf{\dfrac{6 - 8}{2 - 3} = slope}[/tex]

[tex]\huge\textbf{Simplify the equation we came up with:}[/tex]

[tex]\mathbf{\dfrac{6 - 8}{2 - 3} = slope}[/tex]

[tex]\mathbf{\rightarrow \dfrac{-2}{-1} = slope}[/tex]

[tex]\mathbf{\rightarrow -2 \div -1 = slope}[/tex]

[tex]\mathbf{\rightarrow 2 = slope}[/tex]

[tex]\huge\textbf{Thus, the answer should most likely be:}[/tex]

[tex]\huge\boxed{\mathsf{Slope \rightarrow \boxed{\textsf{2}}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphite1040:)}[/tex]

Express the radical using the imaginary unit i

Answers

Answer:

[tex]\huge\boxed{\sf \pm 10i}[/tex]

Step-by-step explanation:

Given radical:

[tex]\pm \sqrt{-100}[/tex]

We can write it as:

[tex]\pm \sqrt{-1 \times 100} \\\\\pm \sqrt{-1} \times \sqrt{100} \\\\\underline{We \ know \ that:}\ i =\sqrt{-1} \\\\\pm i \times 10\\\\\boxed{\pm 10i}\\\\\rule[225]{225}{2}[/tex]

Triangle QRS is to be dilated using the rule D Subscript P, three-fourths.

Point P is the center of dilation. Triangle Q R S is shown. The length of P S is 8.

What will be the distance from the center of dilation, P, to the image S'?

2 units
4 units
6 units
8 units

Answers

The distance from the center of dilation, P, to.the image vertice S' is; 6 units.

What is the distance from the center of dilation, P, to the image S'?

It follows from the task content that the center of dilation of the triangle QRS is point P and the length of segment PS in the pre-image is; 8 units.

Hence, since the dilation factor as given in the task content is; three-fourths, it therefore follows that the distance of point P to S' in the image is; (3/4) × 8 = 6units.

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Petrol costs $1.65 per litre. Calculate how much, correct to the nearest cent, the
petrol will cost Anne for a journey of 120km.

Answers

The petrol cost for Anne's journey of 120km is $16.236

How to find the cost for 120 km?

Her car has a fuel consumption of 8.2 litres per 100 km .

Therefore,

100 km = 8.2 litres

120 km = ?

cross multiply

volume(litres) = 8.2 × 120 / 100 = 984 / 100 = 9.84 litres

Therefore,

1 litres = 1.65 dollars

9.84 litres = ?

cross multiply

cost of fuel used = 1.65 × 9.84 / 1

cost of fuel used = $16.236

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b=(1-1/3).(1-1/3).(1-1/4).................(1-1/2004)

Answers

When the above complex expression has been simplified the solution to the above expression is = 2003/8016.

What is the formula for solving the above?

The formula is given as:

1 - [tex]\frac{1}{n}[/tex] = [tex]\frac{n-1}{n}[/tex]

From the stated express, we have:

(1 - (1/2)) * (1 - (1/3)) * (1 - (1/4)) *( 1 - (1/2004))

→ ((2-1)/2)  ((3-1)/3) ((4-1)/4) ((2004 -1)/2004)

→ (1/2) * (2/3) * (3/4) * (2003/2004)

→ [tex]\frac{ 1* 2003}{4*2004}[/tex]

= 2003/8016

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Answer:

When the above complex expression has been simplified the solution to the above expression is = 2003/8016.

What is the formula for solving the above?

The formula is given as:

1 -  =

From the stated express, we have:

(1 - (1/2)) * (1 - (1/3)) * (1 - (1/4)) *( 1 - (1/2004))

→ ((2-1)/2)  ((3-1)/3) ((4-1)/4) ((2004 -1)/2004)

→ (1/2) * (2/3) * (3/4) * (2003/2004)

= 2003/8016

Step-by-step explanation:

The eleventh term of an AP is four times the second term. If the sum of the first seven terms of the AP is 175, find the first term and the common difference.​

Answers

Step-by-step explanation:

a11 = 4 × a2

a + 10d = 4 × (a + d)

a + 10d - 4d = 4a

a + 6d = 4a

6d = 4a - a

6d = 3a

(6/3)d = a

2d = a ----- eq. 1

now, sum of 7 terms = s7 = 175

7/2 {2a+6d} = 175

7/2 { (2 × 2d ) + 6d} = 175

7 ( 4d + 6d ) = 175 × 2

7 ( 10d ) = 350

70d = 350

d = 350/70

d = 5

Now from eq. 1,

2d = a

2(5) = a

a = 10, d = 5

THANK YOU........

Use the digits 1-20, at most one time each, to create a true statement for polynomial below.
(the _ are blanks that need to be filled in)
_x(x^2 - _x) + _x^3 = _x(_x^2 + _x) - x^2

Answers

The complete equation of the polynomial is 2x(x^2 - 11x) + 10x^3 = 3x(4x^2 - 7x) - x^2

How to complete the blanks?

The equation is given as:

_x(x^2 - _x) + _x^3 = _x(_x^2 + _x) - x^2

Complete the blanks using alphabets

ax(x^2 - bx) + cx^3 = dx(ex^2 + fx) - x^2

Open the brackets

ax^3 - abx^2 + cx^3 = dex^3 + dfx^2- x^2

Factorize the expression

(a + c)x^3 - abx^2 = dex^3 + (df - 1)x^2

By comparison, we have:

a + c = de

-ab = df - 1

Rewrite the second equation as:

ab + df = 1

So, we have:

a + c = de

ab + df = 1

Set a = 2 and c = 10.

So, we have:

a + c = de ⇒ de = 2 + 10 ⇒ de = 12

ab + df = 1 ⇒2b + df = 1

Express 12 as 3 * 4 in de = 12

de = 3 * 4

By comparison, we have:

d = 3 and e = 4

So, we have:

2b + df = 1

This gives

2b + 3f = 1

Set b = 11.

So, we have:

2 * 11 + 3f = 1

This gives

22 + 3f = 1

Subtract 22 from both sides

3f = -21

Divide by 3

f = -7

Hence, the complete equation is:

2x(x^2 - 11x) + 10x^3 = 3x(4x^2 - 7x) - x^2

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The circle above has an area of 36π and is divided into 8 congruent regions. What is the perimeter of one of these regions?


A) 6+1.5π

B) 6+2π

C) 12+ 1.5π

D) 12+2π

Answers

The perimeter of each region is 12 + 1.5π if a circle with an area of 36π is divided into 8 congruent regions

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let r represent the area of the circle, hence:

Area = πr²

36π = πr²

r = 6 units

Perimeter = 2πr = 2π(6) = 12π

The circle has 8 congruent regions, hence:

Perimeter of each region = 6 + 6 + 12π/8 = 12 + 1.5π

The perimeter of each region is 12 + 1.5π if a circle with an area of 36π is divided into 8 congruent regions

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After using a compass and a straightedge to generate this figure, Jeremy claims AABC is an equilateral triangle inscribed in circle O.

How can Jeremy prove his claim?

A.He can show that the measures of arcs AB, AC, and BC are all equal to 60°.
B. He can show that the lengths of segments AB, AC, and BC are all equal to the length of the circle's radius.
C. He can show that the measures of arcs AB, AC, and BC are all equal to 120°.
D.He can show that the lengths of segments AB, AC, and BC are all equal to the length of the circle's diameter.

Answers

Answer: C. He can show that the measures of arcs AB, AC, and BC are all equal to 120°.

Step-by-step explanation:

Each angle of an equilateral triangle measures 60°, so by the inscribed angle theorem, each arc created by a pair of adjacent vertices will measure 120°.

