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Archy [21]
3 years ago
14

Jayden invested $22,000 in an account paying an interest rate of 2.5% compounded

Mathematics
1 answer:
Gemiola [76]3 years ago
3 0

Answer:

12.9

Step-by-step explanation:

30400=

30400=

\,\,22000e^{0.025t}

22000e

0.025t

Plug in

\frac{30400}{22000}=

22000

30400

​

=

\,\,\frac{22000e^{0.025t}}{22000}

22000

22000e

0.025t

​

Divide by 22000

1.3818182=

1.3818182=

\,\,e^{0.025t}

e

0.025t

\ln\left(1.3818182\right)=

ln(1.3818182)=

\,\,\ln\left(e^{0.025t}\right)

ln(e

0.025t

)

Take the natural log of both sides

\ln\left(1.3818182\right)=

ln(1.3818182)=

\,\,0.025t

0.025t

ln cancels the e

\frac{\ln\left(1.3818182\right)}{0.025}=

0.025

ln(1.3818182)

​

=

\,\,\frac{0.025t}{0.025}

0.025

0.025t

​

Divide by 0.025

12.9360062=

12.9360062=t

t = 12.9

12.9

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One side of trapezoid is 10 inches. The side parrellel to this is twice as long as this side. The height is half as long as the
madam [21]
The first side is 10 inches
the side parallel to this is (10×2)= 20 inches
Height is half the length=1/2×20=10 inches
The area of trapezium is given by:
Area=1/2×h×(a+b)
where a and b are the sides, h is the height. Thus the area will be:
Area=1/2×10×(20+10)
=1/2×10×30
=150 sq. inches
7 0
3 years ago
A cone is placed inside a cylinder as shown. The radius of the cone is half the radius of the cylinder. The height of the cone i
kondaur [170]
Given:
Volume of the cone = π r² h/3

radius of the cone is half the radius of the cylinder ⇒ r/2
height of the cone is equal to the radius of the cylinder. ⇒ r

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V = 3.14 * r²/4 * r/3
V = 3.14r³ / 12

4 0
2 years ago
Read 2 more answers
Let C be between D and E. Solve for x <br> DC = 5x + 8<br> CE = 3x + 5<br> DE = 61
morpeh [17]
DE/2 = 30.5
CE=30.5
DC=30.5

3x + 5 = 30.5
3x = 30.5 - 5
3x = 25.5
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8 0
3 years ago
Hector spent $41.75 for 2 DVDs that cost the same amount. The sales tax on his purchase was $3.15. Hector also used a coupon for
kykrilka [37]

Given:

Amount spent on 2 DVDs = $41.75

Sales tax = $3.15

Coupon = $1.00 off

To find:

The cost of each DVD.

Solution:

Let x be the cost of each DVD.

Then, cost of two DVDs = 2x

Amount spent of 2 DVDs = Cost of 2 DVDs + Sales tax - Coupon discount

41.75=2x+3.15-1.00

41.75=2x+2.15

41.75-2.15=2x

39.6=2x

Divide both sides by 2.

\dfrac{39.6}{2}=x

19.8=x

Therefore, the cost of each DVD is $19.8.

8 0
3 years ago
What is the area of the composite figure? (use 3.14 for pi). Explain how you arrived at your answer. Please round to the nearest
maksim [4K]

The area of the given diagram is 29.817 square centimeters. The given diagram is combination of rectangle and semi circle.

Step-by-step explanation:

The given is,

                 Given diagram is combination of Rectangle and Semi circle.

Step:1

         Res the attachment,

                      Area of given diagram = Area of A + Area of B..............(1)

Step:2

         For A,

         The A section in the given diagram is semi circle,

                     Diameter of semi circle = Total distance - ( 2+3)

                                          ( ∵ 2, 3 are top distance in the given diagram)

                                                             = 10 - 5

                                        Diameter, d = 5 cm

                                             Radius, r = \frac{d}{2}

                                                          r = \frac{5}{2}

                                                         r = 2.5 cm

                                          Area, A_{A}  = \frac {\pi r^{2} }{2}........................(2)

                                                    A_{A}  = \frac {\pi (2.5)^{2} }{2}  

                                                           = \frac {\pi ( 6.25) }{2}

                                                           = \frac{19.63}{2}

                                                     A_{A} = 9.8174 cm^{2}

Step:3

               For B,

               Area of rectangle is,

                                                      A_{B} =lb.....................(3)

              Where, l - Length = 10 cm

                          b - Width = 2 cm

              Equation (3) become,

                                                            = (10)(2)

                                                            = 20

                                    Area of B, A_{B} = 20 cm^{2}

Step:4

               From the equation (1),

                               Area of given diagram = 20+ 9.81747

                                                            Area = 29.817 square centimeters

Result:

            The area of the given diagram is 29.817 square centimeters. The given diagram is combination of rectangle and semi circle.

5 0
2 years ago
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