The Discriminant of a quadratic equation is -6. What types of solutions does the equation have?

Answer:

1/5

Step-by-step explanation:

The probability of selecting 5 widgets from the 25 produced where none are defective is 0.2914.

To calculate the probability of selecting 5 non-defective widgets from the 25 produced.

The number of ways to choose 5 non-defective widgets:

[tex]\[ \binom{20}{5} = \frac{20!}{5!(20-5)!} \][/tex]

[tex]\[ = \frac{20 \times 19 \times 18 \times 17 \times 16}{5 \times 4 \times 3 \times 2 \times 1} \][/tex]

[tex]\[ = \frac{20 \times 19 \times 18 \times 17 \times 16}{5 \times 4 \times 3 \times 2 \times 1} \][/tex]

[tex]\[ = \frac{1860480}{120} \][/tex]

= 15504

The total number of ways to choose 5 widgets from the 25 produced:

[tex]\[ \binom{25}{5} = \frac{25!}{5!(25-5)!} \][/tex]

[tex]\[ = \frac{25 \times 24 \times 23 \times 22 \times 21}{5 \times 4 \times 3 \times 2 \times 1} \][/tex]

[tex]\[ = \frac{7893600}{120} \][/tex]

= 53130

The probability:

Probability = (Number of ways to choose 5 non-defective widgets)/(Total number of ways to choose 5 widgets)

[tex]\[ = \frac{15504}{53130} \][/tex]

[tex]\[ = 0.2914 \][/tex]

Complete question:

A widget company produces 25 widgets a day, 5 of which are defective. Find the probability of selecting 5 widgets from the 25 produced where none are defective.

Answer:

  To make 18 oz of furniture​ polish, 4.5 oz of vinegar and 13.5 oz of olive oil are needed.

Step-by-step explanation:

The ratio of ingredients is ...

  oil : vinegar = 3 : 1

So vinegar is 1 of the 3+1 = 4 parts of the polish mix. The amount of vinegar required for 18 oz of polish is ...

  (1/4)×(18 oz) = 4.5 oz

The remaining quantity is olive oil:

  18 oz - 4.5 oz = 13.5 oz

To make 18oz of furniture polish, 4.5 oz of vinegar and 13.5 oz of olive oil are needed. These quantities are found by setting up an equation based on the problem's conditions and solving for x.

To begin solving the problem we need to understand that both the vinegar and the olive oil are together making up the 18oz of furniture polish. Since the amount of olive oil is three times the amount of vinegar, we can denote the quantity of vinegar as 'x'. Thus, the quantity of olive oil will be '3x'.

Adding these together gives us the total ounces, thus, we have our equation: x + 3x = 18. Solving this, we get 4x = 18. Dividing by 4 gives us x = 18/4 = 4.5.

Therefore, to make 18oz of furniture polish, you will need 4.5 oz of vinegar and 13.5 oz (3 times 4.5) of olive oil.

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Answer:

$173.45

Step-by-step explanation:

the beginning value is $400. if it loses 13%, that means it keeps 87% of its value. so you multiply by 0.87 6 times for each year

Answer:

Conjugate

Step-by-step explanation:

Those are conjugates.  In factoring polynomials, if you have one with a + sign separating the a and the square root of b, you will ALWAYS have one with a - sign.  They will always come in pairs.  Same with imaginary numbers.

The sum of the mixed fraction numbers - 6 ⁴/₅ and 6 ⁴/₅ will be 0. Then the correct option is C.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

- 6 ⁴/₅ and 6 ⁴/₅

Convert the mixed fraction number into a fraction number. Then we have

- 6 ⁴/₅ = -34/5

6 ⁴/₅ = 34/5

Then the sum of the expressions will be given as,

⇒ - 34/5 + 34/5

⇒ 0

The sum of the mixed fraction numbers - 6 ⁴/₅ and 6 ⁴/₅ will be 0. Then the correct option is C.

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Answer:

The image is (0 , -6)

Step-by-step explanation:

* Lets explain some important facts

- When a point reflected across a line the perpendicular

 distance from the point to the line equal the perpendicular  

 distance from its image to the same line

- If the line of the reflection is horizontal then the perpendicular

 distance between the point and the line is y - y1 , and the

 perpendicular distance between the image and the line is y2 - y

- If point (x , y) reflected across the x- axis, then its image is (x , -y)

* Lets solve the problem

∵ Point (0 , 0) reflected across the line y = 3

∴ y = 3 and y1 = 0

∴ The distance between the point and the line is 3 - 0 = 3

∴ The distance between the image and the line also = 3

∴ y2 - 3 = 3 ⇒ add 3 to both sides

∴ y2 = 6

∴ The y-coordinate of the image is  6

∴ The image of point (0 , 0) after reflection across the line y = 3 is (0 , 6)

- The image of the point reflected across the x-axis, then change the

  sign of the y-coordinate

∴ The final image of point (0 , 0) is (0 , -6)

* The image is (0 , -6)

Answer:

1

Step-by-step explanation:

The numbers are mutually prime, so the GCF is 1.

Answer:

1

Step-by-step explanation:

n-1 and n are consecutive integers.

Examples of consecutive pairs:

(7,8)

(10,11)

(100,101)

and so on...

The remainder will always be 1 when doing n divided by n-1.

n=(n-1)(1)+1.

All this is here to try to convince you that n and n-1 will only have common factor of 1.

Answer:

13/9

Step-by-step explanation:

Directly proportional means it will be multiply to our constant k.

Inversely proportional means it will divide our k.

So we are given z is directly proportional to x and inversely proportional to y.

This means:

[tex]z=k \cdot \frac{x}{y}[/tex].

We are given (x=4,y=10,z=0.8).  We can use this to find k.  The k we will find using the point will work for any point (x,y,z) since k is a constant.  A constant means it is to remain the same no matter what.

[tex]0.8=k \cdot \frac{4}{10}[/tex]

[tex]0.8=k(.4)[/tex]

Divide both sides by .4:

[tex]\frac{0.8}{0.4}=k[/tex]

[tex]k=2[/tex]

The equation for any point (x,y,z) is therefore:

[tex]z=2 \cdot \frac{x}{y}[/tex].

We want to find z given x=13 and y=18.

[tex]z=2 \cdot \frac{13}{18}[/tex]

[tex]z=\frac{2 \cdot 13}{18}[/tex]

[tex]z=\frac{13}{9}[/tex]

Answer:

90°, 75°, and 15°

Step-by-step explanation:

In a right triangle, one of the angles is 90°.

           Let x = the smallest angle

Then 60 + x = the third angle

The sum of the three angles is 180°.

90 + 60 + x + x = 180

          150 + 2x = 180

                    2x =  30

                      x =   15

      Measure of right angle              = 90°

Measure of smallest angle = x         =  15°

     Measure of third angle = 60 + x = 75°  

The measures of the angles are 90°, 75°, and 15°.

Answer:

Step-by-step explanation:

This is a right triangle with the 90 degree angle identified at D and the 60 degree angle identified at B. Because of the triangle angle sum theorem, the angles of a triangle all add up to equal 180 degrees, so angle C has to be a 30 degree angle.

There is a Pythagorean triple that goes along with a 30-60-90 triangle:

( x , x√3 , 2x )

where each value there is the side length across from the

30 , 60 , 90 degree angles.

We have the side across from the 90 degree angle, namely the hypotenuse. The value for the hypotenuse according to the Pythagorean triple is 2x. Therefore,

2x = 2√13

and we need to solve for x. Divide both sides by 2 to get that

x = √13

Now we can solve the triangle.

The side across from the 30 degree angle is x, so since we solved for x already, we know that side DB measures √13.

The side across from the 60 degree angle is x√3, so that is (√13)(√3) which is √39.

And we're done!

Answer:

we need an image of the spinner to answer the question. are we supposed to just know what it looks like?

Step-by-step explanation:

flvs she cheating

Answer:

  A. The distance from any point in the circle to the origin

Step-by-step explanation:

The distance formula tells you that the distance (d) is related to the coordinates of two points (x1, y1) and (x2, y2) by ...

  d² = (x2 -x1)² +(y2 -y1)²

For points (x, y) on the circle and (0, 0) at the origin, this becomes ...

  d² = (x -0)² +(y -0)²

If we want the distance to the point (x, y) to be equal to the radius of the circle, this becomes ...

  x² +y² = r² . . . . . . the standard equation of a circle centered at the origin

Answer: The distance from any point in the circle to the origin

Step-by-step explanation:

answer key

Step-by-step explanation:

[tex]\angle1\ and\ \angle 2\ \text{are complementary}\to m\angle1+m\angle2=90^o\\\\m\angle ACX=m\angle1+m\angle2=90^o\to XA^{\to}\perp XC^{\to}[/tex]

Answer:  ΔABC ~ ΔBDC ~ ΔADB

Step-by-step explanation:

Match the degrees of each angle:

In ΔABC:  ∠A = 60° , ∠B = 90° , ∠C = 30°

In ΔBDC:  ∠B = 60° , ∠D = 90° , ∠C = 30°

In ΔADB:  ∠A = 60° , ∠D = 90° , ∠B = 30°

Answer:

See below.

Step-by-step explanation:

Triangle ABC is similar to triangle ADB is similar to triangle BDC.

Answer:

The answer is 16%

Step-by-step explanation:

Given a mean of 3 hours and 50 minutes and a standard deviation of 30 minutes

so a time less than or equal to 3 hours and 20 minutes is a time 1 standard deviation OUTSIDE from the mean

Use the probability table:

The probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes

= Probability of z being outside 1 SD from mean

= 1 - Probability of z within 1 SD from mean

= 1 - 0.84

= 0.16 or 16%....

Answer:

[tex]3.6*10^{2}[/tex]

Step-by-step explanation:

we have

[tex]\frac{8.64*10^{4}}{2.4*10^{2}}=\frac{8.64}{2.4}*10^{4-2}\\ \\=3.6*10^{2}[/tex]

Answer:

A) 3.6 × 10^2

Step-by-step explanation:

Got it right in the instruction on Edge 2021 ;D

Answer:

beginning inventory is $245000

Step-by-step explanation:

Given data

ending inventory = $150,000

purchased additional inventory = $375,000

goods sold = $470,000

to find out

beginning inventory

solution

according to question beginning inventory is calculated by this formula i.e.

beginning inventory = ( cost of goods sold  + ending inventory ) - amount of inventory purchase  .....................1

now put all value cost of goods sold, ending inventory and amount of inventory purchase in equation 1 and we get beginning inventory

beginning inventory = ( cost of goods sold  + ending inventory ) - amount of inventory purchase

beginning inventory = ( 470000  + 150000 ) - 375000

beginning inventory  = 245000

so beginning inventory is $245000

Answer:

  2√5

Step-by-step explanation:

The Pythagorean theorem tells you how to find the distance from the origin.

  d = √((-2)² +4²) = √20 = 2√5

The vector's magnitude is 2√5 ≈ 4.47214.

Answer:

The magnitude of the position is [tex]|x|=\sqrt{20}[/tex]

Step-by-step explanation:

Given : Vector whose terminal point is (-2, 4).

To find : What is the magnitude of the position vector?

Solution :

We have given, terminal point (-2,4)

The magnitude of the point x(a,b) is given by,

[tex]|x|=\sqrt{a^2+b^2}[/tex]

Let point x=(-2,4)

[tex]|x|=\sqrt{(-2)^2+(4)^2}[/tex]

[tex]|x|=\sqrt{4+16}[/tex]

[tex]|x|=\sqrt{20}[/tex]

Therefore, The magnitude of the position is [tex]|x|=\sqrt{20}[/tex]

Answer:x=25

Step-by-step explanation:

One line is 180 , AB equals 180 ,angle AD is 110,180-110=70

So corner O on line DC is 70 and angle CE is 60. 60+70=130

180-130=50, 2x=50,50/2=25

Answer:

33.75

Step-by-step explanation:

You first need to determine the total distance of the round trip. This is twice the 45 mile trip in the morning, which is 90 miles. In order to determine the total amount of time spent on the round trip, convert the time travel to minutes.

1 hr + 10 mins = 70 mins

1hr + 30 = 90 mins

So his total travel time would equal to 90+70=160 minutes

his average speed is:

90mi/160min * 60min/1hr = 90*60/160

= 33.75

Elijah's average speed for the round trip is approximately 31.76 miles per hour.

To calculate the average speed for the round trip, we need to determine the total distance traveled and the total time taken.

In the morning, Elijah drove 45 miles in 1 hour and 10 minutes. To convert the minutes to hours, we divide 10 minutes by 60, which gives us 10/60 = 1/6 hours. Therefore, his morning travel time is 1 hour + 1/6 hour = 7/6 hours.

On the way home, the same trip took him 1 hour and 30 minutes. Converting the minutes to hours, we divide 30 minutes by 60, which gives us 30/60 = 1/2 hours. Therefore, his return travel time is 1 hour + 1/2 hour = 3/2 hours.

To calculate the total distance traveled, we sum the distance from the morning trip and the return trip: 45 miles + 45 miles = 90 miles.

The total time taken for the round trip is the sum of the morning travel time and the return travel time: 7/6 hours + 3/2 hours = 17/6 hours.

To calculate the average speed, we divide the total distance by the total time: 90 miles / (17/6 hours).

Dividing 90 miles by 17/6 hours is the same as multiplying 90 miles by 6/17, which gives us (90 * 6) / 17 = 540/17.

Therefore, Elijah's average speed for the round trip is approximately 31.76 miles per hour.

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Answer:

-4,-5/2

Step-by-step explanation:

2x^2+3x-20 =0

2x^2+8x-5x-20 =0

2x(x+4)-5(x+4) =0

(x+4)(2x-5) =0

Either,

x+4=0

x=-4

Or,

2x-5=0

2x=5

x=5/2

[tex]2x^2+3x-20=0\\2x^2+8x-5x-20=0\\2x(x+4)-5(x+4)=0\\(2x-5)(x+4)=0\\x=\dfrac{5}{2} \vee x=-4[/tex]

Answer:

(6^⅕) (cos(-24°) + i sin(-24°))

Step-by-step explanation:

First, we convert from Cartesian to polar:

r = √((-3)² + (-3√3)²)

r = √(9 + 27)

r = 6

θ = atan( (-3√3) / (-3) ), θ in the third quadrant

θ = atan(√3)

θ = 240° + 360° k

Notice that θ can be 240°, 600°, 960°, etc.

Therefore:

-3 − 3√3 i = 6 (cos(240° + 360° k) + i sin(240° + 360° k))

Now we take the fifth root:

[ 6 (cos(240° + 360° k) + i sin(240° + 360° k)) ]^⅕

(6^⅕) [ (cos(240° + 360° k) + i sin(240° + 360° k)) ]^⅕

Applying de Moivre's Theorem:

(6^⅕) (cos(⅕ × 240° + ⅕ × 360° k) + i sin(⅕ × 240° + ⅕ × 360° k))

(6^⅕) (cos(48° + 72° k) + i sin(48° + 72° k))

If we choose k = -1:

(6^⅕) (cos(-24°) + i sin(-24°))

Answer:

  x:(x +15)

Step-by-step explanation:

The corresponding sides that are in proportion are apparently ...

  PS:PQ = PT:PR

PT = x

PR = x+15

so the proportion of interest is ...

  28:40 = x:(x+15)

Answer:

  24,000(0.908)^t > 15,000; no

Step-by-step explanation:

The multiplier each year is 100% - 9.2% = 90.8% = 0.908. There is only one answer choice with this as the yearly multiplier.

_____

In order to answer the yes/no question, we chose to rewrite the inequality as ...

  24000·0.908^t -15000 > 0

The graph shows that is true for t < 4.87. In 5 years, the forest area will be below the minimum.

Answer:

Step-by-step explanation:

Let m represent the number of articles Mustafa has written. Then the total number of articles written must satisfy the inequality ...

  m +m/4 +3m/2 > 22

This has solution ...

  (11/4)m > 22

   m > (4/11)22

   m > 8 . . . . . . . . the solution to the inequality

If all the numbers are integers, and the ratios are exact, then we must have m be a multiple of 4 (that is, 4 times the number of articles Heloise wrote).

The solution set will be ...

  m ∈ {12, 16, 20, 24, ...} (multiples of 4 greater than 8)

Answer:

inequality - m+ 1/4m + 3/2m > 22

solution set - m>8

Step-by-step explanation:

i promise

Answer:

D

Step-by-step explanation:

If the lines are parallel, the slope of both of them are going to be the same. So if one line is 3, the other one will be too.

The answer is:

If the red line has a slope of 3, the slope of the red line will also be 3.

So, the correct option is, D. 3

We need to remember that if two or more lines are parallel, they will share the same slope, no matter where are located their x-intercepts and y-intercepts, the only condition needed for them to be parallel, is to have the same slope.

So, if two lines are parallel, and one of them (the red line) has a slope of 3, the slope of the other line (the green line) will also be 3.

Have a nice day!

Answer:

Each vehicle received [tex]\frac{3}{20}[/tex] of the total capacity of the storage tank

Step-by-step explanation:

we know that

To find out what part of the total capacity of the storage tank that each vehicle received, divide three fourths by five

so

[tex]\frac{(3/4)}{5}=\frac{3}{20}[/tex]

therefore

Each vehicle received [tex]\frac{3}{20}[/tex] of the total capacity of the storage tank

Answer:

18 red marbles.

Step-by-step explanation:

The complete question asks the probability of randomly drawing a red marble is 3/5?

Let x be the number of red marbles that must be added.

To find x we will do the following:

[tex]\frac{x+12}{x+32} =\frac{3}{5}[/tex]

=>[tex]5(x+12)=3(x+32)[/tex]

=> [tex]5x+60=3x+96[/tex]

=> [tex]2x=36[/tex]

This gives x = 18

Hence, 18 red marbles will be added to the bag.

Answer:

a. 1 1/8 b. 8/9

Step-by-step explanation:

You can set this up as a proportion to solve.  For part a. we know that 2/3 of the road is 3/4 mile long.  2/3 + 1/3 = the whole road, so we need how many miles of the road is 1/3 its length.  Set up the proportion like this:

[tex]\frac{\frac{2}{3} }{\frac{3}{4} } =\frac{\frac{1}{3} }{x}[/tex]

Cross multiplying gives you:

[tex]\frac{2}{3}x=\frac{1}{3}*\frac{3}{4}[/tex]

The 3's on the right cancel out nicely, leaving you with

[tex]\frac{2}{3}x=\frac{1}{4}[/tex]

To solve for x, multiply both sides by 3/2:

[tex]\frac{3}{2}*\frac{2}{3}x=\frac{1}{4}*\frac{3}{2}[/tex] gives you

[tex]x=\frac{3}{8}[/tex]

That means that the road is still missing 3/8 of a mile til it's finished.  The length of the road is found by adding the 3/4 to the 3/8:

[tex]\frac{3}{4}+\frac{3}{8}=\frac{6}{8}+\frac{3}{8}=\frac{9}{8}[/tex]

So the road is a total of 1 1/8 miles long.

For b. we need to find out how much of 1 1/8 is 1 mile:

1 mile = x * 9/8 and

x = 8/9.  When 1 mile of the road is completed, that is 8/9 of the total length of the road completed.

Answer:  The length and width of the rectangle are 19 cm and 5 cm respectively.

Step-by-step explanation:  Given hat the length of a rectangle is four centimeters more than three times its width and the area of the rectangle is 95 square centimeters.

We are to find the length and width of the rectangle.

Let W and L denote the width and the length respectively of the given rectangle.

Then, according to the given information, we have

[tex]L=3W+4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

Since the area of a rectangle is the product of its length and width, so we must have

[tex]A=L\times W\\\\\Rightarrow 95=(3W+4)W\\\\\Rightarrow 3W^2+4W-95=0\\\\\Rightarrow 3W^2+19W-15W-95=0\\\\\Rightarrow W(3W+19)-5(3W+19)=0\\\\\Rightarrow (W-5)(3W+19)=0\\\\\Rightarrow W-5=0,~~~~~3W+19=0\\\\\Rightarrow W=5,~-\dfrac{19}{3}.[/tex]

Since the width of the rectangle cannot be negative, so we get

[tex]W=5~\textup{cm}.[/tex]

From equation (i), we get

[tex]L=3\times5+4=15+4=19~\textup{cm}.[/tex]

Thus, the length and width of the rectangle are 19 cm and 5 cm respectively.

The length of the rectangle is 19 and the width is 5 and it can be determined by using the formula of area of the rectangle.

The length of a certain rectangle is four centimeters more than three times its width.

If the area of the rectangle is 95 square centimeters,

The length and width of the rectangle.

Let the length of the rectangle be L,

And the width of the rectangle is W.

The length of a certain rectangle is four centimeters more than three times its width.

The perimeter formulas of different two-dimensional shapes:

Then,

[tex]\rm L = 3W+4[/tex]

And If the area of the rectangle is 95 square centimeters,

It is the number of square units inside the polygon.

The area is a two-dimensional property, which means it contains both length and width

[tex]\rm Area \ of \ the \ rectangle = length \times width\\\\L\times W = 95[/tex]

Substitute the value of L from equation 1,

[tex]\rm L\times W = 95\\\\(3W+4) \times W = 95\\\\3W^2+4W=95\\\\3W^2+4W-95=0\\\\3W^2+19W-15W-95=0\\\\W(3W+19) -5(3W+19) =0\\\\(3W+19) (W-5) =0\\\\W-5=0, \ W=5\\\\3W+19=0, \ W = \dfrac{-19}{3}[/tex]

The width of the rectangle can not be negative than W = 5.

Therefore,

The length of the rectangle is,

[tex]\rm L = 3W+4\\\\L = 3(5)+4\\\\L=15+4\\\\L=19[/tex]

Hence, The length of the rectangle is 19 and the width is 5.

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