Linear Inequalities

y > 2/3 x + 1 ​

Answer:

4/8 and 8/16

Step-by-step explanation:

Multiply 1/2 and 3/4 to find a common fraction between them (4/8) then multiply that fraction by any number greater than 1 to find another fraction equivalent

The present value of an annuity is $736.01

We know that the formula for Present Value of Annuity:

PV = P * [1 - (1 + r)^(-n)]/r

where, PV = present value of an ordinary annuity

P = value of each payment

r = interest rate per period

n = number of periods

From given data:

P = $100, n = 10 and r = 0.06

So, the present value would be,

PV = 100 * [1 - (1 + 0.06)^(-10)]/0.06

PV = 100 * 7.3601

PV = $736.01

Therefore, the present value of an annuity is $736.01

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If one item is chosen at random, the probability that it is less than 13.1 inches long is equal to 0.4176.

First of all, we would determine the z-score of this data set. Mathematically, the z-score of a given sample score in a normal distribution can be calculated by using this formula:

Z-score = (x - μ)/σ

Where:

Substituting the given parameters into the formula, we have;

Z-score, z = (13.1 - 13.6)/(2.4)

Z-score, z = -0.5/2.4

Z-score, z = -0.208

If one item is chosen randomly, the probability that it would be less than 13.1 inches long is given by this mathematical expression:

P(x < 13.1) = P(z < -0.208)

P(z < -0.2083) = 0.4176.

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The length shortest side of the quadrilateral is 5 inches

The length longest side of the quadrilateral is 10 inches;

The length of the other two sides of the quadrilateral will be 7 inches.

What is the perimeter of a quadrilateral?

The length of a quadrilateral's boundary, or what remains after joining all four of its sides to form a single line segment, is referred to as the quadrilateral's perimeter. As a result, a quadrilateral's perimeter is measured in the same linear units as its sides, such as meters, inches, centimeters, etc. We are aware that a quadrilateral's perimeter can be calculated by summing all of its side lengths. This can be stated using a straightforward formula. For instance, the formula for a quadrilateral ABCD's perimeter can be written as,

AB + BC + CD + DA = The perimeter

Let the length shortest side of the quadrilateral be x;

So, According to the question,

length longest side of the quadrilateral will be: 2x;

length of the other two sides of the quadrilateral will be (x +2) inches.

We have given that:

The perimeter of the quadrilateral is 29 inches.

So,

⇒ 2x + (x+2) +(x+2)+x = 29

⇒5x + 4 = 29

⇒5x = 29-4

⇒5x = 25

⇒x =5;

Hence,

the length shortest side of the quadrilateral is 5 inches

length longest side of the quadrilateral is 10 inches;

length of the other two sides of the quadrilateral will be 7 inches.

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Answer:

14/9

Step-by-step explanation:7/15 divided by 3/10 equals 14/9

Answer:

Avi

$21.61

Step-by-step explanation:

I = Prt

Sari: I = Prt = $1230 × 0.045 × 4 = $221.40

Avi: I = Prt = $1105 × 0.055 × 4 = $243.01

$243.01 - $221.40 = $21.61

Answer:

Avi

$21.61

According to the sum of the given supplementary angles, we find out that the value of x is 30.

It is given that ∠A and ∠B are supplementary where,

∠A = (4x + 30)° and,

∠B = (2x - 30)°

We have to find out the value of x.

We know that two supplementary angles add up to 180°.

Since ∠A and ∠B are supplementary angles, therefore

∠A + ∠B = 180°

=> (4x + 30) + (2x - 30) = 180°

=> 6x = 180°

=> x = 30

Thus, for the given supplementary angles, the value of x is 30.

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**According to the sum of the given supplementary angles, we find out that the value of x is 30.

It is given that ∠A and ∠B are supplementary where,

∠A = (4x + 30)° and,

∠B = (2x - 30)°

We have to find out the value of x.

We know that two supplementary angles add up to 180°.

Since ∠A and ∠B are supplementary angles, therefore

∠A + ∠B = 180°

=> (4x + 30) + (2x - 30) = 180°

=> 6x = 180°

=> x = 30 **

Answer:

1.6 liters

Explanation:

400x4=1600

1000ml=1l

1600/1000=1.6

Answer:

1 1/3

Step-by-step explanation:

9*6=54

So 6x=8

x=1 1/3

It will take about 9.1 years for $36000 to grow with interest to $51806.67 after continuous compounding .

What is continuous compounding?

The process of continuously compounding involves calculating interest and reinvested it into the balance of an account over an infinite number of periods. When they specifically state that the amount is "compounded continuously" in a problem, they should use the continuous compounding formula. The mathematical constant "e" is used in this formula, and its value is roughly equal to 2.7182818. Here is the formula for continuous compounding.

