Determine the truth value of the given conditional statement. Given: If 3 is an even number, then 5 + 3 = 8.

Answer:

Option C is correct

Step-by-step explanation:

We need to simplify the radical

[tex]\sqrt{\frac{20x^{13}y^5}{5xy^7}}[/tex]

We know that a^m/a^n = a^m-n and 20/5 = 4

Solving

[tex]\sqrt{4x^{13-1}y^{5-7}}\\\sqrt{4x^{12}y^{-2}}\\[/tex]

Now, √4 = 2 and a^-m = 1/a^m

Applying,

[tex]2\sqrt{\frac{x^{12}}{y^2}}\\[/tex]

So, Option C [tex]2\sqrt{\frac{x^{12}}{y^2}}\\[/tex] is correct.

Answer: c. 15a

explanation: if a movie ticket is 10 per person and a drink is 5 per person and everyone buys a drink that would mean each person would be spending 15 and the # of people is unknown so it would be 15a.

Answer: should be c. 15a because 10+5=15 and the # of people in unknown so the answer should be 15a

Answer:

  17

Step-by-step explanation:

If 3 times the quantity is 57, then the quantity is 57/3 = 19.

If 2 more than the number is 19, then the number is 17.

Answer:

C. SAS

Step-by-step explanation:

Proof:

AB ≅ DC - Given (Side)

∠BAC ≅ ∠DCA - Given (Angle)

AC ≅ AC -  Reflexive Property (Side)

~

Answer:

2.16

Step-by-step explanation:

The question is on mean absolute deviation

The general formula ,

Mean deviation = sum║x-μ║/N where  x is the each individual value, μ is the mean and N is number of values

Team 1

Finding the mean ;

[tex]mean= \frac{51+47+35+48+64}{5}  =49[/tex]

Points     Absolute Deviation from mean

51                          2

47                         2

35                        14

48                         1

64                         15

Sum                    34          

Absolute mean deviation = 34/5= 6.8

Team 2

Finding the mean

[tex]mean=\frac{27+55+53+38+41}{5} = 42.8[/tex]

Points                      Absolute deviation from the mean

27                                    15.8

55                                    12.2

53                                     10.2

38                                      4.8

41                                       1.8

Sum                                 44.8        

Absolute deviation from the mean = 44.8/5 =8.96

Solution

Difference in mean absolute deviation of the two teams = 8.96-6.8 = 2.16

ANSWER

[tex]x = 71 \degree[/tex]

EXPLANATION

The sum of the exterior angles of a polygon is 360°

The angles were given in terms of x.

We add all and equate to 360° to obtain.

[tex]x + (x - 6) + (x + 4) + (x + 2) + (x + 5) = 360 \degree[/tex]

This implies that,

[tex]5x + 5 = 360[/tex]

[tex]5x = 360 - 5[/tex]

[tex]5x = 355[/tex]

[tex]x = \frac{355}{5} [/tex]

[tex]x = 71 \degree[/tex]

Answer: [tex]x=71[/tex]

Step-by-step explanation:

We need to remember that the sum of the exterior angles of a polygon is 360 degrees.

Knowing this, we can write the following expression:

[tex](x+4)+(x+2)+(x+5)+x+(x-6)=360[/tex]

Finally, we need to solve for "x" to find its value. Therefore, this is:

[tex]x+4+x+2+x+5+x+x-6=360\\\\5x+5=360\\\\5x=360-55\\\\5x=355\\\\x=\frac{355}{5}\\\\x=71[/tex]

Answer:

  12.8 years

Step-by-step explanation:

Put the given numbers into the model and solve for t.

[tex]3P_0=P_0e^{.086t}\\\\3=e^{.086t} \qquad\text{divide by $P_0$}\\\\\ln{3}=.086t \qquad\text{take the natural log}\\\\\dfrac{\ln{3}}{.086}=t\approx 12.77[/tex]

It will take about 12.77 years for the population to triple at the current growth rate.

Final answer:

It will take approximately 40.1 years for a country's population to triple if it continues to grow at a rate of 0.86% per year, calculated using the exponential growth formula.

Explanation:

The question asks how long it will take for a country's population to triple if it continues to grow at a continuous compound rate of 0.86% per year. Using the exponential growth formula P = P_0e^{rt}, where P is the final population, P_0 is the initial population, r is the rate of growth, and t is the time in years, we can solve for t when the population triples (P = 3P_0). Thus, the equation becomes 3 = e^{0.0086t}. Solving for t, we take the natural logarithm of both sides to get ln(3) = 0.0086t, which gives us t = ln(3) / 0.0086 years.

Calculating this, t ≈ 40.1 years. Therefore, it will take approximately 40.1 years for the country's population to triple at a continuous compound growth rate of 0.86% per year.

Answer: A

Step-by-step explanation: Complementary angles must add up to 90 degrees.

Answer:

So the three new vertices are (0,0)  , (-1,-0) , and (-1,3)

Step-by-step explanation:

So let's pick a point on the triangle like (-3,-1).

The center point of dilation is (3,1).  The horizontal distance that (3,1) is from (-3,-1) is 3-(-3)=6. The scale factor is 0.5 so multiply 0.5 to the horizontal distance which is 3. The vertical distance that (-3,-1) is from (3,1) is 1-(-1)=2. The scale factor is 0.5 so multiply 2 and 0.5 giving you 1.

So this means the image of the point (-3,-1) is going to be at: starting from center (3,1) move left 3 and down 1 and you are at (0,0).

Or if you prefer just use a formula

(k(x-a)+a,k(y-b)+b)

(x,y) is a point on the triangle

(a,b) is the center=(3,1)

k is the scale factor=.5

So let's do this formula to the other two points...

(x,y)=(-5,-1)

(.5(-5-3)+3,.5(-1-1)+1)

(.5(-8)+3,.5(-2)+1)

(-4+3,-1+1)

(-1,0)

Last point (x,y)=(-5,5)

(.5(-5-3)+3,.5(5-1)+1)

(.5(-8)+3,.5(4)+1)

(-1,3)

So the three new vertices are (0,0)  , (-1,-0) , and (-1,3)

Answer: (4.25,-2)

Step-by-step explanation:

Answer:

(4.25, -2) is the focus point

Step-by-step explanation:

Answer:

C. –120a2b2c2

Step-by-step explanation:

We'll just the multiplications one at a time...

10ac × 6ab × (–2bc) = 60a²bc * (-2bc)  (multiplying 10ac × 6ab)

60a²bc * (-2bc)  = -120a²b²c²

We just have to multiply the numbers together (like 10 and 6),

then all similar letters together (like ac * ab = a²bc).  If a letter is already present (like a in this  example), then we add up its powers a * a = a², a² * a would be a³ and so on).  If the letter is not present (like 'b' in 'ac', we suppose it's there as b^0 which is equal to 1)... so we still add up its exponent (power)... so it makes b^0 * b = b

Answer:  f(x) and g(x) are inverses of each other

Step-by-step explanation:

To find the inverse of a function, swap the x's and y's and then solve for "y"

f(x) = 5x + 2

 y  = 5x + 2

Swap:

     x = 5y + 2

   -2        - 2

x - 2 = 5y

÷5     ÷5      

[tex]\dfrac{x-2}{5}=y[/tex]

****************************************************************

[tex]g(x)=\dfrac{x-2}{5}\\\\y=\dfrac{x-2}{5}\\\\\text{Swap:}\\x=\dfrac{y-2}{5}\\\\\\(5)x=\dfrac{y-2}{5}(5)\\\\\\5x=y-2\\\\5x+2=y[/tex]

The function g(x) = x - 2/5 is the inverse of f(x) = 5x + 2. We can show this by switching the variables in the equation and solving for y.

Step 1: The variable in the function notation f(x) is x. So, we can write the function as an equation: y = 5x + 2.

Step 2: Now, we switch the variables. The equation becomes x = 5y + 2. Solving for y, we get y = (x - 2) / 5.

