Height in meters 15 30 45 60 75 90 105 Distance in kilometers 13.833 19.562 23.959 27.665 30.931 33.833 36.598 1. Determine a function that could be used to model the data in the table. Make sure to use h for height and d for distance.

The drink contains 56mg of the vitamin while RDA is only 40mg.

The SI unit of mass, the kilogramme, is 1000,000,000 times larger than the milligramme (mg), which is a unit of mass. Using a lowercase m and lowercase g, a milligramme is abbreviated as mg.

There are 1000 milligrammes in a gramme, hence the use of the prefix milli to denote the thousandth.

There are 10-6 kilogrammes in a milligramme. When describing drug doses, milligrammes are frequently used.

We have to count 140​% of the RDA to find the how much vitamins its contains.

Here, RDA = 40mg

140​% × 40

140/100 × 40

1.4  × 40

56mg

Thus, the drink contains 56mg of the vitamin while RDA is only 40mg.

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Option -  C and D : -4.5c > 9 and -215 ≤ -52d  will have its inequalities that have symbols that will be reversed when the variable is isolated .

Anytime you are multiplying or dividing an inequality by a negative you must reverse the inequality symbol .

Inequalities in mathematics specify the connection between two non-equal quantities. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. However, a variety of inequalities are employed to compare the values, whether they are less than or more than.

The different inequality symbols, properties, and methods for resolving linear inequalities in one variable and two variables will all be covered in this article along with examples. "A connection is called an inequality if two real numbers or algebraic expressions are connected by the symbols ">,",“<”, “≥”, “≤”,  An inequality statement in algebra uses the inequality symbol to illustrate the relationship between two expressions.

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The sum of numbers at B, C, D, E and F is 110.5

Since B, C, D, E, and F divide the segment AG into 6 equal pieces, each piece has a length of (59-13)/6 = 6.5.

Therefore, the numbers at B, C, D, E, and F are located at 13 + 6.5, 13 + 6.52, 13 + 6.53, 13 + 6.54, and 13 + 6.55 respectively.

The sum of the numbers at B, C, D, E and F is (13 + 6.5) + (13 + 6.52) + (13 + 6.53) + (13 + 6.54) + (13 + 6.55)

= 13 + 6.5*(1+2+3+4+5) = 13 + 6.5*15 = 13 + 97.5

= 110.5

In Maths, number lines are the horizontal straight lines in which the integers are placed in equal intervals. All the numbers in a sequence can be represented in a number line. This line extends indefinitely at both ends.

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The standard equation of hyperbola centered at the origin with the given values is  x^2 / 49  - y^2 / 100 = 1 .

What is Hyperbola ?

a plane curve generated by a factor so moving that the difference of the distances from two constant points is a consistent : a curve formed by way of the intersection of a double right circular cone with a plane that cuts each halves of the cone.

Given,

The standard equation of the hyperbola centered at the origin with given values a=7 and b=10 .

[(x2 / a2) – (y2 / b2)] = 1.

vertical axis with values a = 7 and b=10 .

[(x2 / a2) – (y2 / b2)] = 1.

(x^2 / 7*7)  -  ( y^2/ 10*10)  = 1

x^2 / 49  - y^2 / 100 = 1

Hence , the standard equation of hyperbola centered at the origin with the given values is x^2 / 49  - y^2 / 100 = 1 .

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The first 4 terms and the 10th term of the sequences are listed below

From the question, we have the following parameters that can be used in our computation:

Calculate the first 4 terms and the 10th term.

A)n^2+6

Here, we have

First = 1^2 + 6 = 7

Second = 2^2 + 6 = 10

Third = 3^2 + 6 = 15

Fourth = 4^2 + 6 = 24

Tenth = 10^2 + 6 = 106

B)3n^2

Here, we have

First = 3 * 1^2 = 3

Second = 3 * 2^2 = 12

Third = 3 * 3^2 = 27

Fourth = 3 * 4^2 = 48

Tenth = 3 * 10^2 = 300

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Answer:

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Part A :

If a function is linear, then the function values have equal differences.

If a function is exponential, the function values have equal ratios.

