Eight less than four times a number is less than 56. What are the possible values of that number?

Answer:

Step-by-step explanation:

-8*3= -24+14=-10

Answer:

-12 and 2.

Step-by-step explanation:

-12*2= -24,

-12+2=-10

Answer:

second option

Step-by-step explanation:

Parallel lines have the same slope, and since the slope of the given line is 1/2, we know the slope of the answer will be 1/2, which eliminates the first and last options. We know the slope and a point that belongs to the line, (-2, 1), so we can use point-slope formula to derive the equation of the line.

y - 1 = 1/2(x + 2)

y - 1 = 1/2x + 1

y = 1/2x + 2

Answer:  A) N'=(-2, 2) M'=(-1, 0)  L'=(-5, -2)

Step-by-step explanation:

N = (-2, -4)      M = (-3, -2)       L = (1, 0)

Reflection over y = -1

N' = (-2, 2)      M' = (-3, 0)       L' = (1, -2)

Reflection over x = -2

N'' = (-2, 2) M'' = (-1, 0)  L'' = (-5, -2)

Answer:

72

Step-by-step explanation:

36+36=72

It's adding 3 and subtracting 2 every time.

This means the next two terms would be +3 and -2 since the last one was -2.

The next term = 4+3=7

The next next term = 7-2=5

Answer:

Please see the attached picture.

Hope it helps...

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Answer:

1970.5 thousand

Step-by-step explanation:

Given

Vehicle sales in 2009 = 10,002 thousand

Vehicle sales in 2013 = 17,884 thousand

Required

Determine the average rate of change;

From the given parameters, it can be seen that the number of vehicles is a function of year

Let x represent the years and y represent the number of vehicles;

Such that;

[tex]x_1 = 2009;\ y_1 = 10,002[/tex]

[tex]x_2 = 2013;\ y_2 = 17,884[/tex]

The rate of change is calculate as follows;

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

[tex]m = \frac{10002 - 17884}{2009 - 2013}[/tex]

[tex]m = \frac{-7882}{-4}[/tex]

[tex]m = \frac{-7882}{-4}[/tex]

[tex]m = 1970.5[/tex]

Hence, the average rate of change is 1970.5 thousand

a) Simply do 0.135(13.5%)*550 to get that his rent increases by $74.25.

b) Simply do 550+74.25 to get that his new rent is $624.25.

c) 624.25/550 = 1.135, or 100%+13.5%, the amount his rent increased.

Hope it helps <3

Answer:

A. $74.25

B. $624.25

C. 1.135, and this is a connection to part a because it's what we multiplied 550 by to get our new rent.

Step-by-step explanation:

If Shawn pays $550 per month for rent, and he has a 13.5% increase, we can multiply 550 by [tex]1+\frac{13.5}{100}[/tex] to get our new number.

[tex]1+0.135=1.135[/tex]

[tex]550\cdot1.135=624.25[/tex]

This is the new monthly rent, part B. To find Part A, let's subtract 550 from thi number.

[tex]624.25-550=74.25[/tex]

Now, for part C, let's divide 624.25 by 550.

[tex]624.25\div550 = 1.135[/tex]

If you notice, 1.135 is the same number we multiplied 550 by to get our new cost, and as a percent, 1.135 is 113.5%.

Hope this helped!

Answer:

2 11/12

Step-by-step explanation:

3/4 + 2 1/6

Add the fractions.

35/12

= 2 11/12

Answer:

[tex]2\frac{11}{12}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4}+2\frac{1}{6}=\\\\\frac{18}{24}+2\frac{4}{24}=\\\\2\frac{22}{24}=\\\\2\frac{11}{12}[/tex]

Answer:

3906250

Step-by-step explanation:

We can notice that the ratio is 5. 10/2 = 5

Each term gets multiplied by 5 to get the next term.

250 × 5 = 1250 (5th term)

1250 × 5 = 6250 (6th term)

6250 × 5 = 31250 (7th term)

31250 × 5 = 156250 (8th term)

156250 × 5 = 781250 (9th term)

781250 × 5 = 3906250 (10th term)

The 10th term of the geometric sequence is 3906250.

Answer:

108, 324, 972

Step-by-step explanation:

This sequence is multiplying by ✖️3.

4✖️3=12✖️3=36✖️3=108✖️3=324✖️3=972

Hope this helps!

Answer:

Step-by-step explanation:

This is a permutation problem. Given the 10 cards with numbers 2, 3, 4,5,5,7,7,7,7,7 on it, if Salvador is going to make a row call, the number of ways he can order a row is as shown below;

Total number of cards = 10!

number of times the digit 5 was repeated = 2times

number of times the digit 7 was repeated = 5times

The number of ways he can make a row call = 10!/2!5!

= 10*9*8*7*6*5!/2*5!

=  10*9*8*7*6/2

=  10*9*8*7*3

= 15,120 different ways

Hence, the number of ways he can order the row is 15,120 number of ways.

Answer:

7/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8

7/8 = 1/8 + 6/8

7/8 = 4/8 + 3/8

7/8 = 5/8 + 2/8

Step-by-step explanation:

Hope it helps!

The fraction 7/8 can be written as the sum of unit fraction i.e;

1/8+1/8+1/8+1/8+1/8+1/8+1/8+1/8.

A unit fraction can be defined as a fraction whose numerator is 1.

Given fraction 7/8

can be written as the sum of the unit fraction i.e;

7/8=1/8+1/8+1/8+1/8+1/8+1/8+1/8+1/8

Hence,7/8 can be decomposed into sum of unit fraction as

1/8+1/8+1/8+1/8+1/8+1/8+1/8+1/8.

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A slope is also known as the gradient of a line is a number. The correct option is B.

A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

slope = (y₂-y₁)/(x₂-x₁)

The rate of change shown in the graph is the slope of the given line.

Now, to know the slope of the line consider any two points on the line, such as (0,0) and (5,400).

Therefore, the slope of the line can be written as,

Slope, m = ($400 - $0)/(5-0) hour

               = $400/5 hour

               = $80/hour

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Answer:

[tex]\boxed{y\leq 6}[/tex]

Step-by-step explanation:

[tex]y-8 \leq -2[/tex]

Adding 2 to both sides

[tex]y \leq -2+8[/tex]

[tex]y \leq 6[/tex]

Answer:

see below

Step-by-step explanation:

Using the Pythagorean Theorem:

a^2+ b^2 = c^2

5^2+ 9^2 = 13^2

25+81 = 169

106 = 169

This is not true so it is not a right triangle

Answer:

[tex]\boxed{\sf Not \ a \ right \ triangle}[/tex]

Step-by-step explanation:

Apply Pythagorean theorem to check if the triangle is a right triangle.

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

[tex]5^2+ 9^2 = 13^2[/tex]

[tex]25+81=169[/tex]

[tex]106=109[/tex]

False statement.

The triangle is not a right triangle.

Answer:

47, 40, 33, 26 are the first four terms of the sequence.

Step-by-step explanation:

Expression representing the sequence is,

[tex]a_n=46-7(n-1)[/tex]

where n = number of term in the sequence

For n = 1,

[tex]a_1=47-7(1-1)[/tex]

    = 47

For n = 2,

[tex]a_2=47-7(2-1)[/tex]

    = 47 - 7

    = 40

For n = 3,

[tex]a_3[/tex] = 47 - 7(3 -1)

   = 47 - 14

   = 33

For n = 4,

[tex]a_4=47-7(4-1)[/tex]

    = 47 - 21

    = 26

Therefore, first four terms of the sequence are 47, 40, 33 and 26.

Answer:   [tex]\dfrac{7}{1,337,220}=5.2\times 10^{-6}[/tex]

Step-by-step explanation:

Order does not matter so it is a Combination.

There are 14 men and we are going to choose 12 --> ₁₄C₁₂

There are 27 people and we are going to choose 12  --> ₂₇C₁₂

[tex]\dfrac{_{14}C_{12}}{_{27}C_{12}}\rightarrow\dfrac{14!}{(14-12)!}\div \dfrac{27!}{(27-12)!}=\large\boxed{\dfrac{7}{1,337,220}}[/tex]

Probabilities are used to determine the chances of an event

The probability of selecting 12 males is: [tex]\frac{7}{1337220}[/tex]

The parameters are given as:

[tex]n = 24[/tex] --- sample size

[tex]Male = 14[/tex]

[tex]Female = 13[/tex]

[tex]r = 12[/tex] ---- number of jury pool

The number of ways of selecting 12 members of the jury, from a total of 27 is:

[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]

So, we have:

[tex]^{27}C_{12} = \frac{27!}{(27 - 12)!12!}[/tex]

[tex]^{27}C_{12} = \frac{27!}{15! \times 12!}[/tex]

[tex]^{27}C_{12} = 17383860[/tex]

The number of ways of selecting 12 members of the jury, from a total of 14 male is:

[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]

So, we have:

[tex]^{14}C_{12} = \frac{14!}{(14 - 12)!12!}[/tex]

[tex]^{14}C_{12} = \frac{14!}{2! \times 12!}[/tex]

[tex]^{14}C_{12} = 91[/tex]

So, the probability of selecting 12 males is:

[tex]Pr = \frac{^{14}C_{12}}{^{27}C_{12}}[/tex]

[tex]Pr = \frac{91}{17383860}[/tex]

Simplify

[tex]Pr = \frac{91/13}{17383860/13}[/tex]

[tex]Pr = \frac{7}{1337220}[/tex]

Hence, the required probability is: [tex]\frac{7}{1337220}[/tex]

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Answer:

y=2.2

Step-by-step explanation:

1: Distribute all numbers to get rid of all parenthesis

2: Solve

Hope this helped :) LET ME KNOW IF YOU NEED THE ANSWER IN A DIFFERENT FORM I CAN GET IT FOR YOU

Answer:

A road with a pitch of 1 in 8 is steeper.

Step-by-step explanation:

Let us convert these to the same units so that we can better compare them.

[tex]\frac{1}{8} = 0.125[/tex]

0.125=12.5 %

As 12.5% is greater than 12%, the road with a pitch of 1 in 8 will be steeper.

Answer:

The correct answer will be "56".

Step-by-step explanation:

Use a combination of 8 things taken 3 at a time :

⇒  [tex]8_{C_{3}}[/tex]

⇒  [tex]\frac{8!}{(3!(8 - 3)!)}[/tex]

⇒  [tex]\frac{8!}{(3!5!)}[/tex]

⇒  [tex]\frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{3\times 2\times 1}[/tex]

⇒  [tex]8\times 7[/tex]

⇒  [tex]56[/tex]

Using the principle of combination, the number of different random samples of size 3 that can be selected is 56.

Using the principle of combination :

Hence, we have ;

8C3 = [8! ÷ (8 - 3)! 3!]

8C3 = [8! ÷ 5!3!]

8C3 = (8 × 7 × 6) ÷ (3 × 2 × 1)

8C3 = 8 × 7

8C3 = 56

Hence, there are 56 different possible samples.

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Answer:

The answer is option C.

3a - b = 10

Hope this helps you

Answer:

x = 3

y = -2

Step-by-step explanation:

Given:

8x - 3y = 30 ..................(1)

3x + y = 7 .......................(2)

Eliminate y by adding (1)+3*(2)

8x-3y + 3*( 3x+y) = 30 + 3*7

8x + 9x -3y + 3y = 51

17x = 51

x = 3  .....................(3)

substitute (3) in (2)

3(3) + y = 7

y = 7-9 = -2

y = -2 ....................(4)

Answer:

Step-by-step explanation:

[tex]8x-3y=30\\y=7-3x\\\\8x-3(7-3x)=30\\8x-21+9x=30\\17x=51\\x=3\\\\y=7-3(3)\\y=7-9\\y=-2[/tex]

Answer: 1.7

Step-by-step explanation:

5 divided by 3=1.666666667

1.6 and next 6 in line is over 5 so the 6 turns to a 7

3*1.7= 5.1 but when rounded 1 tells 5 to stay down so it = 5

Answer:

(x,y) = (5,15)

Step-by-step explanation:

y = 3x

2x + 3y = 55

2x + 3(3x) = 55

2x + 9x = 55

11x = 55

x = 5

y = 3(5)

y = 15

You probably want the unsigned area, which means you don't compute the integral

[tex]\displaystyle\int_0^{2\pi}\sin x\,\mathrm dx[/tex]

but rather, the integral of the absolute value,

[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx[/tex]

[tex]\sin x[/tex] is positive when [tex]0<x<\pi[/tex] and negative when [tex]\pi<x<2\pi[/tex], so

[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=\int_0^\pi\sin x\,\mathrm dx-\int_\pi^{2\pi}\sin x\,\mathrm dx[/tex]

[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=(-\cos x)\bigg|_0^\pi-(-\cos x)\bigg|_\pi^{2\pi}[/tex]

[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=\boxed{4}[/tex]

Answer:

my class is 8 th is I don't now this answer

Answer:

1. = 8

2. =40

3. =37

Step-by-step explanation:

1. x = √(17² - 15²) = 8

2. x =√(9² +41²) = 40

3. x =√(12² + 35²) = 37

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Answer:  

[tex]1)\quad f(x)=\bigg\{\begin{array}{ll}12x&0\leq x <9\\18x-48&9\leq x \leq 24\end{array}[/tex]

2) D: x = [0, 24]

3) R: y = [0, 384]

4) see graph

Step-by-step explanation:

Eric's regular wage is $12 per hour for all hours less than 9 hours.

The minimum number of hours Eric can work each day is 0.

f(x) = 12x    for   0 ≤ x < 9

Eric's overtime wage is $18 per hour for 9 hours and greater.

The maximum number of hours Eric can work each day is 24 (because there are only 24 hours in a day).

f(x) = 18(x - 8) + 12(8)

    = 18x - 144 + 96

    = 18x - 48           for 9 ≤ x ≤ 24

The daily wage where x represents the number of hours worked can be displayed in function format as follows:

[tex]f(x)=\bigg\{\begin{array}{ll}12x&0\leq x <9\\18x-48&9\leq x \leq 24\end{array}[/tex]

2) Domain represents the x-values (number of hours Eric can work).

The minimum hours he can work in one day is 0 and the maximum he can work in one day is 24.

D:  0 ≤ x ≤ 24        →        D: x = [0, 24]

3) Range represents the y-values (wage Eric will earn).

Eric's wage depends on the number of hours he works. Use the Domain (given above) to find the wage.

The minimum hours he can work in one day is 0.

f(x) = 12x

f(0) = 12(0)

     =  0

The maximum hours he can work in one day is 24 (although unlikely, it is theoretically possible).

f(x) = 18x - 48

f(24) = 18(24) - 48

       = 432 - 48

       = 384

D:  0 ≤ y ≤ 384        →        D: x = [0, 384]

4) see graph.

Notice that there is an open dot at x = 9 for f(x) = 12x

and a closed dot at x = 9 for f(x) = 18x - 48

Answer:

Since we are talking annual interest and, I assume a time period of 1 year:

The interest earned is the sum of the interest earned on the two loans separately

Let x = amount loaned at 14%

18,500-x = amount loaned at 12%

I = prt

p = x and 18500-x

r = 0.14 and 0.12

t = 1

2390 = 0.14x + 0.1(18500-x)

2390 = .14x + 1850 - 0.1x

x = 13500

x = $13,500 loaned at 14%

18500-x = $5,000 loaned at 12%

Answer:

$8,500 was loaned at 14%, and

$10,000 was loaned at 12%.

Step-by-step explanation:

Total loan: $18,500.

Part at 14%

Part at 12%

Let the part at 14% = x.

Let the part at 12% = y.

Equation of amount of loan:

x + y = 18500

x amount at 14% earns 14% of x = 0.14x interest.

y amount at 12% earns 12% of y = 0.12y interest.

Equation of interest charged:

0.14x + 0.12y = 2390

We have a system of equations.

x + y = 18500

0.14x + 0.12y = 2390

Multiply both sides of the first equation by -0.12. Write the second equation below it, and add the equations.

     -0.12x - 0.12y = -2220

(+)    0.14x + 0.12x = 2390

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

      0.02x             = 170

x = 170/0.02

x = 8500

x + y = 18,500

8500 + y = 18,500

y = 10,000

Answer:

$8,500 was loaned at 14%, and

$10,000 was loaned at 12%.