How many ways can 4 people sit in a table of 6 seats? A.120
B.24
C.360
D.15

When you multiply two fractions together, multiply the two top numbers and then multiply the two bottom numbers.

5/12 x 1/3 = (5x1) / (12x3) = 5/36

Answer:

Step-by-step explanation:

[tex]\frac{5}{12}*\frac{1}{3}\\\\\\=\frac{5*1}{12*3}=\frac{5}{36}[/tex]

The absolute value of any number is never negative. Absolute value represents distance, and negative distance is not possible (it doesn't make any sense to have a negative distance). Specifically, it is the distance from the given number to 0 on the number line.

The result of an absolute value is either 0 or positive.

Examples:

| -22 | = 22

| -1.7 | = 1.7

| 35 | = 35

The vertical bars surrounding the numbers are absolute value bars

Answer:

757

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sum of 3/8 and -5/12:

Least common denominator of 8 & 12 = 24

[tex]\frac{3}{8}+\frac{-5}{12}=\frac{3*3}{8*3}+\frac{-5*2}{12*2}\\\\\\=\frac{9}{24}+\frac{-10}{24}\\\\\\=\frac{-1}{24}[/tex]

Finding -15/8 * 16/27:

[tex]\frac{-15}{8}*\frac{16}{27}=\frac{-5*2}{1*9}=\frac{-10}{9}[/tex]  

Reciprocal of -10/9 = -9/10

-1/24 ÷ -9/10 = [tex]\frac{-1}{24}*\frac{-10}{9}=\frac{1*5}{12*3}[/tex]

= [tex]\frac{5}{24}[/tex]

Answer: y=2x+1

Step-by-step explanation:

plug in the points in to the equation to see what you get

Answer:

They are perpendicular lines

Step-by-step explanation:

If one line has slope -8 and the other one has slope 1/8, they must be perpendicular to each other because the condition for perpendicular lines is that the slope of one must be the "opposite of the reciprocal of the slope of the original line."

the opposite of -8 is 8 , and the reciprocal of this is 1/8

Answer:

Below

Step-by-step explanation:

Let m and m' be the slopes of two different lines.

These lines are peependicular if and only if:

● m×m' = -1

Notice that:

● -8 ×(1/8) = -1

So the lines with the respectives slopes -8 and 1/8 are perpendicular.

Answer:

cos A = 3/5

Step-by-step explanation:

sin A = 4/5

sin^2 A + cos^2 A = 1

(4/5)^2 + cos^2 A = 1

16/25 + cos^2 A = 1

cos^2 A = 9/25

cos A = 3/5

Hey there! I'm happy to help!

A mixed number is a whole number and a fraction. We already see that our whole number is 7.

Our decimal is 0.13. Since this goes into the hundredths place, we can rewrite this as 13/100. This cannot be simplified anymore.

Therefore, 7.13 is 7 13/100 in lowest terms.

Have a wonderful day! :D

Answer:

EM = 42

Step-by-step explanation:

If M is the midpoint, then we can say that EM = MG.

So now, I can set up an equation:

7x = 8x - 6

And solve for x.

7x = 8x - 6

 -8x     -8x

-x = -6

x = 6

Since we are trying to find EM, and EM is 7x, we can multiply x by 7 to find our answer:

7x

7(6)

42

EM = 42

Answer:

Scale factor 2.

Step-by-step explanation:

The vertices of shape I are (2,1), (3,1), (4,3), (3,3), (3,2), (2,2), (2,3), (1,3).

The vertices of shape II are (-4,-2), (-6,-2), (-8,-6), (-6,-6), (-6,-4), (-4,-4), (-4,-6), (-2,-6).

Consider shape I is similar to shape II. The sequence that maps shape I onto shape II is a 180 degree clockwise rotation about the origin, and then a dilation by a scale factor of k.

Rule of 180 degree clockwise rotation about the origin:

[tex](x,y)\rightarrow (-x,-y)[/tex]

The vertices of shape I after rotation are (-2,-1), (-3,-1), (-4,-3), (-3,-3), (-3,-2), (-2,-2), (-2,-3), (-1,-3).

Rule of dilation by a scale factor of k.

[tex](x,y)\rightarrow (kx,ky)[/tex]

So,

[tex](-2,-1)\rightarrow (k(-2),k(-1))=(-2k,-k)[/tex]

We know that, the image of (-2,-1) after dilation is (-4,-2). So,

[tex](-2k,-k)=(-4,-2)[/tex]

On comparing both sides, we get

[tex]-2k=-4[/tex]

[tex]k=2[/tex]

Therefore, the scale factor is 2.

Answer:

180 clockwise rotation about the orgin, 2

Step-by-step explanation:

Formula :-

Volume of cylinder is π r²h .

Given :-

→ Volume = 308 cm³

→ Radius = 7 cm

Solution :-

→ πr²h = 308

→ π (7)²(h) = 308

→ 22×7×7×h/7 = 308

→ 22×7×h = 308

→ 154×h = 308

→ Height = 308/154

→ Height = 2 cm

So the height of the cylinder is 2 cm .

Answer:

16.81

Step-by-step explanation:

That's basically just 4.1×4.1

Answer:

c. variables, constants, and functions

Step-by-step explanation:

A predicate is the property that some object posses. Predicate calculus is a kind of logic that combines the categorical logic with propositional logic. The formal syntax of a predicate calculus contains 3 Terms which consist  of:

1.  Constants and Variables

2. Connectives

3. Quantifiers

But in arguments to predicates and functions, the terms  can only be combination of variables, constants, and functions.

Answer:

The mean ≈ 90

The median = 95

The mode = 95 & 100

The range = 37

Step-by-step explanation:

We will base out conclusion by calculating the measures of central tendency of the distribution i.e the mean, median, mode and range.

– Mean is the average of the numbers. It is the total sum of the numbers divided by the total number of students.

xbar = Sum Xi/N

Xi is the individual student score

SumXi = 63+66+70+81+81+92+92+93+94+94+95+95+95+96+97+98+98+99+100+100+100

SumXi = 1899

N = 21

xbar = 1899/21

xbar = 90.4

xbar ≈ 90

Hence the mean of the distribution is approximately equal to 90.

– Median is number at the middle of the dataset after rearrangement.

We need to locate the (N+1/2)the value of the dataset.

Given N =21

Median = (21+1)/2

Median = 22/2

Median = 11th

Thus means that the median value falls on the 11th number in the dataset.

Median value = 95.

Note that the data set has already been arranged in ascending order so no need of further rearrangement.

– Mode of the data is the value occurring the most in the data. The value with the highest frequency.

According to the data, it can be seen that the value that occur the most are 95 and 100 (They both occur 3times). Hence the modal value of the dataset are 95 and 100

– Range of the dataset will be the difference between the highest value and the lowest value in the dataset.

Highest score = 100

Lowest score = 63

Range = 100-63

Range = 37

Answer:

4√5

Step-by-step explanation:

√80 = √4·4·5 = √4²·5 = 4√5

Answer:

The constant of proportionality is 1/9

Answer:

The answer is actually 3

Step-by-step explanation:

The two triangles are drawn to scale, so we can use the scale factor of \maroonD{1\dfrac{1}{2}}1

2

1

​

start color #ca337c, 1, start fraction, 1, divided by, 2, end fraction, end color #ca337c to find \greenD{x}xstart color #1fab54, x, end color #1fab54.

Hint #22 / 3

\begin{aligned} [\blueD{\text{length on A}}] \cdot [\maroonD{\text{scale factor}}] &= [\greenD{\text{length on B}}]\\\\ \blueD{2}\cdot \maroonD{1\dfrac{1}{2}}&=\greenD{x} \\\\ \greenD{3}&=\greenD{x} \end{aligned}

[length on A]⋅[scale factor]

2⋅1

2

1

​

3

​

=[length on B]

=x

=x

​

which equals 3

Answer:

Step-by-step explanation:

From  x = -2 to x = 0 function is decreasing, but for x= -1 function doesn't exist, so we need to exclude x = -1 from (-2, 0)

[tex] \LARGE{ \boxed{ \mathbb{ \color{purple}{SOLUTION:}}}}[/tex]

We have, Discriminant formula for finding roots:

[tex] \large{ \boxed{ \rm{x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} }}}[/tex]

Here,

1) Given,

3x^2 - 2x - 1

Finding the discriminant,

➝ D = b^2 - 4ac

➝ D = (-2)^2 - 4 × 3 × (-1)

➝ D = 4 - (-12)

➝ D = 4 + 12

➝ D = 16

2) Solving by using Bhaskar formula,

❒ p(x) = x^2 + 5x + 6 = 0

[tex] \large{ \rm{ \longrightarrow \: x = \dfrac{ - 5\pm \sqrt{( - 5) {}^{2} - 4 \times 1 \times 6 }} {2 \times 1}}}[/tex]

[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5 \pm \sqrt{25 - 24} }{2 \times 1} }}[/tex]

[tex] \large{ \rm{ \longrightarrow \: x = \dfrac{ - 5 \pm 1}{2} }}[/tex]

So here,

[tex]\large{\boxed{ \rm{ \longrightarrow \: x = - 2 \: or - 3}}}[/tex]

❒ p(x) = x^2 + 2x + 1 = 0

[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm \sqrt{ {2}^{2} - 4 \times 1 \times 1} }{2 \times 1} }}[/tex]

[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm \sqrt{4 - 4} }{2} }}[/tex]

[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm 0}{2} }}[/tex]

So here,

[tex]\large{\boxed{ \rm{ \longrightarrow \: x = - 1 \: or \: - 1}}}[/tex]

❒ p(x) = x^2 - x - 20 = 0

[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{ - ( - 1) \pm \sqrt{( - 1) {}^{2} - 4 \times 1 \times ( - 20) } }{2 \times 1} }}[/tex]

[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{ 1 \pm \sqrt{1 + 80} }{2} }}[/tex]

[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{1 \pm 9}{2} }}[/tex]

So here,

[tex]\large{\boxed{ \rm{ \longrightarrow \: x = 5 \: or \: - 4}}}[/tex]

❒ p(x) = x^2 - 3x - 4 = 0

[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{ - ( - 3) \pm \sqrt{( - 3) {}^{2} - 4 \times 1 \times ( - 4) } }{2 \times 1} }}[/tex]

[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{3 \pm \sqrt{9 + 16} }{2 \times 1} }}[/tex]

[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{3 \pm 5}{2} }}[/tex]

So here,

[tex]\large{\boxed{ \rm{ \longrightarrow \: x = 4 \: or \: - 1}}}[/tex]

━━━━━━━━━━━━━━━━━━━━

Step-by-step explanation:

a)

given: a = 1, b = 5, c = 6

1) Discriminant → ∆= b² − (4*a*c)

∆= b² - (4*a*c)

∆= 5² - (4*1*6)

∆=25 - ( 24 )

∆= 25 - 24

∆= 1

2)

Solve x = (- b ± √Δ ) / 2a

x = ( 5 ± √25 ) / 2*1

x = ( 2 ± 5 ) / 2

x = ( 2 + 5 ) / 2 or x = ( 2 - 5 ) / 2

x = ( 7 ) / 2 or x = ( - 3 ) / 2

x = 3.5 or x = -1.5

b)

given: a = 1, b = 2, c = 1

1) Discriminant → ∆= b² − (4*a*c)

∆= b² - (4*a*c)

∆= 2² - (4*1*1)

∆= 4 - (4)

∆= 4 - 4

∆= 0

2)

Solve x = (- b ± √Δ ) / 2a

x = ( -2 ± √0) / 2*1

x = ( 2 ± 0 ) / 2

x = ( 2 + 0) / 2 or x = ( 2 - 0 ) / 2

x = ( 2 ) / 2 or x = ( 2 ) / 2

x = 1 or x = 1

x = 1 (only one solution)

c)

given: a = 1, b = -1, c = -20

1) Discriminant → ∆= b² − (4*a*c)

∆= b² - (4*a*c)

∆= -1² - (4*1*-20)

∆= 1 - ( -80 )

∆= 1 + 80

∆= 81

2)

Solve x = (- b ± √Δ ) / 2a

x = ( 2 ± √81 ) / 2*1

x = ( 2 ± 9 ) / 2

x = ( 2 + 9 ) / 2 or x = ( 2 - 9 ) / 2

x = ( 11 ) / 2 or x = ( - 7 ) / 2

x = 5.5 or x = -3.5

d)

given: a = 1, b = -3, c = -4

1) Discriminant → ∆= b² − (4*a*c)

∆= b² - (4*a*c)

∆= -3² - (4*1*-4)

∆= 9 - ( -16)

∆= 9 + 16

∆= 25

2)

Solve x = (- b ± √Δ ) / 2a

x = ( 3 ± √25 ) / 2*1

x = ( 3 ± 5 ) / 2

x = ( 3 + 5 ) / 2 or x = ( 3 - 5 ) / 2

x = ( 8 ) / 2 or x = ( - 2 ) / 2

x = 4 or x = -1

Answer:

The correct option is;

Non of the above

Step-by-step explanation:

Option A is correct when a + b·i is a complex number, the real part = a and the imaginary part = b

Option B.) For the complex number,  a + b·i, a and b are real number

Option C) When a number, a + b·i is a complex number, then b ≠ 0

Option D) Whereby real numbers are numbers of the form  a + b·i, where b = 0, therefore, a real number is a complex number with the imaginary part = 0 and every real number is a complex number.

Greetings from Brasil...

First, let's make the mixed fraction improper:

- (3 3/8)

- { [(8 · 3) + 3]/8}

- { [24 + 3]/8}

- {27/8}

- (3 3/8) - (7/8)

- (27/8) - (7/8)

as the denominators are equal, we operate only with the numerators

- 34/8      simplifying

Answer:

Step-by-step explanation:

-3 3/8 - 7/8

convert -3 3/8 to improper fractions

_   27   _   7

    8            8

_   27 - 7

       8      

simplify

_   34

     8

convert to proper factions

_   17

     4

-  4 ¹/₄

Answer:

21x + 12

Step-by-step explanation:

In math, it is

21x + 2(6).

so we have

21x + 2(6) = 21x + 12.

Answer:

16) Anya, Danny, Bridget, Carl.

17) 217.66 bricks

Challenge) 275.65 minutes

Step-by-step explanation:

16) I think you have Anya and Danny reversed.  It should be:

Anya, Danny, Bridget, Carl.

17) Bridget can do 60 an hour, Danny 50 an hour, Carl 66 an hour, and Anya 41.66 an hour.  60+50+66+41.66=217.66

Challenge: Anya can do .694444 per minute, Bridget 1 per minute, Carl 1.1 per minute, and Danny .83333 per minute.  That makes 3.62777 per minute.  1000 divided by 3.6277777 is 275.65 minutes

Answer:

x = 3

Step-by-step explanation:

7/x - 3/(2x) + 7/6 = 9/x

x(7/x  - 3/(2x)  + 7/6) = x(9x)

x*7/x  - 3*x/(2x) + x*7/6 = x*9x

7 - 3/2 + 7x/6 = 9

7x/6 = 9 - 7 + 3/2

7x/6 = 2 + 3/2

7x/6 = 12/6 + 9/6

7x = 12+9

7x = 21

x = 21/7

x = 3

probe:

7/3 - 3/(2*3) + 7/6 = 9/3

14/6 - 3/6 + 7/6 = 3

(14 - 3 + 7) / 6 = 3

18/6 = 3

Answer:

The question is missing the values, I found a possible matching question:

a city has a population of 380,000 people. suppose that each year the population grows by 7.5%. what will be the population after 6 years

Answer:

After 6 years, the population will be 586, 455 people

Step-by-step explanation:

This growth is similar to the growth of an invested amount of money, which is compounded annually, yielding a future value, when it increases by a certain interest rate. Hence the formula for compound interest is used to determine the population after 6 years as follows:

[tex]FV = PV (1+ \frac{r}{n})^({n \times t})[/tex]

where

FV = future value = population after 6 years = ???

PV = present value = current  population = 380,000 people

r = interest rate = growth rate = 7.5% = 7.5/100 = 0.075

n = number of compounding periods per year = annually = 1

t = time of growth = 6 years

[tex]FV = 380,000 (1+ \frac{0.075}{1})^({1 \times 6})\\FV = 380,000 (1.075)^{6}\\FV= 380,000 (1.5433015256)\\FV = 586,454.58\\FV= 586,455\ people[/tex]

Therefore, after 6 years, the population will be 586, 455 people

[tex]4^5\cdot4^7=4^{5+7}=16,777,216[/tex].

Hope this helps.

Answer:

Volume required in the tank (200 × 150 × 2)m3. therefore, required time= (6000/625)= 96 min.

Answer:

david drove faster than dan bcz

Answer:

David drove faster

Step-by-step explanation:

Dan - 60m/5h = 12 miles an hour

David - 75m/6h = 12.5 miles an hour

Therefore David drove faster.

Answer:

-1-9i (the second option)

Step-by-step explanation:

(2 – 5i) – (3 + 4i)

=2-5i-3-4i

= -1-9i

-1 – 9i this expression is equal to (2 – 5i) – (3 + 4i).

so, 2nd option is correct.

Here, we have,

To simplify the expression (2 – 5i) – (3 + 4i),

we need to perform the subtraction operation for both the real and imaginary parts separately.

The real part subtraction is done as follows: 2 - 3 = -1.

The imaginary part subtraction is done as follows: -5i - 4i = -9i.

Combining the real and imaginary parts, we get -1 - 9i.

Therefore, the expression (2 – 5i) – (3 + 4i) is equal to -1 - 9i.

Among the given options, the expression that matches this result is O-1 - 9i.

Hence, -1 – 9i this expression is equal to (2 – 5i) – (3 + 4i).

so, 2nd option is correct.

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Answer: The LCM of 3 and 8 is 24.

Step-by-step explanation:

So far, the given two numbers are 3 and 8. We have to find the LCM ( Least Common Multiple ) of 3 and 8, not the GCF ( Greatest Common Factor). That means, we have to find the smallest multiple of 3 and 8.

Let's try it out.

3 times 1 = 3. Is that a multiple of eight? No.

3 times 2 = 6. Is that a multiple of eight? No.

3 times 3 = 9. Is that a multiple of eight? No.

3 times 4 = 12. Is that a multiple of eight? No.

3 times 5 = 15. Is that a multiple of eight? No.

3 times 6 = 18. Is that a multiple of eight? No.

3 times 7 = 21. Is that a multiple of eight? No.

3 times 8 = 24. Is that a multiple of eight? YES!

Now try it out for 8.

8 times 1 = 8. Is that a multiple of three? No.

8 times 2 = 16. Is that a multiple of three? No.

8 times 3 = 24. Is that a multiple of three? YES!

So now that 24 occurs in the list for both of them, it is the LCM because there are no other numbers that come before it that are multiples of both 3 and 8.

The LCM of 3 and 8 is 24.

The LCM (Least Common Multiple) of two numbers is the smallest number that is a multiple of both numbers.

To find the LCM of 3 and 8, we can use the following steps:

1. List out the multiples of 3 until we reach a number that is divisible by 8.

2. List out the multiples of 8 until we reach a number that is divisible by 3.

3. The smallest number that appears in both lists is the LCM of 3 and 8.

The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27...

The multiples of 8 are 8, 16, 24, 32 ...

The smallest number that appears in both lists is 24. Therefore, the LCM of 3 and 8 is 24.

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Answer:

10r²

Step-by-step explanation:

The following data were obtained from the question:

Radius (r) = 5r

Length of arc (L) = 4r

Area of sector (A) =?

Next, we shall determine the angle θ sustained at the centre.

Recall:

Length of arc (L) = θ/360 × 2πr

With the above formula, we shall determine the angle θ sustained at the centre as follow:

Radius (r) = 5r

Length of arc (L) = 4r

Angle at the centre θ =?

L= θ/360 × 2πr

4r = θ/360 × 2π × 5r

4r = (θ × 10πr)/360

Cross multiply

θ × 10πr = 4r × 360

Divide both side by 10πr

θ = (4r × 360) /10πr

θ = 144/π

Finally, we shall determine the area of the sector as follow:

Angle at the centre θ = 144/π

Radius (r) = 5r

Area of sector (A) =?

Area of sector (A) = θ/360 × πr²

A = (144/π)/360 × π(5r)²

A = 144/360π × π × 25r²

A = 144/360 × 25r²

A = 0.4 × 25r²

A = 10r²

Therefore, the area of the sector is 10r².

the area of the sector in terms of r is [tex]10r^2[/tex]

Given :

From the given diagram , the radius of the circle is 5r  and length of arc AB is 4r

Lets find out the central angle using length of arc formula

length of arc =[tex]\frac{central-angle}{360} \cdot 2\pi r[/tex]

r=5r  and length = 4r

[tex]4r=\frac{central-angle}{360} \cdot 2\pi (5r)\\4r \cdot 360=central-angle \cdot 2\pi (5r)\\\\\\\frac{4r \cdot 360}{10\pi r} =angle\\angle =\frac{4\cdot 36}{\pi } \\angle =\frac{144}{\pi }[/tex]

Now we replace this angle in area of sector formula

Area of sector =[tex]\frac{angle}{360} \cdot \pi r^2\\[/tex]

[tex]Area =\frac{angle}{360} \cdot \pi r^2\\\\Area =\frac{\frac{144}{\pi } }{360} \cdot \pi\cdot 25r^2\\\\Area =\frac{ 144 }{360\pi } \cdot \pi\cdot 25r^2\\\\Area =\frac{ 2 }{5 } \cdot 25r^2\\\\\\Area=10r^2[/tex]

So, the area of the sector in terms of r is [tex]10r^2[/tex]

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