Dylan invested $6,100 in an account paying an interest rate of 2 % compounded

daily. Violet invested $6,100 in an account paying an interest rate of 2 %

compounded continuously. To the nearest hundredth of a year, how much longer

would it take for Violet's money to triple than for Dylan's money to triple?

Answer:

Likely

Step-by-step explanation:

68% is more than 2/3, so the event is likely to occur.

Answer: Likely

Answer: 180 kilometers

Step-by-step explanation:

Answer:

I think she runs 1 kilometer every 5 minutes

Step-by-step explanation:

The volume of the piece is: 4489.33

To find the volume of this piece, we need to subtract the volume of the cylindrical hole from the volume of the sphere.

The volume of the sphere is given by the formula: V = (4/3) * pi * r^3

Where r is the radius of the sphere, so in this case: V = (4/3) * pi * (7cm)^3 = 1436 * 3.14 cm^3 = 4511.32 cm^3

The volume of the cylinder is given by the formula: V = pi * r^2 * h

Where r is the radius of the cylinder and h is the height of the cylinder, since the hole is drilled through the center of the sphere, the height of the cylinder is equal to the radius of the sphere, so: V = 3.14 * (1cm)^2 * 7cm = 21.99 cm^3

So the volume of the piece is: 4511.32 - 21.99 = 4489.33 cm^3

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The linear equation for the coordinate points given is obtained as y = -3/2x + 19.5.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The coordinate points for the lines are (11,3) and (7,9).

The slope-intercept form of an equation/function is - y = mx + b

To find the slope m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the equation -

[9 - 3]/[7 - 11]

(6)/(-4)

3/-2

So, the slope point is obtained as m = 3/-2.

The equation becomes - y = -3/2x + b

To find the value of b substitute the values of x and y in the equation -

3 = -3/2(11) + b

3 = -33/2 + b

b = 3 + 33/2

b = (6 + 33)/2

b = 39/2

b = 19.5

So, the value for b is 19.5.

Now, the equation becomes -

y = -3/2x + 19.5

The graph for the equation is plotted.

Therefore, the equation is obtained as y = -3/2x + 19.5.

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The angular momentum of an object can be calculated using the formula L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

In the case of the ballet dancer, we are told that they are spinning at 1.5 rev/sec, and that they can be modeled as a cylinder with a moment of inertia of 22 MR^2, a mass of 62 kg, a height of 1.6 m, and a radius of 0.16 m.

We can calculate the moment of inertia of the cylinder using the formula I = (1/2) MR^2, where M is the mass and R is the radius.

Plugging in the values we have, I = (1/2)(62 kg)(0.16 m)^2 = 3.072 kg-m^2

We can then calculate the angular momentum of the dancer by plugging in the values we have into the formula L = Iω,

L = (3.072 kg-m^2)(1.5 rev/sec) = 4.608 kg-m^2/s

So the angular momentum of a ballet dancer who is spinning at 1.5 rev/sec, modeled as a cylinder with a moment of inertia of 22 MR^2, a mass of 62 kg, a height of 1.6 m and a radius of 0.16 m is 4.608 kg-m^2/s.

Answer:

8

Step-by-step explanation:

x= 24/3 = 8

Answer:

[tex] \sf \: x = 8[/tex]

Step-by-step explanation:

Given equation,

→ 3x = 24

Now the value of x will be,

→ 3x = 24

→ x = 24 ÷ 3

→ [ x = 8 ]

Hence, the value of x is 8.

The length of the segment EF for the given trapezoids is 6 cm.

Quadrilaterals called trapezoids have two parallel and two non-parallel sides. It also goes by the name Trapezium. A trapezoid is a closed, four-sided shape.

An opposing set of sides are parallel. The four angles of a trapezium add up to 360 degrees, and their diagonals cut each other in half. It has four odd-numbered sides. Thus, the opposing sides of an isosceles trapezium are congruent, as well as the diagonals.

Trapezoids ABCD and EFGH are similar,

Hence, corresponding sides ratio are equal:

Thus, AB/EF = DC/HG

24/x = 30/7.5

30x = 180

x = 180/30

x= 6

Hence, the length of the segment EF is 6 cm.

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The amounts of each ticket that were purchased are given as follows:

The amounts are obtained using a system of equations, for which the variables are given as follows:

Noah spent $150 to buy movie tickets for 15 students and 3 adults, hence:

3a + 15s = 150

a + 5s = 50

a = 50 - 5s

Adult tickets cost $4 more than student tickets, hence:

a = 4 + s.

The solution for s is then obtained as follows:

50 - 5s = 4 + s

6s = 46

s = 46/6

s = $7.67.

Then the price of an adult ticket is of:

7.67 + 4 = $11.67.

The problem asks for the amounts of each ticket that were purchased.

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The expressions which are having common denominator 24 are

13/24  +  7/12 , 1/8  -  5/3 and for 10 are 5 - 7/10 , 3/2 -  4/5 and for 12 are

7/6  -  5/12, -3/4 - 2/3.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given ,

So given expressions are,

13/24  +  7/12   =  13+ 7*2 / 24  = 13+14 / 24 = 27/24

7/6  -  5/12 = 7*2 - 5 / 12  = 14-5/12 = 9/12

-3/4 - 2/3 = - (3/4 + 2/3 ) = - ( 9 + 8 / 12) = -17/12

5 - 7/10  = 5*10 - 7 / 10  =  50 - 7 / 10 = 43/10

1/8  -  5/3   = 3 - 8*5 / 24  = 3-40 / 24 = -37 / 24

3/2 -  4/5 = 3*5 - 2*4 / 10  = 15-8 / 10  = 7/10

Therefore, The expressions which are having common denominator 24 are 13/24  +  7/12 , 1/8  -  5/3 and for 10 are 5 - 7/10 , 3/2 -  4/5 and for 12 are 7/6  -  5/12, -3/4 - 2/3.

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The values in the empty places are 0.6 and 3.3 respectively.

Multiplication is the process of adding a number repeatedly. When m is multiplied by n, m is being added to itself n times in total. The multiplication sign is "." A way to divide or distribute a number into equal parts is by division. The two key arithmetic operations in mathematics are multiplication and division. Similar to addition and subtraction, the processes of multiplication and division are intimately tied to one another. All real numbers are subjected to these processes.

The value of 3/5 can be calculated by dividing the numerator and the denominator.

3/5 = 0.6

The given expression is:

10 = 33/ x

Isolate the value of x:

10x = 33

x = 33/10

x =3.3

Hence, the values in the empty places are 0.6 and 3.3 respectively.

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The plant that produced the most tomatoes was treated with the old fertilizer, thus it was better. So statement B is correct.

A line plot is one type of graph that helps us to represent the data along the number line. This plot is also referred to as a dot plot. In this plot, we show the data as a check or point above a number line. Each point or check in this plot represents the frequency of each value.

The given plot about fertilizers is a line plot. In this plot, 1 dot over 2 in the old fertilizer treatment means about 2 plants have one tomato.

By comparing the line plot for both the new fertilizer and old fertilizer, we will be able to say that there are more tomatoes produced when the old fertilizer is used than the new fertilizer.

Nearly 65 tomatoes were produced when old fertilizer is used but only 58 tomatoes were produced when new fertilizer is used. Therefore, statement B is correct.

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Answer:

See below

Step-by-step explanation:

No table was given but it should look something like

x   y

-3  1

-2  2

-1   3

0   4

1    5

2   6

3   7

Whatever number you select for x add 4 to it and that will give you your y value

Answer:

LESS THAN ONE

Step-by-step explanation:

1 1/5 - 1/3=0.86666666666

0.86666666666

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The measure of angles a, b, c, d and e are 54°, 18°, 108°, 81° and 99°.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Given that, workers in an office of 40 staff were asked their favorite type of take-away.

Fraction of a person = 1 degree

Here, 360° = 40 people

So, 1 degree = 40/360 =1/9

Now, angle a =6/40 ×360

= 54°

Angle b= 2/40 ×360

= 18°

Angle c= 12/40 ×360

= 108°

Angle d = 9/40 ×360

= 81°

Angle e =11/40 ×360

= 99°

Therefore, the measure of angles a, b, c, d and e are 54°, 18°, 108°, 81° and 99°.

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The distance covered on the yesterday was 24 miles.

Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

Given that, The number of miles is 15 for today and m for yesterday. The number of hours is 2.5 for today and 4 for yesterday, the rate is same for both the days, therefore, this will represent a proportion,

Therefore, establishing the proportion,

15 / 2.5 = m / 4

15 × 4 / 2.5 = m

m = 24

Since, we got the value of m is 24 miles.

Hence, the distance covered on the yesterday was 24 miles.

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Answer:

Step-by-step explanation:

Multiply the numbers:

-5x*15x + 12x - 4x.

Which should get you: -75xx + 12x - 4x

Then combine exponents : -75xx + 12x - 4 = -75x^2 + 12x - 4x

Combine like terms: -75x^2 + 8x

Then find common factor with is -1

Lastly, rewrite in factored form : -1(75x^2 + 8x) = -1(75x - 8)x

The true statement is,  c.) Prism B has a greater volume than Prism C.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

Prism A is a rectangular prism with a height of six inches, length of three inches, and a width of two inches.

Prism B is a rectangular prism with a height of three inches, length of five inches, and a width of two inches.

Prism C is a rectangular prism with a height of two inches, length of seven inches, and a width of two inches.

now,

volume of prism=V = B*H

where, B is the area of base.

so, by calculating we get,

V-prism A= 36 inch^3

V-prism B= 30inch^3

V-prism C=28 inch^3

Hence, c.) Prism B has a greater volume than Prism C.

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Answer:

C

Step-by-step explanation:

Answer:

18.19

Step-by-step explanation:

$ = linear f(t)

$16.03 = f(40) = fixed fee + per min fee = x + 40y

$19.72 = f(81) = fixed fee + per min fee = x + 81 y

use above 2 equations to minus the other

you get:

19.72-16.03 = 41y

so y = 0.09

so x = 16.03 - 40*0.09 =12.43

so for 64 mins

cost = 12.43 + 0.09*64 =18.19

If one set of the opposite sides of a quadrilateral is equal and parallel, the shape is referred to as a parallelogram.

A quadrilateral is a parallelogram if each pair of opposite angles in it is equal. The quadrilateral ABCD is a figure in which A = C and B = D. We are aware that a quadrilateral's angles add up to 360 degrees. ABCD is therefore a parallelogram.

A quadrilateral is a parallelogram if one pair of its opposite sides is both equal and parallel. A quadrilateral becomes a parallelogram if its diagonals cut each other in half.

The opposite sides of a parallelogram are equal to one another. A parallelogram's diagonals are consistently equal. The diagonals do not cross each other in a parallelogram. The diagonals in a parallelogram are always at right angles to one another.

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According to the unitary method,

(a) Ticket cost for 5 people is $28.75

(b) The cost for ticket is $28.75 and the cost for popcorn is $53.25

In math the term called unitary method is defined as a basic concept to find the value of a single unit and then using that value to find the value of multiple units.

Here we have know that each person in a group buys a movie ticket, a drink, and a popcorn.

And the cost for each of the product is listed as Ticket is $5.75, Drink is $2.00 and Popcorn is $3.25.

Then the cost of 5 people is calculated as,

=> 5.75 x 5

=> 28.75

And the third group buys 5 tickets and 4 large bags of popcorn for $82.

Then the cost of the ticket is calculated as,

=> 82 - 28.75

=> 53.25

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Earth is 2.59 x 10⁷ miles farther from the Sun than Venus.

Let us assume that d₁ represents the distance between the earth and the sun.

d₂ represents the distance between the earth and the Venus.

The distance between the earth and the sun is  9.27 x 10⁷ miles.

d₁ =  9.27 x 10⁷ miles

And the distance between the Sun and the Venus is about 6. 68 x 10⁷ miles.

⇒ d₂ = 6. 68 x 10⁷

To find : by how much farther from the Sun is Earth than Venus

We need to find the absolute difference between d₁ and d₂

Let d be the absolute difference between d₁ and d₂

d = |d₁ - d₂|

d = | (9.27 x 10⁷) - (6. 68 x 10⁷ )|

d = |(9.27 - 6.68) x 10⁷ |

d = 2.59 x 10⁷ miles

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The probability of that an incoming call to the service centre is 0.0219. And the probability that an incoming call is a request for purchasing more products is 0.135.

Probability of an event gives the possibility of an event which is never greater than 1 and the probability of impossible event is 0 and the probability of sure event is 1.

Probability = number of favourable cases/ total number of outcomes

a) The probability that an incoming call to the customer service = Probability of incoming calls to the service centre * probability of remaining number of calls in the centre = 0.73* 0.03 = 0.0219.

b) the probability that an incoming call is a request for purchasing more products = Probability of request of calls  in the service centre * probability of request of purchase. = 0.5 * 0.27 = 0.135.

Hence, the probability that incoming call to the service is 0.0219 and of the request of purchase is 0.135.

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Mateo can fill 40 glasses with punch and this can be calculated as :

8 liters = 8 x (5/1) = 40 liters

By solving the above equation following will be obtained.

Therefore, Mateo can fill 40 glasses with punch.

Mathematics, where the numerator and denominator are divided. Each is an integer in a simple fraction. Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.

If numerator value is less than the denominator value, it is a proper fraction.If a numerator value is greater than  denominator value, then it is called an improper fraction.

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Answer:

Step-by-step explanation:

yes the triangle can be formed

===================================================

Explanation:

The price drops by 35%, so it keeps the remaining 65% (since 100-35 = 65)

65% of $60 = 0.65*60 = 39 dollars

-------

A slightly longer method:

35% of 60 = 0.35*60 = 21

You save $21 and the final price is 60-21 = 39 dollars

If Jake finally found the gaming console on a resale platform, it was marked up 40% ,then the amount that Jake has to pay to buy it is $418.6    .

The retail price of the gaming console is = $299  ;

the markup in the price of the gaming console is = 40%  ;

then the new price of the gaming console is = 299 + 40%  of $299  ;

= 299 + 0.40 × 299      ...because 40% is 0.40

Simplifying further ,

we have ;

= 299 + 119.6

= 418.6

Therefore , Jake has to pay $418.6 for the gaming console to buy from the resale platform .

The given question is incomplete , the complete question is

A popular gaming console that retails for $299, was sold out for quite some time. Jake finally found it on a resale platform, but it was marked up 40% , Find the amount that Jake has to pay to buy it .

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When the data have the properties of interval data and the multiplication or division of two values is meaningful, the variable has which scale of measurement is referred to as Ratio Scale.

Now, According to the question:

A scale of measurement can be defined as a classification which is used to illustrate the attributes of the values that are assigned to variables associated with a data set.

The scales of measurement.

Generally, there are four (4) basic scale of measurement for a variable and these include the following;

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Answer:

if younger one weighs 1 ton, then older one is heavier

Step-by-step explanation:

1 ton = 2000lbs