For car 1 :

36450 / 40,500 = 9/10

32805 / 36450 = 9/10

Values of car have equal ratios.

This is exponential function.

For car 2 :

39000 - 42000 = -3000

36000 - 39000 = -3000

Values of car have equal differences

This is linear function.

Part B :

The initial value of car is 45,000.

For car 1 :

f(1) = 40,500, f(2) = 36,450, ............

For car 2 :

f(1) = 42,000, f(2) = 39,000, ..........

Part C :

For car 1 :

f(13) =   = 11438.396

For car 2 :

f(13) =  = 6000

There is a significant difference in the values of the car after 13 years. The value of the car 1 is greater.

Hence the value of the car 1 is described by an exponential function and that of car 2 by linear function. The value of car 1 is greater after 13 years.

Step-by-step explanation:

There are 7 oak trees and 4 maple trees in the community park, so the ratio of oak trees to maple trees can be written as 7:4.

What is ratio?

A ratio is a way of comparing two or more quantities. It is a way of expressing the relationship between two numbers in terms of their size. A ratio can be written in different ways, such as in the form of a fraction, as a decimal, or as a whole number.

We can also write the ratio in different ways, such as:

7/4 = 1.75 oak trees for every 1 maple tree

35:20 = 35 oak trees for every 20 maple trees

14:8 = 14 oak trees for every 8 maple trees

All of these ratios represent the same proportion, which is 7 oak trees to 4 maple trees.

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An expression that represents how much more Elena spent than Taniy is 4.3 + p.

Assuming the variable p, represents the price, in dollars, per pound of cherries, the amount of money Elena spent in buying a watermelon for $6.75 and 3 pounds of cherries is given by:

Elena = 3p + 6.75.

For the amount of money Taniy spent in buying a pineapple for $2.45 and 2 pounds of cherries is given by:

Taniy = 2p + 2.45

For the difference, we have:

Elena's cost = 3p + 6.75 - (2p + 2.45)

Elena's cost = 3p + 6.75 - 2p - 2.45

Elena's cost = 4.3 + p

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Answer:

2a + 16

2(3) + 16

6 + 16 = 22

3b

3(-2) = -6

Step-by-step explanation:

Substitue the appropriate values into the expressions.

The quadratic equation is x²+10x+26=0

A quadratic equation can be written in the standard form as ax2 + bx + c = 0, where a, b, c are constants and x is the variable. The values of x that satisfy the equation are called solutions of the equation, and a quadratic equation has at most two solutions.

Given here: Complex root of a quadratic equation is 5+i

And we know that complex roots always occur in pairs.

Thus the other root must be its conjugate as 5+i

The sum of roots will be given by 5+i+5-i=10

and product of the roots is given by (5+i) (5-i)=25-(-1)

                                                                           =26

∴ The quadratic equation is x²+10x+26=0

Hence, The roots are 5+i , 5-i

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The probability that he'll use both the bus and the train is 0.2222

What is probability and example?

Probability = the number of ways of achieving success. the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .

There are just two ways in which Justin use both the bus and the train on the same day:

1. He used bus in the morning and train in the evening

2. He used train in the morning and bus in the evening

Additionally, every day he has 9 possible ways to used the transportation, 3 in the morning multiply by 3 in the evening. This is:

       3         *         3           =  9

p= 0.222

So, the probability is calculate as a division between the possible ways in which he use both transportations and the total possible ways. This is:

p=0.222

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The measure of ∠ ​ABC is 112°

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a shape with its angles.

Triangle BCD is an equilateral triangle. So all the angles are equal, that is 60° each.

∠ ​ADB = 64° (base angle of an isosceles triangle are equal)

∠ ​ABD = 180° - 64° - 64° (sum of angles in a triangle is 180°)

∠ ​ABD = 52°

∠ ​ABC = ∠ ​ABD + ∠ ​CBD

∠ ​ABC = 52° + 60°

∠ ​ABC = 112°

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Step-by-step explanation:

a0 = 0 ft (starting on the ground)

a1 = a0 + 3 - 1 = a0 + 2

an = an-1 + 3 - 1 if an-1 +3 < 15

an = an-1 + 3 if an-1 + 3 >= 15

so, we need to find the n, so that

an = an-1 + 2 >= 12

but by looking at the structure, we see that every step just adds 2 ft to the total height.

an = a0 + 2n = 0 + 2n = 2n

2n >= 12

n >= 6

so, with day 6 the bug reaches 12 ft height. in day 7 it gets up to 15 ft and reached its goal.

it will take 7 days for the bug to reach the top and get the food.

By 2228 ways i can select the team to have more girls than boys

We have, total number of boys = 6, while the total number of girls = 8

Total size of team = 6

Condition given: In every case the total number of girls should be more than the total number of boys.

As for that we can choose the team like

(6G, 0B) + (5G, 1B) + (4G, 2B)

Making the combination as per above arrangements:

We will get it as:

=8C6*6C0+8C5*6C1+8C4*6C2

As we know,

The formula of combination is:

[tex]$${ }_n C_r=\frac{n !}{r !(n-r) !}$$[/tex]

[tex]${ }_n C_r=$[/tex] number of combinations

n= total number of objects in the set

r= number of choosing objects from the set

So, applying the concept of combination in the above,

So, from above we can write it as:

8C6*6C0+8C5*6C1+8C4*6C2

=[tex][\frac{8!}{6! \times 2!}\times \frac{6!}{6!\times 0!}]+[\frac{8!}{5!\times 3!}\times \frac{6!}{5!\times 1}]+[\frac{8!}{4!\times 4!}\times \frac{6!}{2!\times 4!}]\\\\[/tex]

[tex][\frac{8 \times7\times6! }{6!\times2} \times \frac{1}{1}]+[\frac{8\times7\times6\times5!}{5!} \times \frac{6\times5!}{5!}]+[\frac{8\times7\times6\times5\times4!}{4!\times24} \times \frac{6\times5\times4!}{4!\times2}][/tex]

[28*1]+[336*6]+[70*2]

=28+2016+140

=2228

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The cloud can ascend 9,616 metres in 17.5 minutes, based on the statement made.

Utilizing the measurement of air pressure, altitude may be calculated. The pressure decreases with increasing altitude. An instrument is referred to as a pressure analyzer or pneumatic altimeter when a barometer is given a nonlinear calibration to display altitude.

This may be calculated by dividing the cloud's speed (552 metres per minutes) by the distance it must travel (17.5 minutes). We now know the distance to be 9,616 meters.

The speed of said cloud and the length of time it is going are four pieces of information that must be known in order to determine the minimum distance the cloud might cover in 17.5 minutes. We must increase the cloud's stated speed of 552 meters a minute by the distance it is going across, which in itself is 17.5 minutes. As a result, we now have 9,616 meters overall.

Another way to see this is to picture the cloud beginning at place A (9,200 meters) or terminating at point B. (9,616 meters). The distance between points A and B will be covered in 17.5 minutes if the cloud is moving at a pace of 552 meters per minute.

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So, the teacher can give out the jerseys in 840 ways.

The teacher wants to divide the 12 students into 3 teams, each with at least one girl and one boy.

One possible way to count the number of ways to divide the students is to use the stars and bars method.

For the first team, we have 5 stars and 2 bars, so the number of ways to pick 6 students is:

(5+2)!/(5!2!) = 7

For the second team, we have 4 stars and 1 bar, so the number of ways to pick 6 students is:

(4+1)!/(4!1!) = 5

For the third team, we have 3 stars, so the number of ways to pick 6 students is:

(3+0)!/(3!0!) = 4

Then we can multiply the number of ways to pick students for each team together to find the total number of ways to divide the students:

7 * 5 * 4 = 140

Then, as the jerseys are indistinguishable, we just have to multiply the number of ways to divide the students by the number of ways to distribute jerseys:

140 * 3! = 840

Therefore, the teacher can give out the jerseys in 840 ways.

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A combination chart can be made up of the area, bar, column, dot, and line charts.

Bar charts are one of the most common data visualizations. Each data series can be represented by a different type of chart. They are all then displayed simultaneously on the same chart.

Adding a chart type that displays over another chart type can give you an immediate comparison of two or more data series over a dimension such as time.

Combination charts enable you to compare different series of data through different types of charts on the same axes simultaneously. This is useful for visualizing large quantities of data in varied formats.

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The equation to determine how many bags Trisha brought is: T = 180 - (4 + 6)

We know that the total number of clementines is 180, Sal brought 4 bags and Joe brought 6. To determine how many bags Trisha brought, we need to determine the total number of bags that Sal and Joe brought together. We can do this by combining the two numbers together (4 + 6). This will give us a total of 10 bags. To determine how many bags Trisha brought, we need to subtract the total number of bags that Sal and Joe brought (10) from the total number of clementines (180). This gives us an answer of 170. This means that Trisha brought 170 clementines, or 7 bags. Therefore, the equation to determine how many bags Trisha brought is: T = 180 - (4 + 6).

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Answer:

B is the answer

Step-by-step explanation:

A multiplicative relationship means that 2 quantities can be expressed as multiples of each other

If the owner of a pet food store wants to mix birdseed that cost $1.25 per pound with sunflower seeds that cost $0.75 . The number of pounds of each type of sea he should use is: 25 pounds of $1.25 birdseed and 25 pounds of $.75 sunflower seed.

Let x represent the number of  pounds of $1.25 birdseed that is is used

1.25x+.75(50-x)=50×1

1.25x+37.5-.75x=50

Combine like terms

.50x=50-37.5

.50x=12.5

Divide both side by .50x

x=12.5/.5

x=25 pounds of $1.25 birdseed

So,

50-25=25 pounds of $.75 sunflower seed

Therefore the number of pounds is $1.25 birdseed and $.75 sunflower.

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Answer:

16x20

Step-by-step explanation:

I think, 200% likely means x2. Just an idea, try it if you'd like!

El número natural 169 tiene como raíz cuadrada igual a 13.

Los números naturales comprenden a un conjunto discreto conformado por los números {1, 2, 3, 4, 5, ..., n, ...}, n ∈ N, donde N es el conjunto de los números naturales.

Los números naturales pueden ser números primos o números compuestos, los números compuestos pueden ser definidos como un producto de números primos. El número natural 169 es equivalente al siguiente producto de números primos:

169 = 13 × 13 = 13²

En consecuecia, la raíz cuadrada del número natural 169 es la siguiente: (nótese que la potencia al cuadrado es el opuesto a la raíz cuadrada)

x = √169

x = √(13²)

x = (13²)^(1 / 2)

x = 13

La raíz cuadrada del número natural 169 es igual a 13.

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Answer:

567 minutes each month.

Step-by-step explanation:

Let x be the number of minutes of talk time used each month.

The cost for talk time beyond 500 minutes is $0.08 * (x - 500)

The cost for email is $27.70 * 0.3 = $8.31

The total monthly cost is $27.70 + $0.08 * (x - 500) + $8.31 = $35.99

The total cost for 9 months is $35.99 * 9 = $323.91

So we can set up the equation:

$27.70 + $0.08 * (x - 500) + $8.31 * 9 = $367.29

Solving for x, we get:

x = 567

So the number of minutes of talk time used each month is 567 minutes.

Answer:

x = 6

Step-by-step explanation:

5x+6=7x-6

-6           -6

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

5x = 7x - 12

-7x   -7x

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

-2x = -12

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

-2      -2

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

x = 6

Answer:

6

Step-by-step explanation:

first we combine like terms

6+6=7x-5x

then we simplify

12=2x

lastly we divide both sides by 2

2x ÷2=12÷2

an we simplify again

x=6

then the value of x is 6

check

5(6)+6=7(6)-6

30+6=42-6

36=36

Therefore , the solution of the given problem of surface area comes out to be slant height 43 mm.

How much surface area it occupies is a decent indication of its total size. The surroundings is taken into account while calculating the squared of a right triangle. Anything's overall size is determined by its surface area. The volume of water inside a cuboid is the total of the volumes on each of the six horizontal sides. To determine the box's dimensions, use the formula below: The region is the same in 2lh, 2lw, and 2hw (SA). The overall area of the adaptable shape serves as a representation of the region.

Here,

Given :

Surface area = 5633.16 square millimeters

and

slant height = x

radius = 26 mm

So,

=> SA = πr² + πrl = 5633.16

=>SA = π(r² + rl) = 5633.16

=> SA = 3.14 ( 26² + 26* l) = 5633.16

=> SA = 2122.64 + 81.64l = 5633.16

=> SA = 81.64* l = 5633.16 - 2122.64

=> 81.64*l = 3510.52

=> l = 3510.52/81.64

=> l = 43 mm

Therefore , the solution of the given problem of surface area comes out to be slant height 43 mm .

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Therefore ,option C is correct since the percentage sample would need to be higher than 100 to produce a significant result.

A percentage is a subdivision by 100, also referred to as percent. A percentage, which is defined as "per 100," denotes a component of an overall amount. For instance, 45% represents the number 45 out of 100. Calculating a percentage is the process of finding the proportion of a whole given terms of 100. There are choices for fraction computation and using online calculators.

Given:

A random selection of 75 drug users of drug X and just a random selection of 150 drug users of drug Y are chosen,

Most statisticians agree that you need a 100 sample size to get any kind of statistically meaningful findings. You should absolutely poll each and every person in a population of less than 100.

The representative sample for medication X is therefore insufficient.

Therefore ,option C is correct since the sample would need to be higher than 100 to produce a significant result.

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The maximum area the rectangle can have, is 2.31 square unit.

In the given question, a rectangle has its base on the x axis and its upper two vertices on the parabola 16 - [tex]x^2[/tex].

We have to find the maximum area the rectangle can have.

Let Length is x and width is y.

So, Area of Rectangle = length × breadth

Area of Rectangle = xy

Since, base is on the x - axis, therefore, length will be 2x.

Now, Area of Rectangle = 2xy

The given parabola y = 16 - [tex]x^2[/tex]

Area of Rectangle = 2x(16 - [tex]x^2[/tex])

Area of Rectangle = 32x - 2[tex]x^3[/tex]

For Largest Area find derivative of Area and set equal to zero.

A'(x) = 32 - 6[tex]x^2[/tex]

Now equating equal to zero

32 - 6[tex]x^2[/tex] = 0

Subtract 32 on both side, we get

- 6[tex]x^2[/tex] = - 32

Divide by -6 on both side, we get

[tex]x^2[/tex] = 5.33

Taking square root on both side, we get

x = 2.31

Hence, the maximum area the rectangle can have, is 2.31 square unit.

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When a point has a defined derivative, the point is where a function can be differentiated.

What is differentiable function?

Calculus functions in one variable that have a derivative at every point in their domain are said to be differentiable functions. At every interior point within the domain of a differentiable function, the tangent line to the graph is invariably non-vertical.

No break, cusp, or angle exists in a differentiable function. Continuous functions are never differentiable, but differentiable functions can never be continuous.

If the derivative of a function exists at every point within its domain, the function is said to be differentiable. In particular, f′(a) exists in the domain if a function f(x) is differentiable at x = a.

When a point has a defined derivative, the point is where a function can be differentiated. This indicates that the tangent line's slope from the points on the left is getting close to matching the tangent line's slope from the points on the right.

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[tex]\cfrac{22}{3}x=\cfrac{1.6}{~~ \frac{6 }{11 } ~~}\implies \cfrac{22x}{3}=\cfrac{\frac{16}{10}}{~~ \frac{6 }{11 } ~~}\implies \cfrac{22x}{3}=\cfrac{16}{10}\cdot \cfrac{11}{6}\implies \cfrac{22x}{3}=\cfrac{8}{5}\cdot \cfrac{11}{6}[/tex]

[tex]\cfrac{22x}{3}=\cfrac{8}{6}\cdot \cfrac{11}{5}\implies \cfrac{22x}{3}=\cfrac{4}{3}\cdot \cfrac{11}{5}\implies \cfrac{22x}{3}=\cfrac{44}{15} \\\\\\ \stackrel{\textit{multiplying boths sides by }\stackrel{LCD}{15}}{15\left( \cfrac{22x}{3} \right)=15\left( \cfrac{44}{15} \right)}\implies 110x=44\implies x=\cfrac{44}{110}\implies \boxed{x=\cfrac{2}{5}}[/tex]