To help with his retirement savings, Dan has decided to invest. Assuming an interest rate of 3,43% compounded quarterly, how much would he have to invest
to have $148,700 after 18 years?
Do not round any intermediate computations, and round your final answer to the nearest dollar. If necessary, refer to the list of financial formulas.
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I'm not sure what is meant by "partitioning the x-axis" - partition is a term more often used with computing Riemann sums. So either partitioning has a special meaning for you, or you have to approximate the area with a Riemann sum.

I'm going to assume you just want the exact area of the given region. Notice that the two curves y = 4e ˣ and y = -x + 4 intersect when x = 0 at the point (0, 4). Both curves then meet the vertical line x = 4. The exponential function is increasing while the linear one is decreasing, so 4e ˣ ≥ -x + 4.

The region is then the set of points,

R = {(x, y) | 0 ≤ x ≤ 4 and -x + 4 ≤ y ≤ 4e ˣ}

so the area is given by the integral,

[tex]\displaystyle\int_0^4 (4e^x-(-x+4))\,\mathrm dx=\int_0^4(4e^x+x-4)\,\mathrm dx=\left(4e^x+\frac{x^2}2-4x\right)\bigg|_0^4=\boxed{4e^4-12}[/tex]

Answer:

27

Step-by-step explanation:

Answer:

c i think ???

Step-by-step explanation:

Answer:

Step-by-step explanation:

The Pythagorean theorem says:

[tex]a^2+b^2=c^2[/tex]

where a and b are the two legs of the triangle and c is the hypotenuse.  Here, let's say a = 6 and b = [tex]\sqrt{13}[/tex]. We then get the following equation:

[tex]c^2= (6)^2+(\sqrt{13})^2=49[/tex]

So c = 7. Technically, c can also equal -7 since (-7)^2 = 49 as well but that does not apply here because a side length cannot be <0. So 7 is the answer.

Answer:

a) "engaged" is a quantitative and continuous variable.

b) The sample proportion of students in this high school district who are engaged is 0.4222

Step-by-step explanation:

Given the data in the question;

Polling reports shows that 0.34 12th grade students are engaged

the principal surveyed 90 of the 3600 students,

number of students reported to be engaged is 38

a)

"engaged" is a quantitative and continuous variable.

b) the sample proportion of students in this high school district who are engaged.

Sample proportion of engaged = number of students reported to be engaged / total number of students surveyed

so

Sample proportion of engaged = 38 / 90

Sample proportion of engaged = 0.4222

Therefore, the sample proportion of students in this high school district who are engaged is 0.4222

Answer:

D)  15.5

Step-by-step explanation:

median is the middle line inside the 'box'

Answer:

Step-by-step explanation:

From the given picture,

Given : l₁ and l₂ are the parallel lines and ∠2 ≅ ∠4

To prove: ∠1 ≅ ∠4 and ∠4 ≅ ∠3

          Statements                          Reasons

1). l₁ ║ l₂ and ∠2 ≅ ∠4                  1). Given

2). ∠1 ≅ ∠2                                   2). Vertical angle theorem

3). ∠1 ≅ ∠4                                   3). Given

4). ∠1 ≅ ∠3                                   4). Corresponding angle theorem

5). ∠4 ≅ ∠3                                  5). Transitive property of congruence  

Answer:

0, 0.99 and 0.348483 ( options 5, 4 & 1 )

Step-by-step explanation:

Probability of an event is between 0 & 1, including 0 & 1.

Answer:

b = 9m is the answer.

Step-by-step explanation:

a = 12m

b = ?

c = 15m

According to the Pytagorean theorem,

a² + b² = c²

12² + b² = 15²

144 + b² = 225

b² = 225 - 144

b² = 81

b = 9

∴ The slide is 9m away from the monkey bars.

We can use the formula: is/of = %/100.

% = 60

of = 160

[tex]\frac{x}{160}=\frac{60}{100}[/tex]

100x = 9600

x = 96

96 students participated in the fundraiser.

Answer:

3 2/3 miles

Step-by-step explanation:

1 1/6 + 2 1/2 = 1 1/6 + 2 3/6 = 3 4/6 = 3 2/3

Answer: 3 2/3 miles

Answer:

1. AC=EC=120 ft

2. Given as perpendicular

3. BC=CD

4. Perpendicular means 90° from the bridge

5. Area of Triangle same

Answer:

the distance between-5 to 120 on a number line is 124

Answer:

https://youtu.be/TZbTr1oBwKU

Answer:

2

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(9-7)/(4-3)

m=2/1

m=2

Answer:

none of the above is a pythagorean triple

Answer:

The equations are not equivalent

Step-by-step explanation:

2(3c +2) -2c

6c + 4 - 2c

combine like terms

4c +4 does not equal 4c +2

Answer:

they are NOT equivelent

Step-by-step explanation:

2(3c+2)-2c and 4c + 2

(6c+4)-2c

4c+4>4c+2

Answer:

i think the answer is 5x+1 that how i was taught srry if its wrong

Answer:

False

Step-by-step explanation:

(3/4)(-4/3)=-3/2

Answer:

true

Step-by-step explanation:

your welcome

Answer:

B. 37 + 7 = 44

Step-by-step explanation:

If she jumps 4 more after jumping 3 to 40, means it's 4 + 3 = 7 and it reaches 44.

Answer:

One third or 1/3

Step-by-step explanation:

Answer: x= -1

Step-by-step explanation: 6x = 2x-4 4x= -4 and x=-1

From the given statement the unknown number is found to be - 1

The given statements can written in algebraic form as follows;

the unknown number = x

the number  is multiplied by 6 = 6x

four less than twice the same number = 2x - 4

then, from the given statement the final equation equation becomes;

6x = 2x - 4

This unknown number can be solved by collecting similar terms together;

6x - 2x = -4

4x = -4

divide through by 4

[tex]\frac{4x}{4} = \frac{-4}{4} \\\\x = -1[/tex]

Thus, the unknown number is - 1

Learn more here: https://brainly.com/question/24369824

Answer:

supplementary angle = angle 2 and angle 3

vertical angle = angle 2 and angle 4

hope it helps

Answer:

63

Step-by-step explanation:

angle abc =half of arc DE + half of arc AC

Answer:

Solution given:Barbara reads

100page in 4 days

1 day=100/4=25pages

judy reads

54pages =3days

1 day=54/3=18 pages

nancy reads

160 pages =5 days

1 day=160/5=32 pages

average page=[25+18+32]/3=25 pages per day is a required rate.

9514 1404 393

Answer:

  1487.31 yd³

Step-by-step explanation:

The volume of the composite figure is the sum of the volumes of a hemisphere of radius 7 yd, and a cylinder of the same radius and height 5 yd.

The volume of a sphere is 4/3πr³. The volume of a hemisphere is half that.

The volume of a cylinder is πr²h.

The total volume of this figure is ...

  V = (2/3)πr³ + πr²h

  V = πr²(2/3r +h)

  V = (3.14)(7 yd)²(2/3·7 yd +5 yd) = 3.14·49·29/3 yd³ ≈ 1487.31 yd³

The volume of the figure is about 1487.31 yd³.

Answer:

4187.31 yd³ is thr volume of a fugure