Here the Principal P = $36000 , Total amount A= $39786.15 and

Time t=2.5 yrs.

Now using continuous compounding formula,

=> A = P[tex]e^(rt)[/tex]

=> 39786.15 = 36000*[tex]e^(r*5/2)[/tex]

=> r = 0.04 = 4%

Now A=51806.67 and Again using continuous compounding formula ,

=>  A = P[tex]e^(rt)[/tex]

=> 51806.67 = 36000*[tex]e^(0.04*t)[/tex]

=> t =9.1 years.

Therefore it will take about 9.1 years for $36000 to grow to $51806.67 .

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The area of triangle DEF, in square units, is given as follows:

4.08 units squared.

The area of a triangle is given by half the multiplication of it's base by it's height, as follows:

Area = 0.5 x base x height.

We consider the base as the segment DE, hence it's length is given by the distance between these two points, obtained as follows:

[tex]b = \sqrt{(8 - 3)^2 + (-6 - (-5))^2}[/tex]

[tex]b = \sqrt{26}[/tex]

b = 5.1 units.

The midpoint of the base is given as follows:

(5.5, -5.5).

As it is obtained with the mean of the coordinates.

The height is the distance between the midpoint of the base and the other vertex, hence:

[tex]h = \sqrt{(5.5 - 4)^2 + (-5.5 - (-5))^2}[/tex]

h = 1.6 units.

Hence the area of the triangle is obtained as follows:

Area = 0.5 x 5.1 x 1.6 = 4.08 units squared.

The problem asks for the area of the triangle, as shown in the image given at the end of the answer.

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1. When you travel 3 miles in New York City, the cost of The Red Cabs and The Green Cabs would be the same.

2. The difference in cost between the two companies if you need to travel 8 miles is $5.

3. It is cheaper to travel with Red Cabs than Green Cabs if the total distance is more than 3 miles.

First, for the costs of both companies to be equal, we set the two cost equations to be equal to each other and solve for the unknown variable (miles).

Based on the equations for the two companies, we can determine the total costs of using any option.

The difference between the total costs is obtained by subtracting.

Let cost of Green Cab = 2 + 2m

Let cost of Red Cab = 5 + m

For the two companies costs to be equal, 2 + 2m = 5 + m

= 2m - m = 5 - 2

m = 3

Green Cab = 2 + 2m

= 2 + 2(8)

= 18

= $18

Red Cab = 5 + m

= 5 + 8

= 13

= $13

The difference in cost = $5 ($18 - $13)

Thus, based on the solution to the cost equations, cost-conscious travelers should prefer Red Cabs to Green Cabs when they travel in New York City for a distance exceeding 3 miles.

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3 11/20

Step-by-step explanation:

1 3/4+1 4/5=

7/4+9/5=

7/4x5/5=35/20

9/5x4/4=36/20

35/20+36/20=71/20=3 11/20

There are 28 groups of 1/5 are in 5.

And, The solution of the expression 5 ÷ 4/5 will be 25/4.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

There is a number line shown in figure.

Now,

In a number line,

The groups of 1/5 in 5 = 28 - 0

                                   = 28

Thus, There are 28 groups of 1/5 are in 5.

And, The expression is,

⇒ 5 ÷ 4/5

Solve aa;

⇒ 5 × 5/4

⇒ 25 / 4

Thus, There are 28 groups of 1/5 are in 5.

And, The solution of the expression 5 ÷ 4/5 will be 25/4.

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Answer:

Lucas 29

Kiley 35

Jonathan 58

Step-by-step explanation:

Kiley = Lucas + 6

Jonathan = 2 x Lucas

Kiley + Lucas + Jonathan = 122

1. Replace Kiley and Jonathan with information we have

K + L + J = 122

(L+6) + L + (2L) = 122

4L + 6 = 122

4L = 122 - 6

L = 116/4 = 29

2. Replace Lucas with 29, you have

Kiley = 29 + 6 = 35

Jonathan = 2 × 29 = 58

Answer:

Step-by-step explanation:

To find the value of g(x), find the point x on the horizontal axis, then find the intersection of the vertical segment from that point to the graph, then trace the corresponding value of intersection on the vertical axis. This is the value of the function at the point x.

This is all done on the attached.

The value of g(- 3) is 3.5.

The number of kilometers that Brett and Julian would have run at the 3 / 5 point are:

Brett is running the 5k race at the Memorial Day race which means that when he runs 3 / 5 of the race, he would have ran a total of :
= Distance on Brett's race x Proportion ran

= 5 x 3 / 5

= 15 / 3

= 3 km

Julian on the other hand, is in the 10 k race which means that when they get to 3 / 5 of the race, they would have ran:

= 10 x 3 / 5

= 30 / 5

= 6 km

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a) The ball was struck from a height of one foot.
b) It took the object one second to reach its highest point.

c) The baseball may fly up to a height of 17 feet.

Given the function that represents the height of an object in air expressed as;

h(t)=-16t^2+ 32t+ 1

a) The ball is hit at the point where the time is zero. Equating the function to zero.

h(0) = -16t^2+ 32t+ 1

h(0) = -16(0) + 32(0) + 1

h(0) = 1 feet

Hence the ball was hit at the height of 1 feet

b) At maximum height, the velocity of the object is zero. Hence;

v(t) = -32t + 32

v(t) = 0 = -32t + 32

32t = 32

t = 32/32

t = 1sec

Hence the object reach its maximum height after 1 seconds.

c) Substitute t = 1 into the function to have:

h(1)=-16(1)^2+ 32(1)+ 1

h(1) = -16 + 33

h(1) = 17 feet

The maximum height reached by the baseball is 17 feet.

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The values of x = 2 & y = 3.

A cyclist cycles for x hours at 12 km/hour and y hours at 18km/hour.

To find x and y:

Given kilometers = 78km

Time = 5 hours

So, we know that the

Distance Equation is 12x + 18y = 78 km

Time Equation is x + y = 5 hours

Multiply the equation through the Time Equation by 12:

12x + 18y = 78

12x + 12y = 60

Subtract and solve for "y":

6y = 18

y = 3

So now we have to Solve for "x" using x + y = 5

x + 3 = 5

x = 2

Hence the answer is the values of x = 2 & y = 3.

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Based on the number of members in the Westview Journalism Club, the amount that each student should raise on average to meet the goal is $40.

The amount that the students would have to raise is the amount that is remaining from the amount already raised. This can be found as:

= Amount that club needs to raise - Amount already raised

= 2, 100 - 1, 180

= $920

The average amount that each student has to raised to meet the target would then be based on the number of students in the club which is 23 members.

The average amount is therefore:

= Amount that still needs to be raised / Number of students in the Westview Journalism Club

= 920 / 23

= $40

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The accumulated amount in the annuity if $80 is invested for 40 years at 6% is $25,709.04.

An annuity is when a series of payment is made over a specified period of time. An annuity can either be an ordinary annuity or a beginning annuity. An ordinary annuity is when the series of payment is made at the end of the period. A beginning annuity is when the annuity payment is made at the beginning of the period.

In this question, the annuity would last for 40 years and payments would be made twice a year.

The formula that can be used to determine the accumulated amount is:

Accumulated amount = annuity factor x payment

Annuity factor = {[(1+r)^n] - 1} / r

Where:

Accumulated amount = $80 x [{(1.03^80) - 1} / 0.03]

Accumulated amount = $80 x 321.36302

Accumulated amount = $25,709.04

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The parabola have a vertex of (-1, -64), it's x-intercept is (3, 0), (-5, 0), it's y-intercept is (0, -60) and it's axis of symmetry is x = -1

This is a curve formed by the intersection of a cone with a plane parallel to a straight line in its surface. It can also be defined as a curve formed by a point moving so that its distance from a fixed point is equal to its distance from a fixed line. In mathematics, it is a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone.

f(x) = 4x² + 8x - 60

The vertex = (-1, -64)

The x-intercept = (3, 0), (-5, 0)

The y-intercept = (0, -60)

The axis of symmetry = x = -1

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Number of ticket sold for adult = 70

Number of ticket sold for child = 30

Given that,

The number of tickets sold = 100

Cost of ticket for adult = £5.50

Cost of ticket for child =  £1.50

Total sold amount = £430.

Let number of ticket for adult = x

And number of tickets for child = y

We know that,

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

Therefore,

Forming the equation according to the given information,

We get two equation as,

5.50x + 1.50y = 430  ...(i)

              x + y = 100    ...(ii)

Now, Subtract equation (ii) with multiplication 1.50 from (i)

4x = 280

 x = 70

Now put the values of x in equation (ii)

y  = 30

Hence number of ticket for child is 30 and for adult is 70.

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Answer:

I think 72,000 because since the weightlifter is lifting 72 and it is kg. It is turned into grams. multiplied by 1000 so 72000

A graph of the given set of functions has been plotted and shown in the image attached below.

In Mathematics, a function simply refers to a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable to an output variable.

In Mathematics, a graph is a type of chart that is typically used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).

By critically observing the graph of this set of functions (see attachment), we can reasonably infer and logically deduce that they both represent parallel lines, with function f(x) being transformed to produce function h(x).

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Answer: 930$ and the expression is 1000$ - 70$ = 930$

Step-by-step explanation:

if she has under 100 dollars in her bank account every month for 10 months therefore multiplying it by 10 giving you 1000 but we cant forget about the 7$ monthly fee.  7 times 10 = 70   1000- 70 = 930$

Answer:

Step-by-step explanation: