Just making sure if x + y is xy?

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 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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Answer:

Step-by-step explanation:

(F - 32)0.56 = 4

F - 32 = 4/0.56

F = 39.1⁰ F

Option D is correct. 73.9 percent of the workforce between the ages of 25 and 65 has achieved post-secondary educational credentials in Canada.

According to the most recent data from Statistics Canada, approximately 73.9 percent of the workforce between the ages of 25 and 65 has achieved post-secondary educational credentials in Canada. This data shows a significant increase in the number of Canadians who have pursued higher education in recent years, reflecting a trend towards increased investment in education and training as a means of achieving higher levels of skills and knowledge.

This high percentage of workers with post-secondary credentials is a positive indicator of the strength of Canada's economy, as it demonstrates a well-educated and highly skilled workforce. This, in turn, attracts investment and contributes to the growth of industries, creating new job opportunities and fostering economic prosperity.

Furthermore, the attainment of post-secondary education is associated with higher earnings and improved job prospects, both of which contribute to greater overall financial security and stability. As such, the high percentage of the workforce with post-secondary credentials in Canada is a testament to the country's commitment to education and the pursuit of economic and personal success.

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Answer:

38feet 4.4 inches. .. ..........

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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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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$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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The probability that a standard normal random variable will take a value less than 1.05 is approximately 0.8528.

Probability is a mathematical concept that quantifies the likelihood or chance of an event occurring. It is a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

To find the probability that a standard normal random variable is less than a certain value, use a standard normal table or use a calculator with a cumulative distribution function (CDF) for the standard normal distribution.

Look up that value in the standard normal table and find the corresponding cumulative probability.

Hence, p(z < 1.05) = 0.8528.

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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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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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The lowest energy  and highest energy conformations of 1-chloropropane is as follow

Cl-CH2-CH2-CH3.

For better visualize different conformations of a given molecule,

A drawing convention is convenient to use called the Newman projection.

In a Newman projection,

we look lengthwise down a specific bond of interest – the carbon-carbon bond in ethane.

We depicted the front atom as a dot, and the ‘back’ atom as a larger circle.

the C-C bond in this way, the angle formed between a C-H bond on the front carbon and a C-H bond on the back carbon

carbon is referred to as a dihedral angle.

1-chloropropane. molecular formula  is C3H7Cl

The lowest energy  and highest energy conformations of 1-chloropropane is as follow

Cl-CH2-CH2-CH3.

Cl would be the largest substituent for Carbon 1, and CH3 would be the largest substituent for Carbon 2,

so I would put them opposite from each other on the projection.

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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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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

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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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 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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The position s(t) of the ant at time t is s(t) = 3/(t²+31)^1/2 + 15 - 3/√31

The velocity of an ant moving along the t-axis is given as

                         v(t) = - 3t/(31 + t^2)^3/2

Now, the distance travelled by the ant at time t is :

                         s(t) = -∫3t/(31 + t^2)^3/2 dt

Put t = √31 tanθ

     dt = √31 sec²θ dθ

                         s(t) = -∫3t/(31 + t^2)^3/2 dt

                               = -∫(3√31 tanθ/(31 + 31 tan²θ)^3/2) √31 sec²θ dθ

                               = -93∫ tanθsec²θ/(31 sec²θ)^3/2  dθ

                               = -3/√31∫ tanθ sec²θ/sec³θ  dθ

                               = -3/√31∫ tanθ / secθ  dθ

                               = -3/√31∫ sinθ  dθ

                               = (3/√31) cosθ  + c

we took t = √31 tanθ or tanθ= t/√31

So, cosθ = (31/t²+31)^1/2

                   ∴  s(t)  = (3/√31) (31/t²+31)^1/2  + c

                       s(t)  = 3/(t²+31)^1/2  + c

At t = 0, s = 15

So, s(0) = 3/(0²+31)^1/2  + c

       15 = 3/√31 + c

         c = 15 - 3/√31

Hence, s(t) at time t is s(t) = 3/(t²+31)^1/2 + 15 - 3/√31

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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 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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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 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

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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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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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:

13 people wouldn't have electricity

Step-by-step explanation:

Ratio of people with electricity to people without electricity is 8,000,000,000 : 1,000,000,000 or 8:1

8:1 = 100:x  We need to find x.  To do this, divide 100 by 8.

100/8 = 12.5

Then multiply the other side of the ratio (1) by that number.

12.5 · 1 = 12.5

Out of 100 people in a village 12.5 of them don't have electricity.  (You can't have half of a person so you round it to 13.)

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.

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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