you deposit 2000 in an account earning 3% interest compounded monthly.
a. how much will you have in the account in 20 years
b. how much interest will you earn

Using the arrangements formula, the probability of the butterscotch, cinnamon, and then chocolate candies eaten in this particular order is:

[tex]\frac{1}{6}[/tex].

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

In this problem, there are 3 candies, hence the number of ways they can be eaten is:

[tex]A_3 = 3! = 6[/tex]

The desired order is only one, hence the probability is:

[tex]\frac{1}{6}[/tex].

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Answer:

d.

Step-by-step explanation:

Given a length [tex]l[/tex] and a width [tex]w[/tex], we can express the perimeter of a rectangle as [tex]2(l+w)[/tex].

Therefore the perimeter [tex]P[/tex] can be expressed as

[tex]2\times[(x-8)+(x-9)]\\=2\times(2x-17)\\=4x-34[/tex]

The graph shows the comparison of the human welfare and ecological footprints.

A graph simply means a diagram that shows the relationship between variables.

From the graph, it can be seen that countries such as Norway, Canada, USA, and Australia meet the minimum criteria for sustainability.

The graph also shows that Sierra Leone is the least developed country among the countries compared as it has the lowest human development index.

The threshold for high human development as given as 0.8. Most African countries had a human development index of 0.5 and below.

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The inequalty that represents the statement must be y < - 6 · (x + 2)² + 2. (Right choice: None)

The standard form of the equation of the parabola is defined by the following expression:

y - k = C · (x - h)²     (1)

Where:

Now we proceed to find the vertex constant: (h, k) = (- 2, 2) and (x, y) = (- 4, 14)

14 - 2 = C · [- 4 - (- 2)]²

12 = C · (-2)

C = - 6

The equation of the parabola in vertex form is

y - 2 = - 6 · (x + 2)²

y = - 6 · (x + 2)² + 2

Then, the inequalty that represents the statement must be y < - 6 · (x + 2)² + 2. (Right choice: None)

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Answer:

y < 3(x + 2)2 + 2

Step-by-step explanation:

just do it

The conditional relative frequency for female students who prefer playing sports is 34%.

The table of values is given as:

                        Sports   Dancing Row totals

Male students      18             16        34

Female students  18             35       53

Column totals       36            51         87

Mason's calculation is given as:

P = 21%

This is gotten by

18/87 = 21%

The above represents the joint relative frequency of female students who prefer playing sports.

To calculate the conditional relative frequency, he should divide 18 by the row total.

So, we have

18/53 = 34%

Hence, the conditional relative frequency for female students who prefer playing sports is 34%.

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Answer: i+96

Step-by-step explanation:

Note that [tex]i^{4k}[/tex], where k is an integer, is equal to 1.

This means that [tex]i^{4!}=i^{5!}=i^{6}=\cdots=i^{99!}+i^{100!}=1[/tex]

So, we can rewrite the sum as [tex]i^{1}+i^{1}+i^{2}+i^3+97(1)=i+i-1-i+97=i+96[/tex]

[tex]n![/tex] is divisible by 4 for all [tex]n\ge4[/tex]. This means, for instance,

[tex]i^{4!} = \left(i^4\right)^{3!} = 1^{3!} = 1[/tex]

[tex]i^{5!} = \left(i^4\right)^{5\times3!} = 1^{5\times3!} = 1[/tex]

etc, so that [tex]i^{n!} = 1[/tex] for all [tex]n\ge4[/tex].

Meanwhile,

[tex]i^{0!} = i^1 = i[/tex]

[tex]i^{1!} = i^1 = i[/tex]

[tex]i^{2!} = i^2 = -1[/tex]

[tex]i^{3!} = i^6 = (-1)^3 = -1[/tex]

Then the sum we want is

[tex]i^{0!} + i^{1!} + i^{2!} + i^{3!} + 97\times1 = i + i - 1 - 1 + 97 = \boxed{95+2i}[/tex]

Using the hypergeometric distribution, the probabilities are given as follows:

a) 0.2 = 20%.

b) 0.5539 = 55.39%.

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

Researching this problem on the internet, it is found that the council has 15 members, of which 7 are Democrats and 8 are Republicans.

Item a:

The parameters are:

N = 15, n = 2, k = 7.

The probability is P(X = 2), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,15,2,7) = \frac{C_{7,2}C_{8,0}}{C_{15,2}} = 0.2[/tex]

Item b:

At most one Democrat, with n = 3, hence:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]

In which:

[tex]P(X = 0) = h(0,15,3,7) = \frac{C_{3,0}C_{8,3}}{C_{15,3}} = 0.1231[/tex]

[tex]P(X = 1) = h(1,15,3,7) = \frac{C_{3,1}C_{8,2}}{C_{15,3}} = 0.4308[/tex]

Then:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.1231 + 0.4308 = 0.5539[/tex]

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The location of the center of the circle is (h, k) = (4, 8) and the radius of the circle is equal to 2.5.

In this question we must determine the location of the center and the measure of the radius of a circle. According to Euclidean geometry, diameters are the longest possible chords of a circle. First, we determine the location of the center by definition of midpoint:

(h, k) = (1/2) · (4, 5.5) + (1/2) · (4, 10.5)

(h, k) = (4, 8)

And the radius is found by Pythagorean theorem:

[tex]d = \sqrt{(4 - 4)^{2}+(10.5-5.5)^{2}}[/tex]

d = 5

r = 0.5 · 5

r = 2.5

The location of the center of the circle is (h, k) = (4, 8) and the radius of the circle is equal to 2.5.

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Two ares are congruent if they have the same measure and lengths

The statement is given as:

Two ares are congruent if they have the same measure and ?

The conditions for congruent shapes in geometry are;

This means that the angle and the length must be equal

Hence, the term that completes the blank is length

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Answer:

Step-by-step explanation:

Comment

Let the number of pages = x

Play =    1/3x

Actors = 1/4(x - 1/3 x)

Actors = 1/4(2/3x)

Actors = 2/12 x

Producer Director etc = 2 pages

Equation

Actors = 2 pages

2/12 x = 2

Solution

2x/12 = 2               Multiply both sides by 12

12*2x/12 = 2*12     Combine

2x = 24                  Divide by 2

2x/2 = 24/2           Combine

x = 12

Answer

The program had 12 pages.

Answer:

[tex]\frac{\sqrt{41}}{4}[/tex]

Step-by-step explanation:

sec(theta) is defined as: [tex]sec(\theta)=\frac{1}{cos(\theta)} = \frac{hypotenuse}{adjacent}[/tex]

In the diagram you provided the hypotenuse of the triangle is sqrt(41) and the opposite side is 5, using these two sides, we can solve for the adjacent side by using the Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]

So this gives us the equation where a=adjacent side:

[tex]a^2+5^2=\sqrt{41}^2[/tex]

[tex]a^2+25=41[/tex]

Subtract 25 from both sides

[tex]a^2=16[/tex]

Take the square root of both sides

[tex]a=4[/tex]

So now plug this into the definition of sec(theta) and you get: [tex]\frac{\sqrt{41}}{4}[/tex]. This is in most simplified form since 41, has no factors besides 41 and 1.

Answer:

1.2 × 107 this is the sciencetific notation for 12 million

..

Answer:

x=6

Step-by-step explanation:

This is a vertical line going through (6,0).  If you take this point and the point given and calculate the slope you find the change in y over the change in x.  

0-(-3)/6-6  The slope is undefined because the denominator of the slope would be zero.

Answer:

a.1

b.10

c.120

Step-by-step explanation: don't know that last one

Using the least common factor, they need to wait 14 days until they next get to work together.

To find the time that passes between the events happening at the same time, we need to find the least common multiple of the periods.

In this problem, the periods are of 2 days and 7 days, which already are prime numbers, hence:

lcm(2,7) = 2 x 7 = 14.

They need to wait 14 days until they next get to work together.

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The expanded form of the given exponential equation is 6718464

Exponential equations are inverse of logarithmic equations. The standard exponential equation is expressed as. y = ab^x

where

a is the base

x is the exponent

Given the expression below;

a = 4(6)^8​

Expand to have:

a = 4 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6

a = 4 * 1679616
a = 6718464

Hence the expanded form of the given exponential equation is 6718464

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Answer:

a. 8:15

b. 7:15

Answer:

Well a sovial reason is that no one would no what order yo do it in, which would cause arguments

Answer:

without the order of operations, maths literally doesn't work.

Step-by-step explanation:

like whilst some equations don't rely on a particular order for solving, if you for example, don't solve brackets first, then try to multiply them by something else basically the equation breaks and you get the wrong answer. So... kids remember your BODMAS :)

The exponential equation of the model is A(t) = 2583 * 0.88^t and the multiplier means that the number of new cases in a week is 88% of the previous week

The given parameters are:

New, A(t) = 2000

Rate, r = 12%

The function is represented as:

A(t) = A * (1 - r)^t

So, we have:

2000 = A * (1 - 12%)^t

This gives

2000 = A * (0.88)^t

2 weeks ago implies that;

t = 2

So, we have:

2000 = A * 0.88^2

Evaluate

2000 = A * 0.7744

Divide by 0.7744

A = 2583

Substitute A = 2583 in A(t) = A * 0.88^t

A(t) = 2583 * 0.88^t

Hence, the exponential equation of the model is A(t) = 2583 * 0.88^t

In this case, the multiplier is 88% or 0.88

This means that the number of new cases in a week is 88% of the previous week

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Based on the graph which depicts the United States domestic market for  corn at different prices, we can logically deduce the following information:

Assuming France is the only other corn-producing nations at a domestic price of $4, we can reasonably infer that the United States will export corn while France will import it.

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Using proportions, the numbers that the arrows are pointing to are:

a) 62.

b) 8.8.

c) 2.8.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In item a, the arrow is 2/10 of the way from 60 to 70, hence the number is:

60 + 0.2(70 - 60) = 60 + 2 = 62.

In item b, the arrow is 8/10 of the way from 8 to 9, hence the number is:

8 + 0.8(9 - 8) = 8.8.

In item c, the arrow is 3/10 of the way from 2.5 to 3.5, hence the number is:

2.5 + 0.3(3.5 - 2.5) = 2.8.

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The correct statement is Triangle B is a reflection of triangle A across the x-axis. Triangle C isn't a reflection of triangle A.

Given that in a coordinate plane, triangle A is reflected across the x-axis to form triangle B. Triangle A is rotated to form triangle C.

From the given figure , it says that Triangle B is a reflection of triangle An across the x-pivot. Triangle C isn't a reflection of triangle A" in light of the fact that Triangle A is in the main quadrant and its appearance with x-axis makes the triangle-B in the fourth quadrant and the triangle C which is in second quadrant can not be a reflection and annot be a rotation of triangle-A. Triangle C is drawn by taking firstly the reflection of triangle A and then rotate on the same place and increased x+3 units in above direction.

Hence, the statement correctly describes the diagram is "Triangle B is a reflection of triangle A across the x-axis. Triangle C isn't a reflection of triangle A".

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Answer:

A. Triangle B is a reflection of triangle A across the x-axis. Triangle C is not a reflection of triangle A..

Step-by-step explanation:

goodluck

The paddling rate of Alvin is 9km/hr

Given time against the  river current is 10 hours , speed is 3km/hr

and time with the river current given is 5 hours and the speed is 3km/hr

We need to calculate the paddling rate of Alvin

Let us assume that

r =Alvin's average paddling rate in km/hour

y = speed of the current in km/hour

we know that

speed= distance/time

∴ distance=speed*time

Now,

To Campsite against the current

Speed=(r-y)

∴ Speed=(r-3) ---- (1)

Time=8 hours

Distance=(r-3)*10------ (2)

10r - 30

From Campsite with the current

Speed=(r+y)

∴Speed=(r+3)*5

Time=3 hours

Distance=(r+3)*5----(1)

Equate equation 1 and equation 2

5r +15

because is the same distance

5r + 15 = 10r - 30

5r = 45

r = 9

Hence ,The rate of the paddling rate is 9km/hr

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12,480 es par y la suma de sus digitos da un multiplo de 3, por ello concluimos que es divisible por 6.

Para que un número sea divisible por 6 debe cumplir dos condiciones.

En este caso tenemos 12,480, que sabemos que es par.

La suma de sus digitos da:

1 + 2 + 4 + 8 + 0 = 15

15 es multiplo de 3.

Entonces este número cumple ambas condiciones, por lo que concluimos que 12,480 es divisible por 6.

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Answer:

x=20

Step-by-step explanation:

x-15=5

x=5+15

x=20

The probability that a person chosen at random is younger than 65 is 0.967.

Probability calculates the odds that a random event would happen. The odds that the random event happens lie between 0 and 1.

The probability that a person chosen at random is younger than 65 = (total number of people younger than 65 / total number of respondents)

(350 + 412 + 318 + 200 + 107 + 51 ) / (350 + 412 + 318 + 200 + 107 + 51 + 49)

1438 / 1487 = 0.967

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The process needs to meet the following criterion:The process must make large amounts of product at a low cost. That is option A.

Ammonia is defined as a gas compound that is made up of nitrogen and oxygen in the ratio of 1:3 respectively.

The industrial and modern method constructed by Engineers for ammonia production is called steam reforming.

The natural resources used for industrial production of ammonia can be gotten from natural gas such as methane.

To make profit, natural products are used which costs less to acquire but will lead to the production of large ammonia quantity.

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The slope of the median of the triangle whose vertices are P(-6,1),Q(-2,5) R(8,1) and passes through R is -1/6.

Given that vertices of triangle is P(-6,1),Q(-2,5),R(8,1) and there is a median which passes through R.

Median of a triangle is a line segment which originates from a vertex of triangle and divides the opposite side in two equal parts. let median touches the line at L point.

When line passes through R then it must be a perpendicular on PQ. The coordinates of L is {(-2-6)/2,(5+1)/2}=(-4,3)

Now because median passes through R,it will be LR and we know that the formula of calculating slope of line from two points is [tex](y_{2} -y_{1} )/(x_{2} -x_{1} )[/tex] where [tex](x_{1} ,y_{2} ),(x_{2} ,y_{2} )[/tex] are the points of the end points of line.

Slope=(1-3)/(8+4)

=-2/12

=-1/6

Hence the slope of the median of the triangle whose vertices are P(-6,1),Q(-2,5) R(8,1) and passes through R is -1/6.

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Answer:

the number 27 is a composite

Step-by-step explanation:

Yes, since 27 has more than two factors . 1, 3, 9, 27. In other words, 27 is a composite number because 27 has more than 2 factors

Answer:

The number 27 is composite.

The probability that the ball Deborah picks is green is; 3/5.

Since the bag initially contains; 3 red balls, 4 green balls, and 2 yellow balls, after Deborah pulls out the 4 balls: red, red, green, yellow.

The balls remaining are; 1 red ball, 3 green and 1 yellow.

Hence, the probability that the final ball she picks is green is; 3/(3+1+1) = 3/5.

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