9. Evaluate 14(-6x +10) - 16x - 100x + 140 for x = -2.

Answers

Answer:

680

Step-by-step explanation:

14(-6x +10) - 16x - 100x + 140 for x = -2.

14(-6(-2) + 10) - 16(-2) - 100(-2) + 140

14(12 + 10) + 32 + 200 + 140

14(22) + 372

308 + 372

680

The mapping diagram shows a functional relationship. A mapping diagram shows a relation, using arrows, between domain and range for the following ordered pairs: (8, 4), (negative two-thirds, 3), (11, negative 1), (4, one-half). Complete the statements. f(4) is . f(x) = 4 when x is .

Answers

Answer:

its 1/2 and 8

Step-by-step explanation:

got it right

what should be added to 51 to get the answer -1 ?

Please answer Urgent!

Answers

Answer:

Let the no. be x

51 + x = -1

x = -1-51

x = 1 + 51

x = -52

Answer:

-52

Step-by-step explanation:

51 + (-52) = -1

Deepika has drawn a rhombus and a square, each with side length 5 cm. Which of these will be different for both the shapes?
1. lengths of the two diagonals
2. angles between the two diagonals
3. lengths of the adjacent sides
4. angles between the adjacent side

Answers

The difference for both the rhombus and square are as follows;

Lengths of the two diagonalsAngles between the two diagonalsAngles between the adjacent side

Properties of a square?All the sides are equal.Opposite sides are parallel.All the angles are 90 degrees each.The diagonal bisect each otherProperties of a rhombusAll the sides are equal.Opposite sides are parallel.All the angles are not 90 degrees.The length of the diagonals are not the same.

Therefore, the difference for both the shapes(square and rhombus)are as follows:

Lengths of the two diagonalsAngles between the two diagonalsAngles between the adjacent side

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The price of a technology stock was $9.69 yesterday. Today, the price rose to $9.80. Find the percentage increase. Round your answer to the nearest tenth of a percent.

Answers

Answer:

Percent increase was 1.1%

Step-by-step explanation:

Step 1

Find the price increase in number:

$9.80 - $9.69 = $0.11

Step 2

Find the percent increase, relevant to initial price:

$0.11/$9.69 × 100% = 1.1% (rounded to the nearest tenth)

Simplify the following:
A.
(-x)^4/4x * 8(-x)^-3/x^-3/4

Answers

Answer:

Answer for (a)   -2x^4/3

Answer for (b)  2^5x/4^3x

Answer:

a. [tex]-2x\sqrt[3]{x}[/tex]

b. [tex]\frac{1}{2^x}[/tex]

Step-by-step explanation:

a.

Original equation:

[tex]\frac{(-x)^4}{4x}*\frac{8(-x)^{-3}}{x^{-\frac{4}{3}}}[/tex]

So (-x)^4 can be seen as (-x * -x) * (-x * -x), which becomes x^2 * x^2 = x^4, the negatives cancel out of the degree is even. So it becomes:

[tex]\frac{x^4}{4x}*\frac{8(-x)^{-3}}{x^{-\frac{4}{3}}}[/tex]

Cancel out one of the x's on the left fraction:

[tex]\frac{x^3}{4}*\frac{8(-x)^{-3}}{x^{-\frac{4}{3}}}[/tex]

Rewrite the exponent in the numerator: [tex]a^{-x} = \frac{1}{a^x}[/tex]

[tex]\frac{x^3}{4}*\frac{8*\frac{1}{-x^3}}{x^{-\frac{4}{3}}}[/tex]

Simplify the numerator:

[tex]\frac{x^3}{4}*\frac{\frac{8}{-x^3}}{x^{-\frac{4}{3}}}[/tex]

Keep numerator, change division to multiplication, flip the denominator:

[tex]\frac{x^3}{4}*\frac{8}{-x^3} * \frac{1}{x^{-\frac{4}{3}}}[/tex]

multiply the denominator using the exponent identity: [tex]x^a*x^b=x^{a+b}[/tex]

[tex]\frac{x^3}{4}*\frac{8}{-x^{\frac{5}{3}}}[/tex]

Multiply the numerators and denominators:

[tex]\frac{8x^3}{-4x^{\frac{5}{3}}}[/tex]

Use the fact that: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex] to divide the x^3 and x^(5/3) and divide the 4 by the -8

[tex]-2x^{\frac{4}{3}}[/tex]

Rewrite the exponent using the exponent identity: [tex]x^{\frac{a}{b}} = \sqrt[b]{x^a}=\sqrt[b]{x}^a[/tex]

[tex]-2\sqrt[3]{x^4}[/tex]

Rewrite as two radicals: [tex]\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{ab}[/tex]

[tex]-2\sqrt[3]{x^3} * \sqrt[3]{x}[/tex]

Simplify:

[tex]-2x\sqrt[3]{x}[/tex]

b.

[tex]2^{2x}\div4^{3x}*64^{\frac{x}{2}}[/tex]

Rewrite the 4 as 2^2

[tex]2^{2x}\div(2^2)^{3x}*64^{\frac{x}{2}}[/tex]

Use the exponent identity: [tex](x^a)^b=x^{ab}[/tex]

[tex]2^{2x}\div2^{6x}}*64^{\frac{x}{2}}[/tex]

Use the exponent identity: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]

[tex]2^{2x-6x} = 2^{-4x}[/tex]

Rewrite this part using the definition of a negative exponent: [tex](\frac{a}{b})^{-x} = \frac{b}{a^x}[/tex].

[tex]\frac{1}{2^{4x}} * 64^{\frac{x}{2}}[/tex]

Multiply:

[tex]\frac{64^{\frac{x}{2}}}{2^{4x}}[/tex]

rewrite 64 as 2^6

[tex]\frac{(2^6)^{\frac{x}{2}}}{2^{4x}}[/tex]

Use the identity: [tex](x^a)^b=x^{ab}[/tex]

[tex]\frac{2^{3x}}{2^{4x}}[/tex]

Use the identity: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]

[tex]2^{-x}[/tex]

rewrite using the definition of a negative exponent: [tex](\frac{a}{b})^{-x} = \frac{b}{a^x}[/tex]

[tex]\frac{1}{2^x}[/tex]

Pls answer ASAP it is almost due TYSMMM


There are 357 people attending a school play.
Assuming that all but one row of seats in the
theatre is completely full and that each row fits
24 people, how many rows of seats are there in
the theatre?

Answers

There are 15 rows of seats in the theater

How to determine the number of rows?

The given parameters are:

Total number of people = 357People per row = 24

The number of rows is calculated as:

Rows = Total number of people/People per row

This gives

Rows = 357/24

Evaluate the quotient

Rows = 14.875

Round up the number

Rows = 15

Hence, there are 15 rows of seats in the theater

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Given a sphere with a radius of 2 cm, find its volume to the nearest whole
number.
A. 8 cm³
B. 17 cm³
о C. 33 cm³
O D. 3 cm³

Answers

Answer: 34

Step-by-step explanation:

[tex]V=\frac{4}{3}(\pi)(2^{3}) \approx \boxed{34}[/tex]

Choose the expression that is equivalent to the expression: 2³
a.2x2x2
b.2x3
c.3x3
d.2x2x3

Answers

Hello,

2³ = 2 × 2 × 2 → answer A

The answer is a because exponents just show how many times a number is multiplied by itself.

HELPPP MEEE PLSSSS meee outttt

Answers

Answer: x = 32

Step-by-step explanation:

If m∠ORS = m∠SRQ = 3x - 6 and since the two angles are a linear pair they total 180°. This means half or only one section = 90°

solve for x

3x - 6 = 90

add 6 to both sides

3x = 96

divide each side by 3

x = 32

Other Questions
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