Which equation represents a line that has a slope of One-third and passes through point (–2, 1)?
y = one-third x minus 1
y = one-third x + five-thirds
y = one-third x minus five-thirds

As per the concept of counting problem, the reason that the answers in part (a) and part (b) are not the same is because Q1 and Q2 are treated as two different coins in part (a) whereas they are effectively treated as the same coin in part (b). And the reason they are treated as one coin is because they both contribute the same amount to the sum of money.

Counting Problems

Basically, counting refers the process of finding the number of elements of a finite set of objects.

Given,

Suppose you have a nickel, two dimes, and a quarter. One of the dimes was minted in 1976, and the other one was minted in 1992.

While we looking into the given problem,

For A) states that,  If you choose at least one coin, this means you could choose 1, 2, 3 or 4 coins. Let us label the dime as D, the penny as P, the quarter minted in 1976 as Q1 and the quarter minted in 1992 as Q2.

Here in this process if you choose one coin, you could choose either D, P, Q1, or Q2. This gives us 4 possible sets.

And If you choose two coins, you choose the following sets of coins: DP, DQ1, DQ2, PQ1, PQ2, Q1Q2. This gives us 6 possible sets.

Then If you choose three coins, you could the following sets of coins: DPQ1, DPQ2, DQ1Q2, PQ1Q2. This gives us 4 possible sets.

So, If you choose four coins, you can only choose DPQ1Q2. This gives us 1 possible set.

So, the total number of different sets of coins you can form is 4 + 6 + 4 + 1 = 15 different sets of coins can be formed.

Similarly, for b) If you choose at least one coin, this means you could choose 1, 2, 3 or 4 coins.

Then If you choose one coin you could choose either D, P, Q1, or Q2. However, since Q1 and Q2 give us the same sum, they are effectively the same set. This gives us 3 possible sums.

So, If you choose two coins, you could choose the following sets of coins : DP, DQ, PQ, Q1Q2.And this gives us 4 possible sums

Then If you choose three coins, you could choose the following sets of coins: DPQ, DQ1Q2, PQ1Q2. And this gives us 3 possible sums

Then If you choose four coins, you can only choose DPQ1Q2. This gives us 1 possible sum.

So, the total number of different sums of coins you can form is 3 + 4 + 3 + 1 = 11 different sums of money can be produced.

Finally, c) The reason that the answers in part (a) and part (b) are not the same is because Q1 and Q2 are treated as two different coins in part (a) whereas they are effectively treated as the same coin in part (b). And the reason they are treated as one coin is because they both contribute the same amount to the sum of money.

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Answer:6x

Step-by-step explanation: Put the x's on one side and other on the other side

Answer:

The equation has a solution,

Step-by-step explanation:

Given equation,

→ 8x + 16 = 2x + 16

Now the value of x will be,

→ 8x + 16 = 2x + 16

→ 8x - 2x = 16 - 16

→ 6x = 0

→ x = 0/6

→ [ x = 0 ]

Hence, the value of x is 0.

Answer:

B. 1 over 3 x 12 hours

Step-by-step explanation:

The oil company fills 1/12 of a tank in 1/3 an hour. So, you multiply 1/3 times 12, since 12 is a full tank. It'll take 4 hours to fill the tank at this rate.

1/12 tank: 1/3 hour

2/12 tank: 2/3 hour

3/12 tank: Full hour

3/12 is equivalent to 1/4, meaning 1/4 of the tank is filled after 1 hour. Thus, it'll take 4 hours.

23/25 is greater than 9/10

23/25=92/100

9/10=90/10

92>90

Answer:

f(-5) = -16

Step-by-step explanation:

f(-5) =  -  [tex](-5)^{2}[/tex] + 9

-(25) + 9

-25+9

-16

In the expression 5x + 5 = 95,  the value of x is 18

What is an angle ?

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

The given angle 5x + 5 is equal to 95

We need to calculate the value of x

5x + 5 = 95

5x = 95 - 5

5x = 90

x = 90/5

x = 18

Therefore, the expression 5x + 5 = 95 is solve and the value of x is 18

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Answer:

===========================

Sum of interior angles of a regular polygon is:

Find the measure of interior angle a:

Equate the values of angle a and solve for z:

Correct choice is B.

Answer:

z = 12

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Interior angle of a regular polygon}\\\\$\dfrac{180^{\circ}(n-2)}{n}$\\\\where $n$ is the number of sides.\\\end{minipage}}[/tex]

Given that the regular polygon has 5 sides, then the measure of one interior angle is:

[tex]\implies \dfrac{180^{\circ}(5-2)}{5}=\dfrac{180^{\circ}(3)}{5}=\dfrac{540^{\circ}}{5}=108^{\circ}[/tex]

If "a" is the measure of one angle, and m∠a = (3z + 72)° then:

[tex]\implies m \angle a=108^{\circ}[/tex]

[tex]\implies (3z+72)^{\circ}=108^{\circ}[/tex]

[tex]\implies 3z+72=108[/tex]

[tex]\implies 3z+72-72=108-72[/tex]

[tex]\implies 3z=36[/tex]

[tex]\implies \dfrac{3z}{3}=\dfrac{36}{3}[/tex]

[tex]\implies z=12[/tex]

Answer:( 3.5 , -2 )

Step-by-step explanation:

The smallest number of people when one could have been at the party is 211 people.

This is a least common multiple question, also known as an LCM. We know this because all groups would have formed evenly if the one extra person had not arrived at the party. This means that there are 1 more people at the party than a number 2, 3, 5, or 7.

In this case, the number will be:

= (2 × 3 × 5 × 7) + 1

= 210 + 1

= 211

Applicable multiples of 7

(7 × 10) = 70 → 70 + 1 = 71 → 71/3 = 23 R2 → not possible

(7 × 20) = 140 → 140 + 1 = 141 → 141/3 = 47 → not possible

(7 × 30) = 210 → 210 +1 = 211 → 211/3 = 70 R1 → possible.

Therefore, the number of people is 211.

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The r - values that represents the weakest linear correlation is ;

-0.312 is the weakest negative correlation and 0.558 is the weakest positive correlation.

Given,

The r- values;-

- 0.904, -0.312, 0.558, 0.870

We have to find the r - values that represents the weakest linear correlation;

r- values represents correlation between two variables. The r- value lies from -1 to 1.

So, here.

-0.904 is close to -1, so it represents strong negative correlation.

-0.312 is close to -0.5, so it represents weak negative correlation.

0.558 is close to 0.5, so it represents weak positive correlation

0.870 is close to 1, so it represents strong positive correlation.

Therefore,

The r - values that represents the weakest linear correlation is ;

-0.312 is the weakest negative correlation and 0.558 is the weakest positive correlation.

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Answer:

-0.312

Step-by-step explanation:

−0.312

The size of the correlation, r  indicates the strength of the linear relationship between x and y. Values of r which are closer to −1 or to +1 indicate a stronger linear relationship between x and y.

Lenny's total wage is $7000

In this question, Lenny works a basic week of 32 hours. His basic rate of pay is $1,750. During a certain week he worked 9 hours overtime for which he was paid triple time.

32 hours of work = $1750

In a certain week, we work 9 hours as over time

For this overtime which he was paid triple time.

1750 * 3 = $5250

So, Lenny's total wage would be,

$1,750 +  $5250 = $7000

Therefore,  Lenny's total wage is $7000

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The volume of the solid bounded above by the parabolic cylinder is 191π/64.

Given:

the Parabolic cylinder z=1−y^2 and below the plane 3x+3y+z+10=0 and on the sides of circular cylinder x^2+y^2−x=0.

[tex]x^2+y^2-x=(x-\frac12)^2 +y^2-\frac14=0[/tex]

Recenter the circle with x−1/2=u and integrate the volume over the disk

u^2+y^2 = 1/4.

[tex]\int_{u^2+y^2 < \frac14} [(1-y^2)-( -2x-3y-10)][/tex]

[tex]=\int_{u^2+y^2 < \frac14} (2u+3y-y^2 +12)[/tex]

[tex]=\int_{u^2+y^2 < \frac14} (12-y^2)[/tex]

[tex]=\int_0^{2\pi}\int_0^{1/2} (12-r^2 \sin^2\theta)rdr d\theta =\frac{191\pi}{64}\\[/tex]

Therefore The volume of the solid bounded above by the parabolic cylinder is 191π/64.

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The slope of a line that is parallel to the line y = x + 2 is 1.

What is slope?

A line's steepness is determined by its slope. In mathematics, the slope is determined by "rise over run" (change in y divided by change in x).

Given the equation of line: y = x + 2

We have to find the slope of a line that is parallel to the given line.

Since any line parallel to the given line  y = x + 2  will have the same slope as that of a given line

The general equation of line is given as y = mx + c

where. m is the slope of the line and c is y-intercept.

Thus for given equation of line y = x + 2

Comparing , we get

slope is m=1

Thus, any line with slope 1  is parallel to the given line y = x + 2

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Answer:

f(x) = - x² + 2x - 2 :

x → - ∞

f(x) → - ∞

f(x) = x⁴ + 3x² + x - 3 :

x → ∞

f(x) → ∞

Answer: 0

Step-by-step explanation:

8x-4=4(2x+1)

8x-4=8x+4

0= 8

This isn't true as 0 can't equal to 8 so there are 0 solutions

The monthly installment to be paid is $17.85.

Given:

A washing machine is priced at $450. A man buys the washing machine on HP according to the following terms: A deposit of 15% and the remaining to be paid in monthly installment over 2 years at a simple interest rate of  12 % per annum.

Remaining amount = 450 - 450*15/100

= 450 - 9*15/2

= 450 - 67.5

= $382.5

1 month amount = 382.5 + 382.5*0.12 / 24

= 428.4/24

= $17.85.

Therefore the monthly installment to be paid is $17.85.

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Answer: 60%

Step-by-step explanation:

(5 × p) / 100 = 3

((5 × p) / 100) × 100 = 3 × 100

5p = 300

5p / 5 = 300 / 5

p = 60

Percent Increase = 60

Answer:

A = ₤500

B = ₤420

C = ₤340

D = ₤260

See Image 1 attached for the plot.

Step-by-step explanation:

The bank account starts with ₤500, so that is the amount at 0 months on the chart.

After one month, ₤80 is withdrawn, and the total becomes:

[tex]500-80=420[/tex]

After two months, another ₤80 is withdrawn from the account:

[tex]420-80=340[/tex]

Finally, after 3 months, ₤80 is withdrawn again:

[tex]340-80=260[/tex]

Answer: 0.555555556

Step-by-step explanation:

15/27=0.555555556

Checking work by plugging it in: 27x0.555555556=15

======================================================

Work Shown:

a = old value = 15

b = new value = 27

c = change in values

c = b-a

c = 27-15

c = 12

The positive c value tells us that we have an increase.

Then divide over the starting value a = 15

c/a = 12/15 = 0.80

Move the decimal point two spots to the right to go from 0.80 to 80%

Or multiply 0.80 with 100% to get 0.80*100% = 80%

We have a percent increase of 80%

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

Check:

80% of 15 = 0.80*15 = 12

If the stock increases by 80%, then it has increased by $12 to go from $15 a share to 15+12 = 27 dollars a share. This confirms the answer.

A slight shortcut would be to say 1.80*15 = 27

The multiplier 1.80 represents an increase of 80% since 100% + 80% = 1 + 0.80 = 1.80

The equations that represent the left side, right side, top side and bottom side are y = 3x+2, y = 3x-10, y = 5 and y = -1 respectively

The slope-intercept form of the equation of a line is y =mx+c,

where m is the slope and c is the y-intercept

slope(m) = y2-y1 / x2-x1

Left side

The line moves from point 1 (-1, -1) to point 2 (1,5)

x1 = -1, y1 = -1 and x2 = 1, y2 = 5

Slope(m) = 5-(-1) / 1-(-1)  = 6/2 = 3

Using the equation of a line for 2 points:

y-y1 = m(x-x1)

y-(-1) = 3(x-(-1))

y+1 = 3(x+1)

y+1 = 3x+3

y = 3x+2

Right side

The line moves from point 1 (3, -1) to point 2 (5,5)

Slope(m) = 5-(-1) / 5-3  = 6/2 = 3

y-(-1) = 3(x-3)

y+1 = 3x -9

y = 3x-10

Top side

y = 5

Bottom side

y = -1

Therefore, equation for the left side : y = 3x+2, equation for the right side: y = 3x-10, equation for the top side: y = 5 and equation for the bottom side: y = -1

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The height of a cylinder is D. 7 halves inches

The volume of a cylinder is calculated as:

V = πr²h

r = radius = 1/3

h = height = ?

v = volume = 1 2/9

We will slot the value info the formula. This will be:

V = = πr²h

1 2/9 = 22/7 × 1/3 × 1/3 × h

1 2/9 = 22/63h

Divide through by 22 / 63

h = 1 2/9 ÷ 22/63

h = 11/9 × 63/22

h = 7/2

The correct option is D.

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Answer:

7/2 is your answer i have the same test :)))

Step-by-step explanation:

The volume of a cylinder is calculated as:

V = πr²h

r = radius = 1/3

h = height = ?

v = volume = 1 2/9

We will slot the value info the formula. This will be:

V = = πr²h

1 2/9 = 22/7 × 1/3 × 1/3 × h

1 2/9 = 22/63h

Divide through by 22 / 63

h = 1 2/9 ÷ 22/63

h = 11/9 × 63/22

h = 7/2

The correct option is D.

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Answer:

$16.28

Step-by-step explanation:

44.%

Move the decimal up by two numbers to get a whole number, .44

and multiply .44 by $37

Answer:

361

Step-by-step explanation:

Answer:

Neither, Perpendicular, Parallel, Neither

Step-by-step explanation:

Parallel lines have the same slope.

Perpendicular lines have slopes that are negative reciprocals.

Answer:

y=-x+16

Step-by-step explanation:

let’s put this equation in slope intercept form: y=mx+b

2x+2y=-8

-2x.      -2x

2y=-2x-8

/2.  /2.  /2

y=-x-4

We know parallel lines have the same slope as each other so let’s fill in the equation with the given point

10=-(6)-4

10=-10

We need to add 20 more to the y intercept to make this true like this

y=-x-4+20

y=-x+16

Now let’s see if it works

10=-(6)+16

10=10

It works so this is the equation

Hopes this helps please mark brainliest

Answer: y = -x +16

Step-by-step explanation:

rearrange the equation to make y the subject

2y = -2x -8

y = -x-4

equation of line parallel to the line (gradient will be the same)

y = -x +c

Substitute the x and y values into the parallel line equation

10 = -6 + c

10 + 6 = c

16 = c

Therefore, the equation of the line parallel to 2x + 2y = -8 is y = -x +16

The side length, x, of the right triangle will be 26 units.

According to the question,

We have the following information:

In a right triangle, two of the sides are 24 units and 10 units.

The complete question is that 24 units is the perpendicular and 10 units is the base of the given right triangle.

Let's denote hypotenuse with h, perpendicular with p and base with b.

We will find the hypotenuse of the triangle using the Pythagoras theorem:

[tex]h^{2} = b^{2} +p^{2}[/tex]

[tex]h^{2}= (24)^{2}+ (10)^{2}[/tex]

[tex]h^{2} = 476+100\\h^{2} = 576[/tex]

h = √576

h = 26 units

Hence, the side length, x, of the right triangle will be 26 units.

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Answer:The answer is:

k

=

2

.

Given two point,

A

(

x

a

,

y

a

)

and

B

(

x

b

,

y

b

)

the slope of the line that passes from them is:

m

=

y

b

−

y

a

x

b

−

x

a

.

So:

−

2

=

6

−

2

k

−

4

⇒

−

2

(

k

−

4

)

=

4

⇒

−

2

k

+

8

=

4

⇒

−

2

k

=

−

4

⇒

k

=

2

.

Step-by-step explanation:The answer is:

k

=

2

.

Given two point,

A

(

x

a

,

y

a

)

and

B

(

x

b

,

y

b

)

the slope of the line that passes from them is:

m

=

y

b

−

y

a

x

b

−

x

a

.

So:

−

2

=

6

−

2

k

−

4

⇒

−

2

(

k

−

4

)

=

4

⇒

−

2

k

+

8

=

4

⇒

−

2

k

=

−

4

⇒

k

=

2

.

Answer: The answer is 81m + 27t

Step-by-step explanation:

Answer: (3t)^t+3 and 3^t^2 x 27^t are both equivalent to the expression while 9^t x 27^t is not equivalent.

Step-by-step explanation: