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The values for the  quadratic equation,

x₁ + x₂ = -5 and x₁ × x₂ = 3.

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. They are also known as quadratic equations.

Given equation,

3x² + 15x + 9 = 0

and given x₁ and x₂ are the solution of the equation or roots or zeros of the equation.

for any quadratic equation, the sum of the roots is equal to the -b/a

here x₁ + x₂ = -15/3 = -5

and the product of the roots is equal to the product of c/a

x₁ × x₂ = 9/3

x₁ × x₂ = 3

Hence x₁ + x₂ = -5,

x₁ × x₂ = 3.

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Answer:

Answer: 24.5

Step-by-step explanation:

The geometric mean between 24 and 25 is about 24.49.

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Mean = Sum of observations/the number of observations

Median represents the middle value of the given data when arranged in a particular order.

We are given that;

The numbers 24 and 25

Now,

To find the geometric mean between two numbers, we need to use the formula:

Geometric mean=ab​

where a and b are the two numbers.

Since we have 24 and 25 as the two numbers, we can plug them into the formula and get:

geometric mean=24×25​=600​≈24.49

Therefore, by the mean the answer will be 24.49.

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The simplified form of the expression of the square root [tex]\sqrt{20x^8}[/tex] is [tex]2\sqrt{5}x^4[/tex].

A square root of a number x in math is a number y such that y² = x. In other words, a square root  is the factor that we can multiply by itself to get that number. The symbol of square root is called a radix or a radical sign "√".

We're given a square root of an algebraic term. And, we're asked to simplify the square root so that the perfect square is removed from inside the square root, assuming that x is positive. We can find the simplified form of the square root as follows:

[tex]\sqrt{20x^8}=\sqrt{4\cdot 5x^8}=\sqrt{2^2\cdot 5x^8}}=\sqrt{2^2}\cdot \sqrt{x^8}\cdot \sqrt{5}=\2x^4\sqrt{5}=2\sqrt{5}x^4[/tex]

We have confirmed that [tex]2\sqrt{5}x^4[/tex] is indeed the simplified form of [tex]\sqrt{20x^8}[/tex].

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Answer:

1: x = 5

4 x 5 = 20

20 + 10 = 30

2:

x = 7

4 x 7 = 28

28 - 8 = 20

Answer: 4x+10=30              4x-8=20

10-10=                                8+(-8)=0

30-10=20                           20+ 8= 28

4x=20                                 4x=28

4/4=1                                    4/4=1

20/4=5                                 28/4=7

x=5                                     x=7

Step-by-step explanation: Hope this helps!! :))

Answer:

(-32c+3)/15

Step-by-step explanation:

(c+1)/5-7c/3 =

= (3×(c+1) -5×7c)/15 =

= (3c+3-35c)/15 =

=( -32c+3)/15

The trigonometric ratios for sine and tangent, where arctan(√3/3) is β, indicates that we get;

α = 60°, β = 30°, h = √3, k = 3, and r = 2·√3

Trigonometric ratios expresses the relationship between an interior angle and two of the sides of a right triangle.

The details of the question are;

arctan(√3/3) = Angle β

The trigonometric ratio for tangent indicates that we get;

tan(β) = h/k

Therefore, arctan(h/k) = β

However, arctan(√3/3) = β

The comparison of the above two equations indicates that we get;

h/k = √3/3

Therefore, if h = √3, k = 3

tan(α) = k/h

Therefore, tan(α) = 3/√3 = √3

r = √(h² + k²)

r = √(3 + 9) = √(12) = 2·√3

sin(β) = h/r

Therefore, sin(β) = √3/(2·√3) = 1/2

β = arcsin(1/2) = 30°

The specified triangle is a right triangle, therefore;

α + β = 90°

α = 90° - β

α = 90° - 30° = 60°

α = 60°

Therefore, α = 60°, β = 30°, h = √3, k = 3, r = 2·√3

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The angle where the tangent intersect is as follows:

m∠L = 55 degrees.

A line that touches the circle at a single point is known as a tangent to a circle.

Therefore, the measure of the angle formed by the intersection of tangents is equals to half the difference of the intercepted arcs.

Hence,

m∠L = 1 / 2 (235 - (360 - 235))

m∠L = 1 / 2 (235 - 125)

m∠L = 1 / 2 × 110

m∠L =  55 degrees

Therefore, the measure of the angle formed by the intersection of the tangent is 55 degrees.

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Meeting the quilting group has helped Jada to realize that her friends are not the only people who understand her, and that there are other people in the world who share her interests and struggles.

Meeting is a gathering of two or more people to discuss a certain matter of common interest. It can be held in a physical or virtual space. The purpose of a meeting is usually to come up with a consensus on a certain topic, to resolve an issue, to discuss the progress of a project, or to make a decision. Meetings can be formal or informal and can take place in a variety of settings, such as a conference room, a boardroom, or even online. During a meeting, participants should be able to engage in a productive dialogue. The participants should also be able to listen to each other and exchange ideas.

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The equation of the diagonal BD is 2x - 3y + 9 = 0

We have the following parameters

Equation of AC = 3x + 2y - 7 = 0

Coordinate of B = (3, 5)

Make y the subject in the equation

So, we have

y = -3/2x + 7/2

The diagonals BD and AC are perpendicular

This means that

Slope of BD = -1/slope of AC

So, we have

m = 2/3

The equation is then calculated as

y = mx + c

This gives

y = 2/3x + c

Introduce the points

5 = 2/3 * 3 + c

Evaluate

c = 3

So, we have

y = 2/3x + 3

Rewrite as

3y = 2x + 9

This gives

2x - 3y + 9 = 0

Hence, the equation is 2x - 3y + 9 = 0

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The probability that a student has a GPA under 2.0 given that he has skipped many classes is 8/11.

From the table we see that,

The student who have a GPA under 2.0 = 80

The student who has skipped many classes = 80 + 25 + 5

The student who has skipped many classes = 110

Hence, the probability that a student has a GPA under 2.0 given that he has skipped many classes = The student who have a GPA under 2.0/The student who has skipped many classes

The probability that a student has a GPA under 2.0 given that he has skipped many classes = 80/110

The probability that a student has a GPA under 2.0 given that he has skipped many classes = 8/11

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The complete question is:

One thousand students at a city high school were classified both according to GPA and whether or not they consistently skipped classes.

What is the probability that a student has a GPA under 2.0 given that he has skipped many classes?

A. 0.080

B. 0.281

C. 0.285

D. 0.314

E. 0.727

Nicole's daily salary is $116.67.

The formula for Hourly pay is defined as:

Hour Pay = Month Salary ÷ Hours Per Month.

The formula for Dialy pay is defined as:

Daily Pay = Hour Pay x Hours Per Day.

let $x be Nicole's daily salary. From the given information x can be determined as:

24% of x=28

24*1/100*x=28

Multiplying 100 on both sides.

24*1/100*x*100=28*100

24*x=28*100

Divide 24 into both sides.

24*x/24=28*100/24

By solving we get x value:

x=116.67

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The drums of sealant will be needed if each drum covers 150 sa yd are 5.

The total area of the four driveways is 84.8 sq yd + 124.1 sq yd + 98.9 sq yd + 344.7 sq yd = 652.5 sq yd.

So, the number of drums of sealant needed is given by the total area divided by the area covered by each drum:

652.5 sq yd / 150 sq yd/drum = 4.35 drums (rounded up to the nearest whole number, 5 drums will be needed).

Therefore, 5 drums of sealant will be needed if each drum covers 150 sa yd.

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Answer:

Probability of getting a:

Teddy bear = 0.25

Turtle = 0.5

Monkey = 0.25

Step-by-step explanation:

The probability of getting one teddy bear , would be the number of teddy bears over the total number of animals, so 2/8, which is 1/4, in decimals 0.25

The probability of getting one turtle , would be the number of turtles over the total number of animals, so 4/8, which is 1/2, in decimals 0.5

The probability of getting one monkey , would be the number of monkeys over the total number of animals, so 2/8, which is 1/4, in decimals 0.25

The value of y in the given ordered pair is 30.

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Given that, the rate of change at which the water level rise is 15/4 cm/minute.

Hence, the slope of the line is 13/6.

Taking x to represent the time in minutes and y to represent the rise in cm then,

Therefore,

4 minutes = 15 cm

So, in 1 minute, the rise is 15/4 cm

Thus, in 8 minutes, the rise will be ;

= 30 cm

Therefore, (x, y) will be (8, 30)

Finding the slope of the line using point (8, 30) and (x, y)

m = y₂-y₁ / x₂-x₁

m = 15 - x / 4 - y

m = 15/4

The rate of change at which the water level rises equals the slope of the line. This is the justification.

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The response to the above question regarding the dot plot is as follows:

Dot plot is is a statistical chart consisting of data points plotted on a fairly simple scale, typically using filled in circles.

The plot groups the data as little as possible and the identity of an individual observation is not lost. A dot plot uses dots to show where the data values (or scores) in a distribution are.

According to this question, a teacher puts all her students' quiz on the dot plot above. Based on the dot plot graph, the corresponding answers to the above attached questions is as illustrated in the main answer part.

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As the given interval is a half-open interval, it is a closed interval. So, the extreme value theorem is not applicable and the correct option is B) The domain of f is not a closed and bounded interval.

We are given f(x) = x sinx

Let us first take x in f(x).

In the question, the domain of f(x) is [0, ∞) which means x ∈ [0, ∞).

Hence, the range of x is also [0, ∞)

Now, let us take sinx.

The range of sin x is [-1, 1] for all x ∈ R.

For x ∈ [0, ∞), the range of sinx will remain. [-1, 1]

Hence, we can conclude that the range of f(x) is (-∞, ∞) and its domain is [0, ∞)

Therefore, it can be concluded that the domain of f is not a closed and bounded interval.

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by definition a capable process is one that is operating at the so called  capability sigma level

The statistical difference between a process operating at a 5 sigma level and a process operating at a 6 sigma level is markedly different when it comes to the number of defects present, which is a true statement because as we know process sigma indicates the process variation and is measured in terms of data units, while process sigma count Z, or process sigma level, is a count with no unit of measure and sigma is a statistical term that measures how much a process varies from perfection, based on the number of defects per million units. And also we know that a six sigma process is 1 in which 99.99966 percent of all chances to provide some characteristics of a part are statistically assumed to be free regarding defects.

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In this case, the integrand is evaluated at the bounds of the integral, both integrals.

We can make the substitution u = cos(t) and du = -sin(t) dt.

The integral becomes: ∫0 ecos(t)sin(2t) dt = -∫0 eu * sin(2arcsin(u)) du

Now we can use integration by parts, letting dv = eu and u = sin(2arcsin(u)), so v = -e * arcsin(u).

The integral becomes: ∫0 ecos(t)sin(2t) dt = [-e * arcsin(u) * sin(2arcsin(u))]0 - ∫0 e * arcsin(u) * cos(2arcsin(u)) du

Using the identity sin(2θ) = 2sin(θ)cos(θ), we can simplify the first term to:

∫0 ecos(t)sin(2t) dt = [2e * arcsin(u) * sin(arcsin(u))cos(arcsin(u))]0 - ∫0 e * arcsin(u) * cos(2arcsin(u)) du

Since u = cos(t), we can write the first term as: ∫0 ecos(t)sin(2t) dt = [2e * arcsin(cos(t)) * sin(t)cos(t)]0 - ∫0 e * arcsin(cos(t)) * cos(2arcsin(cos(t))) du

The first term is equal to 0 since it is evaluated at the bounds of the integral. The second term can be simplified using the identity cos(2θ) = cos^2(θ) - sin²(θ), so: ∫0 ecos(t)sin(2t) dt = -∫0 e * arcsin(cos(t)) * (cos^2(arcsin(cos(t))) - sin^2(arcsin(cos(t)))) du

Using the trigonometric identities sin^2(θ) + cos²(θ) = 1 and cos²(θ) = 1 - sin²(θ), we can simplify the integrand to: ∫0 ecos(t)sin(2t) dt = -∫0 e * arcsin(cos(t)) * (1 - 2sin²(arcsin(cos(t)))) du

Since the integrand is separable, we can rewrite it as: ∫0 ecos(t)sin(2t) dt = -∫0 e * arcsin(cos(t))du - 2∫0 e * sin²(arcsin(cos(t))) du

The first integral is straightforward to evaluate, giving us:

∫0 ecos(t)sin(2t) dt = -e * arcsin(cos(t)) |0

The second integral is a bit more complicated, but we can use the identity sin²(θ) = (1 - cos(2θ)) / 2, so:

∫0 ecos(t)sin(2t) dt = -e * arcsin(cos(t)) |0 - e * (1 - cos(2arcsin(cos(t)))) / 2 |0

Thus, the integrand is evaluated at the bounds of the integral, both integrals.

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PICTURE 1: the value of h is 8√2 units

PICTURE 2: the angle measures of the triangle are 30,60,90

PICTURE 3: x = 5√2 units

PICTURE 4: x = 5√3 units

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

PICTURE 1

sin 45° = 8/h

h =  8/sin 45°

h = 8√2 units

PICTURE 2

We have a 90° there already (the box)

Let the unknown angles be x and y respectively

sin x = 6/12

sinx = 1/2

x = arcsin (1/2)

x = 30°

y = 90 - 30 = 60°

Thus, the angle measures of the triangle are 30,60,90

PICTURE 3

sin 45 = x/10

x = 10 sin 45

x = 5√2 units

PICTURE 4

tan 30 = x/15

x = 15 tan 30

x = 5√3 units

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Answer:12

Step-by-step explanation:

When x = 2, y = 3(2^2) = 3(4) = 12. So the value of y when x = 2 is 12.

$2,444.44 was invested in the 7.5% bond and $20,555.56 was invested in the 13% bond.

Let x be the amount invested in the 7.5% bond

(23,000 - x) be the amount invested in the 13% bond.

The interest earned by 7.5% bond = (7.5/100) * x = 0.075x.

The interest earned by 13% bond = (13/100) * (23,000 - x) = 0.13 * (23,000 - x).

The total interest earned on both investments = 0.075x + 0.13 * (23,000 - x) = 2,880.

We can solve for x by substituting 0.075x + 0.13 * (23,000 - x) = 2,880 and solving for x.

0.075x + 0.13 * 23,000 - 0.13x = 2,880

0.045x = 2,880 - 0.13 * 23,000

0.045x = 2,880 - 2,990

0.045x = -110

x = -110 / 0.045 = 2,444.44 (rounded to two decimal places)

So, x = $2,444.44 was invested in the 7.5% bond and (23,000 - $2,444.44) = $20,555.56 was invested in the 13% bond.

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We got 1 blue and 4 green packs. The solution has been obtained by using the linear equation.

What is a linear equation?

A linear equation has the degree of one that is highest. It follows that a linear equation with an exponent greater than one cannot have any variables. This equation results in a straight line on the graph.

Let the pack of blue cards be 'x' and pack of green cards be 'y'.

We are given that the blue cards came in packs of 5 and the green cards came in packs of 6 and in total we had 29 cards.

So, from this we get

5x + 6y = 29   ...(1)

Also, it is given that we have total of 5 packs,

So,

x + y = 5   ...(2)

From (2), we get

x = 5 - y

Substituting this value in (1), we get,

⇒5(5-y) + 6y = 29

⇒25 - 5y + 6y = 29

⇒25 + y = 29

⇒y = 4

So, x = 5-4 = 1

Hence, we got 1 blue and 4 green packs.

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The definition of percent helps you write fraction and decimal equivalents by understanding that "per cent" means "per hundred".

For example, if you are asked to write the fraction and decimal equivalent of 25%, you would divide 25 by 100 to get the fractional equivalent of ¼, and divide 25 by 100 to get the decimal equivalent of 0.25.

The decimal equivalent of a fraction or percentage is the numerical value expressed in decimal form. For example, the decimal equivalent of 1/2 is 0.5 and the decimal equivalent of 25% is 0.25. Decimal equivalents are useful for calculations and can be used to convert fractions and percentages into decimal form.

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The errors in the equations are given as follows:

a. We should multiply the constants 4 and 3, not add them, hence the result would be 12a^7.

b. The exponent one was forgotten, hence the correct result is of x^(6 + 1 + 3) = x^10.

c. The terms have different bases, hence the exponents cannot be added.

When two terms with the same base and different exponents are multiplied, we must keep the bases and then add the exponents.

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The above question, we may conclude that 50% of the data values are more than 45. This conclusion was reached utilizing the box-whisker plot approach.

In a box-whisker plot, as seen in the illustration, The minimum, first quartile, median, third quartile, and maximum quartiles are shown by a rectangular box with two lines and a vertical mark. In descriptive statistics, it is employed.

In light of the above, the box-whisker plot reflects a particular data set. In this case, 45 is the 50th percentile, meaning that 50% of the values are larger than 45 and 50% of the values are greater than 45. There is a number 45 right next to it, and a vertical line next to it indicates that 45 is the median of the data.

Using this technique, we can easily determine the proportion of data for which the value is higher or lower. It aids in data analysis and result interpretation. Therefore, 50% values exceed 45.

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After 2.94 Hr. or approximately 3 Hr. both cars will be 250 miles apart.

We have,

The value of the speed of the car moving in the north direction =35 mph

The value of the speed of the car moving in the south direction=50 mph

From above, we can conclude that both are going in the opposite direction

So, the value of the net speed/ relative speed of both the car will be =35+50=85 mph

As we know,

The value of distance can be determined by using the relationship:

Distance = speed * time

So, for determining the value of time, we will put the value of total distance covered and the value of relative speed in the above expression.

Thus, we will get it as:

250=85*t

So, the value of the time taken = t=250/85=2.94 hours approx 3 hours

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The complete question should be like:

Two cars leave the origin; one goes north at 35mph and the other goes south at 50 mph. After how many hours will they be 250 miles apart?

The height of the cylinder is 5 m.

The surface area of a cylinder is [tex]28 \pi m^{2}[/tex].

The total surface area of a cylinder is equal to the sum of the areas of all its faces. The total surface area with radius ‘r’, and height ‘h’ is equal to the sum of the curved area and circular areas of the cylinder.

Let's call the height of the cylinder "h". The surface area of a cylinder can be calculated as

Where r is the radius of the base.

Since the diameter of the base is 4 meters, the radius is 4/2 = 2 meters.

We know the surface area of the cylinder is [tex]28 \pi m^{2}[/tex], so we can use this information to find h:

⇒[tex]28 \pi = 2 \pi(2)h + 2 \pi(2)^{2}[/tex]

Expanding and simplifying the equation:

⇒28π = 4πh + 8π

Subtracting 8π from both sides:

⇒20π = 4πh

Dividing both sides by 4π:

⇒h = 5

Therefore, the height of the cylinder is 5 meters.

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The probability that neither of the 3 bits is recovered successfully is 8/729.

Each bit is transmitted over the channel with a success probability of 1/3 and a failure probability of 2/3. The success and failure of each bit are independent, meaning that the success of one bit does not affect the success of another bit.

The probability of successfully recovering all 3 bits is (1/3) * (1/3) * (1/3) = 1/27.

Similarly, the probability of failing to recover all 3 bits is (2/3) * (2/3) * (2/3) = (8/9)^3 = 8/729.

This means that there is a 8/729 chance that the transmission of all 3 bits will fail.

So, the probability that neither of the 3 bits is recovered successfully (the probability of 3 failures) is 8/729.

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The value of the equation is A = 10 1/10

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first fraction be p = 7 3/5

p = 38/5

Let the second fraction be q = 2 1/2

q = 5/2

Substituting the values in the equation , we get

A = p + q

A = 38/5 + 5/2

A = ( 76 + 25 ) / 10

On simplifying the equation , we get

A = 101 / 10

A = 10 1/10

Therefore , the value of A is 10.1

Hence , the equation is A = 10 1/10

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