Find the sum or difference. Write all fractions in simplest form and improper fractions as mixed numbers 8/2-3/5

The solutions to the equation x³ - x² - 18 = 0 are given as follows:

x = 3, x = -1 ± 2.236i.

The equation for this problem is defined as follows:

x³ - x² - 18 = 0

x - 3 is a factor, hence one solution is given as follows:

x - 3 = 0

x = 3.

Also considering that x - 3 is a factor, and x - 3 is of the first degree while the equation is of the third degree, we have that:

(x - 3)(ax² + bx + c) = x³ - x² - 18

ax³ + (b - 3a)x² + (c - 3b)x - 3c = x³ - x² - 18

Hence the coefficients are given as follows:

Hence the remaining solutions are given as follows:

x² + 2x + 6 = 0.

Using a quadratic function calculator:

x = -1 ± 2.236i.

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After solving the equation for n and b we find out that Lin bought 1 necklace and 4 bracelets.

We can set up the following system of equations based on the given information: n = number of necklaces, b = number of bracelets

4n + b = 20 (Lin spends $20 on necklaces and bracelets)

where 4n represents the cost of n necklaces and b represents the cost of b bracelets. This system of equations can be used to solve for n and b. we can solve for n and b using the system of equations:

n + 1b = 5

4n + 1b = 20

We can use the first equation to solve for n in terms of b: n = 5 - b

Substitute this expression for n into the second equation: 4(5 - b) + b = 20

Simplifying this equation, we get: 20 - 4b + b = 20

Solving for b, we get: b = 4

Substituting this value of b back into n = 5 - b, we get: n = 1

Therefore, Lin bought 1 necklace and 4 bracelets

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Complete Question

At a local fair , Lin purchases necklaces and bracelets. Necklaces cost $4 each and bracelets cost $1 each, Lin spends $20 on these items. Let n represent the number of necklaces Lin buys and b represent the number f bracelets Lin buys. Find the number of necklaces and bracelets Lin purchased.

(a) The percentage of people that left the event in the afternoon is 8%

(b) The total number of people that were there at the start of the fund-raising event were 68.

Let x be the number of people at the start of the event. Then, 0.6x were males and 0.4x were females.

In the afternoon, 0.2 * 0.4x = 0.08x females left the event.

So, there were 0.4x - 0.08x = 0.32x females left at the event.

In the evening, 33 + 35 = 68 people left the event, and x - 68 people were left.

Out of the x - 68 people, 0.6(x - 68) were males.

So, we have 0.75 * (x - 68) = 0.6 * (x - 68).

We can now solve for x:

0.75 * (x - 68) = 0.6 * (x - 68)

0.15 * (x - 68) = 0

x - 68 = 0

x = 68

Thus, there were 68 people at the start of the fund-raising event.

(a) The percentage of people who left the event in the afternoon was 0.08x / x * 100% = 0.08 * 100% = 8%.

(b) There were 68 people at the start of the fund-raising event.

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Step-by-step explanation:

A.Rational because by using the discrmant formula, Since our coefficients are integers, and if we get a perfect square, inside a radicand , we will have a rational numbers.

For example:

[tex] \sqrt{ {7}^{2} - 4(4)(3) } = \sqrt{49 - 48} = \sqrt{1} = 1[/tex]

Since root 1, is a perfect square, we will have rational roots.

B.

[tex] {b}^{2} - 4ac < 0[/tex]

[tex]49 - 16c < 0[/tex]

[tex] - 16c < - 49[/tex]

[tex]c > \frac{49}{16} [/tex]

If c is greater than 49/16, we will have no x intercepts.

Answer:

yes

Step-by-step explanation:

Answer: a and b

Step-by-step explanation: lol it obvious

Answer: Quadrilateral, Parallelogram

Step-by-step explanation:

A Quadrilateral is any closed 4 sided figure

A Parallelogram is a quadrilateral with two sets of parallel and opposite sides.

Answer: Approximately 226 miles

Step-by-step explanation:

Km. to Mi.

364 = 226

The ordered pair that represent the number of red beads and gold beads is A. D, and E.

Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion.

From the table we observe that the number of red beads and the gold beads are in the proportion x : y = 4 : 3.

Using the proportion we see that:

A: (20, 15) = 20 : 15 = 4 : 3

D: (80,60) = 4: 3

E = (100, 25)= 4:3

Hence, the ordered pair that represent the number of red beads and gold beads is A. D, and E.

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Answer:

Plug your values into the equation A=1/2bh and do the math. First multiply the base (b) by 1/2, then divide the area (A) by the product. The resulting value will be the height of your triangle!

Step-by-step explanation:

Total ways can 4 seniors and 2 juniors be chosen to participate in a charity event is 1,91,100.

There are 16 seniors and 15 juniors in a particular social organization and

4 seniors and 2 juniors had to be chosen to participate in a charity event.

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by [tex]^nC_r[/tex] and it is given by,                   [tex]^nC_r = \frac{n!}{r!(n-r)!}[/tex] , where 0 ≤ r ≤ n.

Therefore the total ways that 4 seniors and 2 juniors be chosen to participate in a charity event = [tex]^{16}C_{4}.^{15}C_{2}[/tex]

= [tex]\frac{16!}{4!(16-4)!}$\times \frac{15!}{2!(15-2)!}[/tex]

= 1820 × 105

= 1,91,100

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The complete question is:

There are 16 seniors and 15 juniors in a particular social organization. In how many ways can 4 seniors and 2 juniors be chosen to participate in a charity event?

The area of the shaded region is 12.5 square inches.

First we can subtract the area of the smaller triangle from the area of the larger triangle.

The larger triangle has a base of 8 inches and a height of 5 inches, so its area is:

(1/2) * base * height = (1/2) * 8 in. * 5 in. = 20 in²

The smaller triangle has a base of 3 inches and a height of 5 inches, so its area is:

(1/2) * base * height = (1/2) * 3 in. * 5 in. = 7.5 in²

Subtracting the area of the smaller triangle from the area of the larger triangle, we get:

20 in² - 7.5 in² = 12.5 in²

Therefore, the area of the shaded region is 12.5 square inches.

Therefore the option is F. 15 in² (none of the given answer choices match the calculated area of 12.5 in²)

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the probability of having 4 months containing exactly 2 birthdays and 4 months containing exactly 3 birthdays among 20 people is approximately 0.000008, or about 0.0008%

The problem of calculating the probability of a certain pattern of birthdays among a group of people can be approached using the techniques of combinatorics and probability. To calculate the probability of having 4 months containing exactly 2 birthdays and 4 months containing exactly 3 birthdays among 20 people, we can use the following steps: First, we need to choose which 4 months will have exactly 2 birthdays and which 4 months will have exactly 3 birthdays. There are 12 months to choose from, so the number of ways to make these choices is given by the binomial coefficient: C(12, 4) × C(8, 4). This is the number of ways to choose 4 months out of 12 to have exactly 2 birthdays, multiplied by the number of ways to choose 4 months out of the remaining 8 to have exactly 3 birthdays. Next, we need to assign the people to the months. To do this, we can use the principle of inclusion-exclusion, which states that the number of ways to assign the people to the months so that each of the chosen months has the correct number of birthdays is: N = (20!/(2!²× 3!⁴)) × (4¹² - 6 × 3¹² + 4 × 2¹²). This expression counts the number of ways to distribute the 20 people among the 12 months so that the chosen months have the correct number of birthdays, and subtracts the cases where one or more of the chosen months have too many or too few birthdays. The factor (20!/(2!⁸ × 3!⁴)) accounts for the fact that we are counting distinguishable arrangements of people. Finally, we can calculate the probability of the desired pattern of birthdays by dividing the number of favorable outcomes (N) by the total number of possible outcomes, which is simply the total number of ways to assign the people to the months, given by: 12²⁰. Putting it all together, we get: P(4 months with 2 birthdays, 4 months with 3 birthdays) = N / 12²⁰. Evaluating this expression gives: P(4 months with 2 birthdays, 4 months with 3 birthdays) ≈ 0.000008. Therefore, the probability of having 4 months containing exactly 2 birthdays and 4 months containing exactly 3 birthdays among 20 people is approximately 0.000008, or about 0.0008%.

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The correlation of 0.5 indicates that the data points are not perfectly related - there is some degree of variation, which could be caused by a number of factors. If some data points have significantly different values than others, they can reduce the overall correlation.

Alternatively, the data could also have other confounding variables, such as additional features that are not considered in the linear relationship between x and y. These additional variables could also reduce the correlation, as they introduce noise into the analysis. In either case, the correlation of 0.5 could be due to the presence of outliers and/or confounding variables.

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For the required linear function , the height of the candle when the amount of time for  burning a candle is 16 hours is equal to 18.8 centimeters.

Let 'h' be the height of the candle.

And 't' be the amount of time used for burning.

Required linear function is :

h = mt + c

When t = 8 hours  , h = 20.4centimeters

20.4 = 8m + c ___(1)

When t = 19 hours  , h = 18.2centimeters

18.2 = 19m + c ___(2)

Subtract (2) from (1) we get,

20.4 = 8m + c

18.2 = 19m + c

2.2 = -11m

⇒ m = -2.2 / 11

⇒ m = -0.2

Substitute in (1) we get,

20.4  = 8( -0.2 ) + c

⇒ c = 20.4 + 1.6

⇒ c = 22

Now , h = -0.2t + 22

When t = 16 hours

⇒ h = -0.2(16) + 22

⇒ h = -3.2 + 22

⇒ h = 18.8 centimeters

Therefore, the height of the candle when amount of time of burning is 16 hours is equal to 18.8 centimeters.

The above question is incomplete, the complete question is:

Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 8 hours of burning, a candle has a height of 20.4 centimeters. After 19 hours of burning, its height is 18.2 centimeters. What is the height of the candle after 16

hours?

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The rationalized form of the surd is;

1) 25/13

2) 144/3

3) 36

We have to note that the term surd would have to refer to an irrational number as we know it.

1) The conjugate of the surd is;

5/4 + √3

Rationalizing we have;

5/4 -  √3 * 5/4 + √3

25/16 + 4√3 - 4√3 -3

25/13

2) The conjugate is √7 - 2

Rationalizing we have;

12/√7 + 2  * 12/√7 - 2

144/7 -2√7 + 2√7 -4

144/3

3) The conjugate of the surd is √2 + √3

Rationalizing we have;

6/ √2 -  √3  * 6/ √2 + √3

36/4 +√6 - √6 - 3

36/1 = 36

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If there are 8 men and 5 women , then the number of ways of selecting a 4 people committee is 715 ways  .

The number of ways to select a committee of 4 people from a group of 13 people, where 5 are women and 8 are men, is calculated by Combination ;

where , "n" is = total number of people, "r" is = number of people to be selected,

In this case, we have:

the total number of people is = 8 + 5 ⇒ n = 13 ;

the number of committee member to be selected is "r" = 4 ;

So, the number of ways to select a committee of 4 people from a group of 13 people is  :  ¹³C₄ = 715 ways ;

Therefore, there are 715 ways to select a committee of 4 people from a group of 5 women and 8 men.

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The given question is incomplete , the complete question is

There are 5 women and 8 men is a department . Find the Number of ways can a committee of 4 people be selected ?

Answer:  x=3, y=-1

Step-by-step explanation:

2x+y=5

2y=2x-8

In equation 1, y=5-2x.

Substitute this value in equation 2.

2(5-2x)=2x-8

10-4x=2x-8

Thus,

4x+2x=10+8 (collecting terms)

6x=18

x=3

Now, we said earlier that y=5-2x.

Therefore, y=5-2(3) [because x=3]

y=5-6

y=-1

Hope this helps :]

Let's call the number of hours of labor required to replace the water pump as "x".

The total cost of the water pump and labor was $668, so we can write an equation:

$490 + $89x = $668

Now we can solve for x by subtracting $490 from both sides:

$89x = $668 - $490

$89x = $178

And finally, dividing both sides by $89:

x = $178 / $89

x = 2 hours

So, 2 hours of labor were required to replace the water pump.

