For the following problems, write the equation that is relevant to solve the problem, the values of the variables that you will use in that equation, and a complete sentence stating what your answer to the question is. Your answer must include appropriate units 1. Five and a half years ago, Elena invested $20,000 in a retirement fund that grew at a rate of 2.96% compounded continuously. What is the investment worth today? What was the interest earned for that investment so far? 2. How long will it take for an investment with an annual rate of 2.85% compounded quarterly to double in value? (Doubling time). How long will it take for the same investment to quadruple in value?

If 15 baseballs weigh 75 ounces, how many baseballs weigh 15 ounces?

1: 5 baseballs

2:10 baseballs

3: 3 baseballs

4:75 baseballs

75oz / 15 baseballs = 5 oz each

15 oz / 5 oz = 3 baseballs

Its linear speed would be 1637.75  miles/hour

Vt =  435,49 Km/min

Vt  =  26129 Km/hour

Vt = 16630, 35  miles/hour

The distance from the earth center up to the satellite position is:

Earth radius  + distance above the earth  

radius of satellite  6400 + 1250   =  7650 Km

linear speed = Vt  = 2π*r/T

where

r is the radius of the satellite and T period  =  110 min

Then

Vt  =  6,28* 7650 / 110

Vt = 4804/110

Vt  =  43,674.54 Km/min

To get it in Km/h we must multiply by 60

Vt  =  26204m/hour

And finally, to get it in miles per hour we divide it by 16

Vt = 1637.75  miles/hour

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The rank of population size from fastest to slowest growth is N = 1250, N = 1500, N = 1000, N = 750, N = 500, and N = 250.

The population growth rate is the measure that helps to determine how much the population size changes over time. The population growth rate shows either logistic growth or exponential growth. The formula for logistic population growth is given by [tex]\frac{dN}{dt}=r_{\text{max}}N\left(\frac{K-N}{N}\right)[/tex]. Here, N is the population size, t is time, r (max) is the maximum rate of increase, and K is the carrying capacity.

The one that grows fast will have a large population size, and the one that grows slowly will have a small population size. To rank the population size, arrange the given population size from the largest to the smallest. As a result, we get,

Fastest growth rate N=1250, N=1500 , N=1000, N= 750, N= 500, N= 250 Slowest growth rate

The complete question is -

Arrange the following population sizes in the order of decreasing growth rate. Rank the population sizes (N) from fastest to slowest growth. If two population sizes have the same growth, overlap them.

N = 1250, N = 1500, N = 1000, N = 750, N = 500, N = 250

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We can expect to find 185 defective fuses each day.

The correct answer is c) 185.

At first we have to find the expected number of defective fuses each day, we can use the formula for the expected value of a binomial distribution:

Expected Value (μ) = n * p

where:

n = number of trials (in this case, the number of fuses produced each day) = 500

p = probability of success (in this case, the probability that a fuse is defective) = 37/100 = 0.37

Expected Value (μ) = 500 * 0.37 = 185

So, we can expect to find 185 defective fuses each day.

The correct answer is c) 185.

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Answer:

=

Step-by-step explanation:

Answer:

The answer is    x=2

Step-by-step explanation:

1. Rearrange terms-

29x + 3 (  5 - 35x) = - 119 - 9x

29x + 3 ( - 35x + 5) = - 119 - 9x

2. Distribute-

29x + 3 ( - 35x + 5) = - 119 - 9x

29x - 105x + 15 = - 119 - 9x

3. Combine like terms-

29x - 105x + 15 = - 119 - 9x

- 76x + 15 = -119 -9x

4. Rearrange terms-

- 76x + 15 = - 119 - 9x

- 76x + 15 = - 9x - 119

5. Subtract 15 from both sides-

- 76x + 15 = - 9x - 119

- 76x +15 -15 = -9x - 119 - 15

6. Simplify-

- 76x = - 9x - 134

7. Add 9x to both sides-

- 76x + 9x = - 9x - 134 + 9x

8. simplify-

- 67x = - 134

9. Divide both sides by the same factor-

[tex]\frac{-67x}{-67} = \frac{-134}{-67}[/tex]

10. Simplify-

x = 2

The number of 3-foot pieces of rope that Rami's grandfather could make would be = 23.8 pieces.

Rope is a thick cord that is material up of synthetic or organic materials that are interwoven together which can be used to support a structure.

The amount of money paid by Rami's grandfather for the rope = $67.83

The amount that the rope is sold per foot = $0.95/ft

To calculate the number of ft he bought;

= 67.83/0.95

= 71.4ft of rope

The number of 3-foot piece that he can cut

= 71.4/3

= 23.8 pieces.

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The smallest possible value of c is 1 in this case.

If the integer a, b and c are in arithmetic progression.

Then we can write,

b = (a+c)/2

If the integer a, b and c are in geometric progression,

Then, we can write,

b = √(ac)

Now, we can write,

a+b = 2√(ac)

Squaring both sides,

a²+c²+2ac = 4ac

(a-c)² = 0

So,

a = c.

If a = c.

Then,

b = (a+a)/2

b = a

So, a = b = c.

Smallest possible positive integer is 1.

So, the smallest possible value of c is 1.

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Answer: Yes

Step-by-step explanation:

If you were to be given the numbers for the corresponding coefficient you can solve this question just like as if they were real numbers. Even if you weren't given values, The coefficients unknown value is usually presumed as 1.

if a= 10 b=5 c=6 d=50 e=100 f=1

ab= 10:5

ac= 10:6

de= 50:100

ef= 100:1

if they were all one then they would just be 1:1

The slope is -1/3.

The slope of a line, also known as the gradient is defined as the value of the steepness or the direction of a line in a coordinate plane. Slope can be calculated using different methods, given the equation of a line or the coordinates of points lying on the straight line.

Slope = m = tan θ = (y2 - y1)/(x2 - x1)

Slope  = 2−1 / 2−1

           = 4-0 / -2-10

           =  4 /-12

          = −1/3.

The slope is -1/3.

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The dimensions of the rectangular prism with the volume 33x cubic units are 11units, 9units, 4 units.

As given in the question,

Dimension of the rectangular prism in form of x are :

( x - 3 ) , ( x - 1 ) , and ( x - 8 )

Volume of the rectangular prism = 33x cubic units

⇒ ( x - 3 )( x - 1 )( x - 8 ) = 33x

⇒ ( x² -4x + 3 )( x - 8) = 33x

⇒ x³ -12x² + 35x -24 = 33x

⇒  x³ -12x² + 2x -24 = 0

⇒ x² ( x - 12 ) + 2 ( x - 12 ) = 0

⇒ ( x - 12 )( x² + 2 ) = 0

⇒ x = 12 or x = √ -2

Dimensions cannot be square root of negative.

⇒ x = 12

x - 3 = 9 units

x -1 = 11 units

x - 8 = 4 units

Therefore, the dimensions of the rectangular prism are 9 units, 11unitsm and 4 units.

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The cube root of unity are found to be 1, -1±i√3/2 and -1±i√3/2.

In order to find the cube root of unity let us say,

x³ = 1

Solving further,

x³-1 = 0

Now,

(x-1)(x²+x+1)=0

For, x-1=0

x = 1.

And,

For, (x²+x+1)

Solving by using quadratic formula,

x = -1±√(-3)/2.

x = -1±i√3/2

x = -1+i√3/2 and,

x = -1-i√3/2

also, x = 1.

So that cube root of unity are 1, -1±i√3/2 and -1±i√3/2.

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Answer:

2

Step-by-step explanation:

one apple and another equals to 2.

Answer: 11

Step-by-step explanation: you put one and one together lol

To find out how many weeks it will take for John and Sarah to save the same amount of money, we must set their respective functions equal to each other and solve for x.

J = S

28 + 4x = x2 + 2x + 20

x2 + 2x - 4x - 8 = 0

x2 - 2x - 8 = 0

(x - 4)(x + 2) = 0

x = 4 or x = -2

Since x must be a positive value, the answer is that it will take John and Sarah 4 weeks to have the same amount of money saved.

A researcher can draw conclusions about a particular group using inferential statistics, which is a "true" statement.

Inferential statistics use data from the experiment's sample of subjects to compare the different treatments and draw conclusions about the subject population as a whole.

Thus, a researcher can draw conclusions about a particular group using inferential statistics, which is a "true" statement.

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Answer:

23°F

Step-by-step explanation:

because its from a negative temp to a positive the inc is positive and -16-+7 is 16+7 = 23

Answer:

52[tex]a^{2}[/tex] + 26

The age of the fossil is 24, 312 years assuming an exponential decay model.

Exponential decay model refers to model in which the amount of something decreases at a rate proportional to the amount left and this rate is given by a constant ratio k. The formula for remaining quantities of a substance is given by:

P = 100 e^(-kt)

Where P is the remaining quantity, k is the constant of decay, and t is time.

As the half life of the carbon 14 is 5700, when 50% of the substance remains,

50 = 100 e^(-5700k)

1/2 = e^(-5700k)

In(1/2) = In(e^(-5700k))

- In (2) = -5700k

k = In(2)/5700 = 0.0001216

Since, 5.2% carbon-14 remains,

5.2 = 100 e^(-0.0001216t)

0.052 = e^(-0.0001216t)

In(0.0052) = - 0.0001216

t = In(0.052) * - 0.0001216

t ≈ 24, 312 years.

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The probability that the sample mean will be between 1195 and 1205 is 0.445

What is a probability distribution?

In mathematics, a probability distribution is a function that expresses the likelihood of many possible values for a variable. Graphs and probability tables are common ways of displaying probability distributions.

Given, mean = [tex]\mu[/tex] = 1200

standard deviation = [tex]\sigma[/tex] = 60

n = 50

[tex]\mu_{\bar x} = 1200\\\sigma_{\bar x} =\sigma / \sqrt(n) = 60/ \sqrt50=8.485[/tex]

[tex]P(1195 < \bar x < 1205 ) = P[(1195-1200) / 8.485 < (\bar x - \mu\bar x ) / \sigma\bar x < (1205-1200) / 8.485)][/tex]

= P(-0.59 < Z <0.59 )

= P(Z <0.59 ) - P(Z <-0.59 )  

Using the z table, we get

=0.7224-0.2776

=0.4448 = 0.445 ( rounded to 3 decimal places)

Hence, the probability that the sample mean will be between 1195 and 1205 is 0.445

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The numeric values of the function are given as follows:

An appropriate domain for the situation is of:

{x ∈ N | x ≥ 0.}

The function in this problem is defined as follows:

f(x) = 6x - 70.

In which the variables are given as follows:

Hence when x = -2, the numeric value is given as follows:

f(-2) = 6(-2) - 70 = -82.

This point is outside of the domain, as the number of shirts cannot be negative, hence an appropriate domain for the function is of:

{x ∈ N | x ≥ 0.}

As the number of shirts is also a countable amount.

When x = 12, the numeric value is given as follows:

f(12) = 6(12) - 70 = 72 - 70 = 2.

When x = 17.5, the numeric value is given as follows:

f(17.5) = 6(17.5) - 70 = 35.

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The percent of the ship's passengers held round-trip tickets is 50/100 = 50%.

Since the number of passengers on the ship is immaterial, let the number of passengers on the ship be 100 for convenience.  

Let x be the number of passengers that held round-trip tickets.  

Then, since 20 percent of the passengers held a round-trip ticket and took their cars aboard the ship, 0.20(100) = 20 passengers held round-trip tickets and took their cars aboard the ship.  

The remaining passengers with round-trip tickets did not take their cars aboard, and they represent 0.6x (that is, 60 percent of the passengers with round-trip tickets).  

Thus, 0.6x + 20 = x, from which it follows that 20 = 0.4x, and so x = 50.  

The percent of passengers with round-trip tickets is, then, 50/100 = 50%

A roundtrip flight is a flight itinerary that includes one flight to a vacation spot and some other flight lower back from that destination, which include flying from NYC to Paris after which Paris lowers back to NYC. The direction might also include layovers or connections, however, the beginning and endpoint are equal.

Ask the enterprise to alter the round-trip ticket for one-way usage. although airways exercise a varying degree of flexibility, many airlines will regulate a round-ride fare to permit one-manner use, though a few airlines might also charge a penalty or charge for this provider.

also known as “return air tickets,” round-journey tickets are flights from and again to the equal place beginning. A one-manner price tag, then again, simplest lets you to fly your destination, now not back from it.

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Answer:

y= -2x -1

Step-by-step explanation:

m= (5-7)/(-3- -4) = -2/1 = -2

y-intercept = -1

y= -2x -1

Answer:

A

Step-by-step explanation:

3 - (-1.5)
when you open the backet it will be 3 - - 1.5
minus and minus makes plus
therefore it will be 3+1.5
so the answer is 4.5

Answer:

Proportional

y is 0.4 times x

or

y is 2/5 times x

Both numbers are the same, I don't know which form the computer expects you to enter

Step-by-step explanation:

x and y are proportional since there is a linear relationship between y and x.

Let's verify this

When x = 5, y = 2. So y/x = 2/5 = 0.4
So y = 0.4x  

When x = 10, y = 4
So y/x = 4/10 = 2/5 = 0.4

Again y = 0.4x

So the answer is 0.4, same as 2/5

Answer:

Step-by-step explanation:

the x and y are proportional because the number increases by the same number each time. so y =2 and x=5 then on the next one, if it's proportional, y will = 4 and x will = 10. another way you can be sure that it is proportional is that every time you add the first number you can divide it and get the first number. for example if you divide 4 by 2 you will get 2. if you divide 10 by 2 you get 10. so in a short answer yes it is proportional

Step-by-step explanation:

v=1/3πr²h

98=1/3×22/7×(5.13)²×h

98=1/3×22/7×(27.2403)×h

98=28.537×h

h=28.537/98

h=0.291m

hope it helps. please mark brainliest

Answer:

Answer to your question is in the attachment

here you are the answer.

The sum of DE+FG+HI=90 if DE, FG, HI are all parallel to BC and BC=60.

Quadrilaterals with at least one set of parallel sides are referred to as "trapezoid" quadrilaterals. In British and other dialects of English, the word "trapezium" is used.

Euclidean geometry dictates that a trapezoid must be a convex quadrilateral. The base of the trapezoid is referred to by its parallel sides. If the other two sides are parallel, the trapezoid is a parallelogram, and there are two pairs of bases. If not, the other two sides are known as the legs (or lateral sides). Unlike the specific situations below, a scalene trapezoid is a trapezoid where none of the sides have equal lengths.

Given,

ΔABC is a scalene triangle.

And BC=60

DE, FG, HI are all parallel to BC.

From the midpoint-theorem,

DE||BC then,

DE=(1/2)BC

FG||BC

FG=(1/2)BC

HI ||BC

HI=(1/2)BC

DE+FG+HI=(1/2BC+1/2BC+1/2BC)

=(1/2(3BC))

1/2(3(60))

=90

Therefore,

The sum of DE+FG+HI=90

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Answer:

ITS B

Step-by-step explanation: