8x-5x+21 = 36-6y

Write the equation so that y is a function of x.

Flight will reach Auckland at 11:22 am with respect to Auckland time.

We have the following given information which states as follows

A flight to Sydney to Auckland takes 3 hours and 12 minutes.

∴ Total journey time = 3hr 12min.

Auckland times is 2 hours ahead of Sydney's time.

∴ Change in time will be 2hr

The flight departed Sydney at 10:10 am

∴ Flight will reach Auckland after the journey time

∴ Flight will reach Auckland after 3hr 12min

∴ Flight will reach Auckland at 01:22 pm

But Auckland times is 2 hours ahead of Sydney's time.

∴ Change in time will be 2hr

∴ Flight will reach Auckland 2hr less than the considered reach time with respect to Sydney.

∴ Flight will reach Auckland at 11:22 am.

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When we say that the tails of the normal curve are asymptotic to the x axis, it mean the tails get closer and closer to the x axis but never touch it

The tails of normal curve are actually asymptotic. To say they are asymptotic, then it means that they approach the x axis but never quite meet its horizons.

These tails will extends indefinitely in both directions without crossing and touching the x axis or the horizontal axis.

Tails of normal curve or normal curve itself is asymptotic to the x-axis. That is the curve touches the x-axis only at -∞ and +∞. So the curve only approaches nearer and nearer to x-axis but never touches or crosses it.

For this reason, the correct choice is get closer and closer to the x-axis but never touches it.

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As shown in the reference graph attached hereby with the question statement, if the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds, then,

(A) During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.

(B) During (0 ≤ x ≤ 2) seconds, the height of the water balloon is increasing.

(C) During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.

(D) From Part (C), it can be justified that 5 ≤ x ≤ 9.5 is the interval where the balloon's height is decreasing, and, (5 ≤ x ≤ 6) is the interval where the slope is the steepest.

As per the question statement and the reference graph attached alongside, the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds.

We  are required to determine the correct time domains for four different situations, by observing the plotted graph.

Part (A) is to determine the correct time domain where the water balloon's height remains the same.

From the graph, it is clear that, the height remains constant at (y = 70), parallel to the x-axis from the 2nd second to the 5th second. Hence, During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.

Part (B) is to determine the correct time domain where the height of the water balloon is increasing.

From the graph, it is clear that, the slope of the concerned graph rises only from [(y = 40) to (y = 70)], starring from the 0th second until the 2nd second. Hence, During (0 ≤ x ≤ 2) seconds in the time domain, , the height of the water balloon is increasing.

Part (C) is to determine the correct time domain where the height of the water balloon decreases the fastest.

From the graph, it is clear that, the graph decreases thrice, first from [(y = 70) to (y = 40)], starting at the 5th second uptil the 6th second, then from [(y = 40) to (y = 10)], starting at the 6th second uptil the 9th second and lastly, from [(y = 10) to (y = 0)], starting at the 9th second till the 9.5th second. Here, we can easily calculate that, the balloon dropped 30ft in 1 sec at the first instance, 30ft in 3 seconds at the second instance and, 10ft in 0.5 seconds.

Since, [(30/1) > (10/0.5) > (30/3)],

Or, [30 > 20 > 10],

Thus, During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.

Part (D) is to determine the correct statement mentioned under it's options, with judgement based on Part (C).

Option (i) states that [(5 ≤ x ≤ 9.5) is the interval where the balloon's height is decreasing] which is true, as we can observe from the graph that the slope is decreasing during the time interval of 5 to 9.5th seconds, although at different rates at different intervals.

Option (ii) states that [(8 ≤ x ≤ 9.5) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is false, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.

Option (iii) states that, [(6 ≤ x ≤ 8) is the interval where the balloon's height decreases the most] which is false, as balloons height falls the farthest by 30fts in two separate intervals, between (5 ≤ x ≤ 6) seconds and (6 ≤ x ≤ 9) seconds.

Finally, Option (iv) states that [(5 ≤ x ≤ 6) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is true, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the maximum in the shortest time period.

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The standard form of the equation representing magazines and paperback books bought is is 6x + 3y = 54

Information given in the question include:

Eugene bought magazines for $6 each and paperback books for $3 each total of $54

Definition of variables

let the number of magazines bought be x

let the number of paperback books bought be y

The total amount paid for the magazines = $5 * x = 6x

The total amount paid for the paperback books = $3 * y = 3y

Finding the equation

Summing the amounts paid to be equal to the total amount spent which is $54 is given in the equation as written below

6x + 3y = 54

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Answer:

it says 50 points

Step-by-step explanation:

Answer:

can u give me a hint?

Step-by-step explanation:

Your profit on each model spaceship sold is; (1.2d + 1.5) dollars

We are told that the original cost of the spaceship model was d dollars. Now, you buy each kit on sale at 30% of the original price.

Thus;

Amount of each kit with the 30% of original price = 30%d = $0.3d

Total cost of each kit with shipping fee = (0.3d + 3.5) dollars

Now, he sells each model at (2.5d + 5) dollars.

Now, formula for profit is;

Profit = Selling Price - Cost Price

Profit = (2.5d + 5) -  (0.3d + 3.5)

Profit = (1.2d + 1.5) dollars

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Answer:

7

Step-by-step explanation:

(4+6+7+8+10)/5=7

the median is the middle number=7

Answer:

22

Step-by-step explanation:

Answer:

48.

Step-by-step explanation:

The sequence is

1, 3, 6, 11,

The differences are 2, 3, 5, 8, 12, 17

2nd difference            1   2  3  4   5                      

So, the next difference is 5+3 = 8 (Friday) so on that day you had 11+8 = 19 cups.

The next 2 differences are 8+4 = 12 and 12 + 5 = 17.

Saturday you had 19+12 = 31.

Sunday you had 31 + 17 = 48.

Answer:

x/x+2

Step-by-step explanation:

from numerator factor out an x to get x(x-2), in the denominator you can factor it because its a perfect square to get (x+2)(x-2)

cause there are no more add or subtract, you can cancel out x-2 to get x/x+2

Answer:

X³ -4x-2

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

x

Answer: Graph the line using the slope and y-intercept, or two points.

Slope: 3

y-intercept: (0,0)

Step-by-step explanation: Example graph for c=3p .

A mathematical phrase in which the sides are not equal is referred to as being inequal. The point (80, 35) exists in the solution space. The coach could buy 80 pull buoys and 35 kick boards.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

A mathematical phrase in which the sides are not equal exists directed  to as being inequal. In essence, a comparison of any two values reveals whether one exists less than, larger than, or equivalent to the value on the opposite side of the equation.

A) The sum of costs must not exceed the budget:

5.50x +10.00y ≤ 800

B) Let the inequality be 5.50(0) +10.00(50) = 500 ≤ 800

Yes, the coach could buy these

C) Let the inequality be 5.50(125) +10.00(25) = 937.50 > 800

No, they cost too much

D) The point (80, 35) exists in the solution space. The coach could buy 80 pull buoys and 35 kick boards.

The complete question is:

A swim coach has at most $800 to buy equipment for the swim team. Each pull buoy costs $5.50 and each kickboard costs $10. Let x represent the number of pull buoys and y represent the number of kickboards.

A) Write an inequality for the scenario

B) could the coach purchase zeros pull buoys and 50 kickboards?

C) could the coach purchase 125 pull buoys and 25 kickboards?

D) What other combination of pull buoys and kickboards works for your inequality?

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Answer:

Should be 0

Step-by-step explanation:

The side length of the square seat cushion which was given as; √65 is an irrational number.

It follows from the task content that the side length of the square seat cushion is to be determined as rational or irrational.

It follows from the definition of rational numbers that they are numbers which can be written as a ratio of quotients (fractions) while irrational numbers are the exact opposite and can not be expressed as a ratio of quotients.

Hence, since the number given √65 is not a perfect square, it follows that the number is an irrational number.

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The average temperature on Earth than the average temperature on Jupiter is greater by

225°F.

Temperature simply means the degree of hotness and coldness that can be found in a body.

Average temperature on Earth = 59°F

Average temperature on Jupiter = -166°F

Therefore, the increase will be illustrated as:

= 59 - (-166)

= 59 + 166

= 225°F

The correct option is 225°F

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The fraction 70 1/3% in simplest form is 24.67%.

Firstly converting mixed fraction to fraction. For conversion to fraction rewriting the fraction -

Fraction = (3×70 + 1)/3%

Then performing the multiplication in numerator of the fraction to find the fraction in simplest form

Fraction = (73 + 1)/3%

Performing addition in numerator of the fraction to find the fraction in simplest form

Fraction = 74/3 %

We have got the improper fraction as numerator is greater than denominator. Now performing division to find the fraction in simplest form

Fraction = 24.67%

Thus, the fraction in simplest form is 24.67%

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The mistake is at a + 7 = -11 ⇒ a = -18 and not -4.

Betsie made a mistake while solving the equation 3(a+7) = -33

We try to solve this equation step-by-step and will identify her mistake on the way.

3(a+7) = -33

Dividing by 3 on both sides,

⇒ (a+7) = -11

Subtracting 7 from both sides,

⇒ a = -11 -7

⇒ a = -18 is the solution.

Betsie made the mistake at the step where we have to subtract 7 from both sides. Instead of subtracting 7 from the right side, she added 7 on the next step.