Step 3: To find the inverse of g(x), we need to switch the variables in the equation: x = (y - 2) / 5. Solving for y, we get y = 5x + 2. This is the original function f(x). Therefore, g(x) = x - 2/5 is the inverse of f(x) = 5x + 2.

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Let n = how much each new member must pay each month.

$160 - $28 = $132

n = $132 ÷ 12 months in a year

n = $11

You can also look at it this way:

n = (160 - 28)/12

After paying a $28 registration fee, the remaining cost of the membership is divided into 12 monthly payments of $11. The variable 'M' can be defined to represent the monthly payments.

The subject of the question is Mathematics, particularly in the area of basic algebraic operations and real life applications of mathematics. The problem involves calculating the cost of a membership at recplex. This is a real-world problem that uses mathematical concepts of subtraction and division. First, we isolate the cost that will be paid on a monthly basis. The total cost of the membership is $160, but $28 is paid up front; hence, the total amount to be divided into monthly payments is $160 - $28, which equals $132. The question doesn't specify the number of months, but since this is a yearly membership, we can assume it is 12. Therefore, $132 divided by 12 is $11 per month.

In this scenario, the variable could be defined as 'M', where 'M' represents the monthly payment.

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Answer:

The image of [tex](7,2)[/tex] is [tex](2,12)[/tex]

Step-by-step explanation:

First you need to find the translation vector.

Let the translation vector be [tex]u=(a,b)[/tex]. Then the translation rule is

[tex](x,y)\to (x+a,y+b)[/tex].

From the equation, the image of [tex]P(2,-4)[/tex] is  [tex]P'(-3,6)[/tex].When we apply this rule using the translation vector, we get

[tex]P(2,-4)\to P'(2+a,-4+b)[/tex]

Now we have

[tex]P'(2+a,-4+b)=P'(-3,6)[/tex]

We can therefore equate corresponding coordinates

[tex]2+a=-3[/tex] and [tex]-4+b=6[/tex]

This implies that:

[tex]a=-3-2[/tex] and [tex]b=6+4[/tex]

[tex]a=-5[/tex] and [tex]b=10[/tex]

Hence our translation vector is [tex]u=(-5,10)[/tex]

The translation rule now becomes:

[tex](x,y)\to (x-5,y+10)[/tex].

To find the image of (7,2), we plug it into the translation rule.

[tex](7,2)\to (7-5,2+10)[/tex].

[tex](7,2)\to (2,12)[/tex].

Answer:

  48

Step-by-step explanation:

The total number of ratio units is 3+2 = 5, and the 3 ratio units representing large bandages make up 3/5 of that total. Thus, large bandages will make up 3/5 of the total number of bandages:

  3/5×80 = 48 . . . . number of large bandages in the kit

let's multiply both sides in each equation by the LCD of all fractions in it, thus doing away with the denominator.

[tex]\begin{cases} \cfrac{1}{2}x+\cfrac{1}{3}y&=7\\\\ \cfrac{1}{4}x+\cfrac{2}{3}y&=6 \end{cases}\implies \begin{cases} \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{6}}{6\left( \cfrac{1}{2}x+\cfrac{1}{3}y \right)=6(7)}\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{1}{4}x+\cfrac{2}{3}y\right)=12(6)} \end{cases}\implies \begin{cases} 3x+2y=42\\ 3x+8y=72 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{using elimination}}{ \begin{array}{llll} 3x+2y=42&\times -1\implies &\begin{matrix} -3x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~-2y=&-42\\ 3x+8y-72 &&~~\begin{matrix} 3x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+8y=&72\\ \cline{3-4}\\ &&~\hfill 6y=&30 \end{array}} \\\\\\ y=\cfrac{30}{6}\implies \blacktriangleright y=5 \blacktriangleleft \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{substituting \underline{y} on the 1st equation}~\hfill }{3x+2(5)=42\implies 3x+10=42}\implies 3x=32 \\\\\\ x=\cfrac{32}{3}\implies \blacktriangleright x=10\frac{2}{3} \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left(10\frac{2}{3}~~,~~5 \right)~\hfill[/tex]