The volume of the solid of revolution is equal to 21π cubic units.

In this problem we find the representation of a figure, whose area is also shown and whose solid of revolution is can be defined by following formula:

V = π · A

Where:

First, the area of the representation is found by summing the areas of two compounding rectangles:

A = 5 · 3 + 2 · 3

A = 21

Second, compute the volume of the solid of revolution:

V = 21π

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There are 11 observations in the subset data.e need to count the number of observations in the subset data.

1. First, we need to filter out the observations that have a date on or after May 1, 1975. For this, we can use the following code:

x3[x3$DATE >= "1975-05-01",]

2. Then, we need to count the number of observations in the subset data. We can do this by using the nrow() function:

nrow(x3[x3$DATE >= "1975-05-01",])

The output is 11.

If we wanted to subset the data set to include only observations that have a date on or before February 1, 1985, we can use the following code:

x3[x3$DATE <= "1985-02-01",]

Then, we can count the number of observations in the subset data usingthe nrow() function:

nrow(x3[x3$DATE <= "1985-02-01",])

The output is 19.

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The value of x is given as follows:

[tex]x = 2.5\sqrt{2}{/tex]

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

For a right triangle with an angle of 45º, we have that:

This is because the angle of 45º has an equal value of the sine and of the cosine.

Hence the side length of the top triangle is given as follows:

s = 5.

For the bottom triangle, the side length is of x, while the hypotenuse is of 5, hence:

x² + x² = 5²

2x² = 25

[tex]x = \sqrt{\frac{25}{2}}[/tex]

[tex]x = \frac{5}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}[/tex]

[tex]x = 2.5\sqrt{2}{/tex]

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The equation of the trend line in the graph can be found to be y = 5 x + 15

The equation of the trend line takes the form :

y = Slope ( x ) + y intercept

From the diagram, we know the y - intercept is 15 as this is where the line intercepts the y - axis.

The slope can be found by picking a point and using the formula. We will pick ( 1, 20 ).

The slope is:

20 = Slope ( 1 ) + 15

Slope = 20 - 15

Slope = 5

The equation is:

y = 5 x + 15

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The value of sin (θ/2) in the trigonometry is π/9

Information given in the problem

tan θ = 7/8,

where

0 < θ <  π/2

solving for θ, from tan θ = 7/8

tan θ = 7/8

θ = arc tan (7/8)

θ = 0.7188 radians

soling for sin (θ/2)

= sin (θ/2)

= sin (0.7188/2)

= 0.3517 approximately π / 9

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The value of ZE angle is 72 degree and LF is 18 degree.

Complementary and supplementary angles are defined as the addition of two angles. If the sum of two angles is 180 degrees, one is a complementary angle and together they form a linear angle. When the sum of two angles is 90 degrees, they are called complementary angles and together form a right angle.

ZE and LF are complementary. The measure of ZE is 54° more than the measure of LF.

let ZE angle value is x

and ZE is 54 degree more than LF

LF + 54 = ZE  degree  

When the sum of two angles is equal to 90 degrees, they are called complementary angles.

LF +ZE = 90 degree

x+x-54 = 90

2x = 36

x = 18

so ZE angle = 72 degree and LF is 18 degree

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Answer: 4(9a-4) and x = 18

Step-by-step explanation:

36a - 16 a common factor in this is 4 so if we factor out 4 we would get

4(9a-4)

1/2x - 7 = 1/3(x-12) we would distribute out the 1/3 so 1/3x and 1/3 x - 12 which would simply into 4

1/2x - 7 = 1/3x - 4 get the x's into one side so subtract 1/3x and add 7 on both sides

1/2x - 1/3x = 3 --- multiply 1/2x with 3/3 and 1/3x with 2/2

3/6x - 2/6x = 3

1/6x = 3 --- isolate x by multiplying 6 on both sides

x = 18

Step-by-step explanation:

Rather than give you the full answer, let me point out the things that you need to know to work this out for yourself.

The surface area of the solid is the sum of all of the areas of its faces.

The area of a right triangle is a well-known formula. You should already know this.