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Total cost, 3 bottles of soda and 8 bags of chips: 9.15, Total cost, x bottles of soda and y bags of chips: 1.25x + 0.9y as calculated from the provided material through mathematical concepts.

These basic mathematics skills are addition, subtraction, multiplication, and division. Concepts included in basic math include learning shapes, patterns, fractions, decimals, percentages, exponents, ratios, scientific notation, and formulas.

The five fundamental concepts which we aim to consider briefly are those of natural number, unknown, postulate, function and group

These functions such as addition, subtraction, multiplication, and division have their application present even in the most advanced mathematical theories.

The total price can be calculated as it is equal to the unit price multiplied by the quantity.

3*1.25 + 6*0.9

= 3.75 + 5.4

= 9.15

Then if we take it as x and y, we get the equation

1.25x + 0.9y

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Step-by-step explanation:

forty-two thousand, six hundred eighty-three times seven equals blank

42683 × 7 = _____

42683 × 7 = 298781

z = [tex]\frac{13}{20}+\frac{19}{20}i[/tex] is in the form z = a+ ib, where a = 13/20 and b = 19/20

Exact value of |z| = 1.151

Argument of z = 55.6197

Consider the complex number z = (2+7i)/(6+2i)

6a. Here z is in a rational form and we need to simplify it to represent it in the form a+ ib.

Multiplying and dividing the conjugate of the denominator to z, we get,

z = [tex]\frac{2+7i}{6+2i} \times \frac{6-2i}{6-2i}[/tex]

⇒ z = [tex]\frac{12 +38i +14}{6^2+2^2}[/tex]

⇒ z = [tex]\frac{26+38i}{40}[/tex]

⇒ z = [tex]\frac{13}{20}+\frac{19}{20}i[/tex]

is in the form z = a+ ib, where a = 13/20 and b = 19/20

6b.modulus of z = |z| = √(a²+b²)

                                  = [tex]\sqrt{\frac{13^2}{20^2} +\frac{19^2}{20^2} }[/tex]

                                  = [tex]\sqrt{\frac{530}{400}}[/tex]

                                  = √(53/40)

                                  = 1.151

6c. Argument of z = tan⁻¹(b/a)

                              = tan⁻¹((19/20)/(13/20))

                              = tan⁻¹(19/13)

                              = 55.6197

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The graph of the coordinate plane is attached below.

Any point on a plane can be uniquely identified by a pair of numerical coordinates using a cartesian coordinate system, which employs signed distances between two fixed perpendicular oriented lines and the point measured in the same unit of length.

The graph of the line decreases between  (2.5, 2) and (4.5, 0.25) and the graph increases between (2.5, 2) and (4.5, 0.25)

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We can write the system of equations:

x = y + 15

x + y = 105

Solving the system, we will see that Robin has 45 apples and Linda 60 apples.

Here we can only solve the first part, as the second is incomplete.

Let's define the variables:

x = apples that Linda has.

y = apples that Robin has.

We know that Linda has 15 more apples than Robin, and that between the two there are 105 apples, so we can write the system of equations:

x = y + 15

x + y = 105

To solve this, we can replace the first equation into the second one, so we get:

(y + 15) + y = 105

2y + 15 = 105

2y = 105 - 15 = 90

y = 90/2 = 45

So Robin has 45 apples, and Linda has 15 more, so she has:

x = 45 + 15 = 60

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a) 20% 60 of  is 12

b) 25% of 24 is 6

c) 4% of 600 is 24

Here the problem we are dealing with is related to percentage, which could be a division or a proportion in which the value of the entire is continuously 100. is represented by the symbol "%".

a) let us consider the missing number to be x

so, the problem will be 20% of  x= 12

=> 20/1000* x= 12

=>20x= 12*100

=> x= 12*100/20 = 60

b) let the percentage be x

so, the problem will be x% of 24 =6

=>x/100* 24= 6

=>24x=600

=>x=600/24 =25

c)  here, we are given  4% of 600=?

=4/100* 600

=24

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Answer:

1x-5

Step-by-step explanation:

3x-(2x-5) Write equation

3x-2x-5  Open Parentheses

1x-5 Answer; This is how much it can be simplified.

An 8-inch violin string has a frequency of 640 cycles per second using the  inverse variation equation.

Given: A 16-inch violin string is known to vibrate at 320 cycles per second.

We know that,

Using the frequency equation where l for the length of the string and f for the frequency.

f = k/l

320  = k/16

k = 5120

So, the equation becomes f = k/l

For l = 8

f = 5120/8

f = 640

Therefore, the frequency of an 8-inch-long violin string is 640 cycles per second.

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The probability formula is given by:

The person selects one of six envelopes.

There is a probability that the person selects an envelope that contains a $491 of 3 envelopes OR an envelope that contains a $1003 check of 3 envelopes

Then, the expected value is given by