Answer:

289 numbers

Step-by-step explanation:

Above you will find the list of integers from 1 to 243 in base 3:

(1, 2, 10, 11, 12, 20, 21, 22, 100, 101, 102, 110, 111, 112, 120, 121, 122, 200, 201, 202, 210, 211, 212, 220, 221, 222, 1000, 1001, 1002, 1010, 1011, 1012, 1020, 1021, 1022, 1100, 1101, 1102, 1110, 1111, 1112, 1120, 1121, 1122, 1200, 1201, 1202, 1210, 1211, 1212, 1220, 1221, 1222, 2000, 2001, 2002, 2010, 2011, 2012, 2020, 2021, 2022, 2100, 2101, 2102, 2110, 2111, 2112, 2120, 2121, 2122, 2200, 2201, 2202, 2210, 2211, 2212, 2220, 2221, 2222, 10000, 10001, 10002, 10010, 10011, 10012, 10020, 10021, 10022, 10100, 10101, 10102, 10110, 10111, 10112, 10120, 10121, 10122, 10200, 10201, 10202, 10210, 10211, 10212, 10220, 10221, 10222, 11000, 11001, 11002, 11010, 11011, 11012, 11020, 11021, 11022, 11100, 11101, 11102, 11110, 11111, 11112, 11120, 11121, 11122, 11200, 11201, 11202, 11210, 11211, 11212, 11220, 11221, 11222, 12000, 12001, 12002, 12010, 12011, 12012, 12020, 12021, 12022, 12100, 12101, 12102, 12110, 12111, 12112, 12120, 12121, 12122, 12200, 12201, 12202, 12210, 12211, 12212, 12220, 12221, 12222, 20000, 20001, 20002, 20010, 20011, 20012, 20020, 20021, 20022, 20100, 20101, 20102, 20110, 20111, 20112, 20120, 20121, 20122, 20200, 20201, 20202, 20210, 20211, 20212, 20220, 20221, 20222, 21000, 21001, 21002, 21010, 21011, 21012, 21020, 21021, 21022, 21100, 21101, 21102, 21110, 21111, 21112, 21120, 21121, 21122, 21200, 21201, 21202, 21210, 21211, 21212, 21220, 21221, 21222, 22000, 22001, 22002, 22010, 22011, 22012, 22020, 22021, 22022, 22100, 22101, 22102, 22110, 22111, 22112, 22120, 22121, 22122, 22200, 22201, 22202, 22210, 22211, 22212, 22220, 22221, 22222, 100000)

If you count them, you will find that there are 289 numbers in total!

Final answer:

When writing the integers from 1 to 243 in base 3, there are exactly five zeros written. These are associated with the numbers that are powers of 3 (3, 9, 27, 81, 243) each represented in base 3 by a 1 followed by zeros (10, 100, 1000, etc.). Zeroes are not used as trailing digits in any other non-zero numbers in base 3.

Explanation:

Calculating Zeroes in Base 3 from Integers 1 to 243

To determine how many zeroes are written when we write all the integers from 1 to 243 in base 3, we need to understand the representation of numbers in base 3. Every integer can be expanded in powers of 3, where, similar to the decimal system, we have different 'places' representing powers of 3 instead of 10. In base 3, we do not have the digit '0' at the end of any non-zero integer, as that would imply a multiple of 3, which is not represented in the standard form of base 3 notation. Therefore, the only time we write a zero is within the numbers themselves.

Let's look at how numbers are built in base 3:

Thus, for every power of 3, we write a single '0' at the end of the number in base 3 notation (excluding the number 3⁰, which is 1). To find out how often this occurs up to 243, we list the powers of 3:
3¹ = 3, 3² = 9, 3³ = 27, 3⁴ = 81, 3⁵ = 243, hence there are 5 powers of 3 within our range.

Therefore, we have the number 3¹ written as 10, the number 3² written as 100, and so on, up to 3⁵, which is written as 100000 in base 3. Each of these numbers includes exactly one zero, leading to a total of five zeroes when writing out all the integers from 1 to 243 in base 3.

Answer:

(0,4) vertex and (1,3) another pt

Step-by-step explanation:

The parabola has been shifted up 4 units from parent function (there is also a reflection)...but we only really care about the shift 4 units up from (0,0) for our vertex... Our vertex is (0,4)

Now just plug in another number to find another point...let's do x=1

Plug in you get -1^2+4=-1+4=3 so another point is (1,3)

Answer:

C. 5

Step-by-step explanation:

Since Triangle ABC is congruent to EDF it mean that the sides are the same so the length of BC is congruent to the length of DF:

distance formula:

d = √(x2 - x1)^2 + (y2 - y1)^2

d = √(2 - 2)^2 + (-1 - 4)^2

d = √(0)^2 + (-5)^2

d = √0 + 25

d = √25

d = 5

Answer:

y = 3x - 2

Step-by-step explanation:

You can easily find the equation of a line through two points by using the point-slope form, [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is one of the points.

First, let's find the slope of the line through (0, -2) and (4, 10).

[tex]m=\displaystyle \frac{y_2-y_1}{x_2-x_1} = \frac{10-(-2)}{4-0}=\frac{12}{4}=3[/tex]

Next, we plug this into point-slope form. Remember that we let (0, -2) be our first point, [tex](x_1,y_1)[/tex].

[tex]y-(-2)=3(x-0)[/tex]

Finally, we rearrange this equation to get the slope-intercept form [tex]y=mx+b[/tex], where b is the y-intercept.

[tex]y+2=3x \\ y=3x-2[/tex]

We can verify using the attached graph that both points lie on this line.

Formula and set up:

A = P(1 + r/n)^(nt)

You want A.

A = 1200(1 + (0.06)/2)^(0.06)(2)

Plug right side into calculator to find A.

Answer:

about 0.81 miles

Step-by-step explanation:

Alyssa's route can be considered a right triangle with legs of length 19 and 28 (hundredths). The Pythagorean theorem tells us the hypotenuse (x) will satisfy ...

x^2 = 19^2 +28^2

x^2 = 1145

x = √1145 ≈ 34 . . . . hundredths of a mile

Then Alyssa's total route is ...

0.19 + 0.28 + 0.34 = 0.81 . . . . miles

Answer:

about 0.81 miles

Step-by-step explanation:

Alyssa's route can be considered a right triangle with legs of length 19 and 28 (hundredths). The Pythagorean theorem tells us the hypotenuse (x) will satisfy ...

x^2 = 19^2 +28^2

x^2 = 1145

x = √1145 ≈ 34 . . . . hundredths of a mile

Then Alyssa's total route is ...

0.19 + 0.28 + 0.34 = 0.81 . . . . miles

Answer:

  9840

Step-by-step explanation:

1 - 18% = 82% survive, so the number available for sale is ...

  0.82 × 12,000 = 9,840

Answer:

9,840 apples.

Step-by-step explanation:

We have been given that in an apple farm each year, about eighteen percent of the collected apples must be thrown out because of rot.

To find the number of apples that survive for the farmer to sell, we need to find 82% of 12,000. As 18% apples must be thrown each year, so left apples (100-18=82) will be available to sell.

[tex]\text{Apples survive for the farmer to sell}=12000\times \frac{82}{100}[/tex]

[tex]\text{Apples survive for the farmer to sell}=120\times 82[/tex]

[tex]\text{Apples survive for the farmer to sell}=9840[/tex]

Therefore, 9,840 apples survive for the farmer to sell.

Answer:

D. –X+XY–7y

Step-by-step explanation:

We just have to combine (add) the similar terms... so all terms that have an x in them for example.

–3x + 2xy + 4y – xy + 2x – 11y

Let's first re-write it placing similar terms next to each other

(-3x + 2x) + (2xy - xy) + (4y - 11y)

Then we sum them up, for each similar terms

1x + 1xy -7y

so, x + xy -7y

Answer D.

Answer:

Step-by-step explanation:

Fill in the given numbers and solve for k.

  y = kx²

  1000 lb = k(5 in)²

  (1000 lb)/(25 in²) = k = 40 lb/in² . . . . . . divide by the coefficient of k

__

Fill in the given numbers and solve for x.

  y = kx²

  16000 lb = (40 lb/in²)x²

  16000 lb/(40 lb/in²) = x² = 400 in² . . . . . . divide by the coefficient of x²

  20 in = x . . . . . . . . . take the square root

The depth to support 16,000 pounds should be 20 inches.

ANSWER

[tex]{(x - 3)}^{3} = {x}^{3} - 9 {x}^{2} + 27x - 27[/tex]

EXPLANATION

We want to expand:

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

Using the identity;

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

We substitute y=3 into the above identity to obtain:

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

Let us simplify to get:

[tex]{(x - 3)}^{3} = {x}^{3} - 9 {x}^{2} + 27x - 27[/tex]

Answer:

  y = -6x -9

Step-by-step explanation:

The derivative is ...

  f'(x) = 2x

so the slope at x=-3 is ...

  f'(-3) = 2(-3) = -6

Then the point-slope form of the tangent line can be written ...

  y = m(x -h) +k . . . . . . for line with slope m through point (h, k)

  y = -6(x -(-3))+9 = -6x -18 +9 . . . . . filling in your values, eliminating parens

So, the slope-intercept equation of the tangent line is ...

  y = -6x -9

Answer:

(a) 15:8

(b) 7:15

Step-by-step explanation:

a: All the books together is 15. The ratio of all books(15) to used books(8) is therefore 15:8

b: As I said above, all the books together is 15. So the ratio of the new books(7) to all books(15) is 7:15

The ratio of all books to used books 15:8

The ratio of new books to all books 7:15

A ratio indicates how many times one number contains another.

Given:

New books =7

used books= 8

total books =8+7=15 books

a) ratio of all books to used books,

= total books: used books

= 15:8

b) ratio of new books to all books,

= new books: all books

=7:15

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Answer:

Y = 2/3x - 3

Step-by-step explanation:

Recall the general equation for a straight line is

y = mx + b

where m is the gradient and b is the y-intercept

given 2 points whose coordinates are (x1, y1) and (x2, y2), m can be found with the following formula:

m = [tex]\frac{y1-y2}{x1-x2}[/tex]

in this case, x1 = 3, y1 = -1, x2 = 6, y2=1

applying these values to the formula for m will give

m =  (-1 -1) / (3-6) = 2/3

We can see immediately that only the first (top-most) answer has this value for m and we can guess that this is probably the answer.

But we can still check to confirm:

If we substitute this back into the general equation, we get:

y = (2/3)x + b

In order to find the value for b, we substitute any one of the 2 given points back into this equation. Lets choose (6,1)

1 = (2/3)(6) + b

1 = 4 + b

b = -3

Confirm  Y = 2/3x - 3 is the answer.

Answer: [tex]115in^3[/tex]

Step-by-step explanation:

The volume of a cone can be calculated with the following formula:

[tex]V_{(cone)}=\frac{1}{3}\pi r^2h[/tex]

Where "r" is the radius and "h" is the height.

The radius is half the diameter, then "r" is:

[tex]r=\frac{7in}{2}\\\\r=3.5in[/tex]

Since we know that radius and the height, we can substitute them into the formula.

The volume of the cone  to the nearest cubic inch is:

 [tex]V_{(cone)}=\frac{1}{3}\pi (3.5in)^2(9in)[/tex]

 [tex]V_{(cone)}=115in^3[/tex]

Answer:

The  volume of cone = 115 cubic inches

Step-by-step explanation:

Points to remember

Volume of cone = (πr²h)/3

Where r - Radius of cone and

h - Height of cone

To find the volume of cone

Here diameter = 7 in then r = 7/2 = 3.5 in and h = 9 in

Volume = (πr²h)/3

 = (π * 3.5² * 9)/3

 = (3.14  * 12.25 * 9)/3

 = 115.395 ≈ 115 cubic inches

Therefore volume of cone = 115 cubic inches