An investment of $10,000 is invested for 6 years at r% pa compounded weekly. If the investment grows to $14320.44, calculate the value of r.

Answer:

17

Step-by-step explanation:

two negative signs makes a positive result

Work Shown:

A = pi*r^2

A = 3.14*(4.25)^2

A = 56.71625

A = 56.72

Answer:

7.92 cm²

Step-by-step explanation:

Area of Trapezium :

In this question, we are presented with two triangles are required to find he missing sides in them. the missing side in the first triangle is equal to 8 and the missing sides in the second triangle are 8.660, 5 and 60 for the adjacent, opposite and the second angle respectively

In the first triangle, we need to use trigonometric ratio to find the missing side in the triangle

Data;

To find the adjacent side, we need to use cosine rule on this problem.

[tex]cos\theta = \frac{adjacent}{hypothenuse} \\cos45 = \frac{x}{8\sqrt{2} } \\x = 8[/tex]

The adjacent side is equal to 8 units

In the second triangle, we also need to use trigonometric ratio, but let's write down our data

We can use both cosine and sine rule here or use one and use Pythagoras's theorem to find the other side.

[tex]cos \theta = \frac{adjacent}{hypothenuse} \\cos 30 = \frac{x}{10} \\x = 8.660[/tex]

The adjacent side is equal to 8.660, let's find the opposite side using sine rule

[tex]sin\theta = \frac{opposite}{hypothenuse} \\sin 30 = \frac{y}{10} \\y = 5[/tex]

And lastly, the value of the other angle is

[tex]90 + 30 + z = 180\\z = 180 - 120\\\\z = 60[/tex]

From the calculations above, the missing side in the first triangle is equal to 8 and the missing sides in the second triangle are 8.660, 5 and 60 for the adjacent, opposite and the second angle respectively

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Answer:

Direction: Opens Up

Vertex:(3,−14)

Focus:(3

Step-by-step explanation:

hope this help if not let me know have a blessed day

The rule that the defines the sum Sn is [tex]S_n =\frac{9 * (1 - r^n )}{0.6}[/tex]

The formula of the sequence is given as:

an = 9(0.4)^n

The above means that:

The sum Sn is then represented as:

[tex]S_n =\frac{a(1 - r^n )}{1 - r}[/tex]

So, we have:

[tex]S_n =\frac{9 * (1 - r^n )}{1 - 0.4}[/tex]

Evaluate the difference and divide

[tex]S_n =\frac{9 * (1 - r^n )}{0.6}[/tex]

Hence, the rule that the defines the sum Sn is [tex]S_n =\frac{9 * (1 - r^n )}{0.6}[/tex]

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Answer:

It depends

Step-by-step explanation:

Based on the given info it depends on how much the recipe calls for.  32 fluid ounces is equal to 4 cups, 1 quart, .25 gallons, 64 tablespoons, 192 teaspoons, and 2 pints.  I really hope this answer helped you, and it honestly depends on how much the recipe calls for. :)

Answer:7

Step-by-step explanation:

The answer would be 115

Step-by-step explanation:

Answer:

81000000

[tex]\frac{90}{100} *90000000\\ 90*900000\\ 9*9=81\\ then write all the zeros[/tex]

Answer:

636/928 = 137/200

0.685

68.5%

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

its correct

Step-by-step explanation:

a)

y = 2x³ + 4x

a polynomial of 3rd degree cannot have an axis of symmetry.

it can only have a point of symmetry, like in this case.

(0, 0) is the point of symmetry, because due to the fact there is no squared term, any negative x values create exactly the same values (in absolute values) as their positive counterparts - just negative.

the vertex of a polynomial of 3rd degree is the point where the function changes directions.

that point for x³ is the origin, as it is for x. the factors only stretch the graph, but the vertex stays the same.

only if we had a term like (x+a)³ in the polynomial, this would shift the vertex.

so, the point of symmetry and the vertex are the same :

(0, 0).

b)

y = -x² + 4x - 5

the vertex form of a quadratic function is

f(x) = a(x − h)² + k

with (h, k) is the vertex.

x = h is the axis of symmetry.

we use "complete the square" to get it into that form.

-x² + 4x - 5 = -(x² - 4x + 5) = -(x - 2)² - 1

therefore,

y = -(x - 2)² - 1

h = 2, k = -1

the vertex is (2, -1)

the axis of symmetry is x = 2

The solution to the question is arrived at using the knowledge of mathematical models.

A mathematical model is a linguistic and mathematical concepts-based description of a system.

The appropriate model for the given data is:

Because there are discrepancies and no direct equation that can complete all of these points, a Least Square Regression Line is the best option for resolving this problem.

They could be outliers, so we need use a calculator to create a regression line to find the residual value.

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Answer:

Shown below.

Step-by-step explanation:

Test Marks          Tally          Frequency          Percentage

1                                                    8                   8/60 = 0.133

2                                                   6                   6/60 = 0.100

3                                                   5                   5/60 = 0.083

4                                                   5                   5/60 = 0.083

5                                                   5                   5/60 = 0.083

6                                                   8                   8/60 = 0.133

7                                                   6                   6/60 = 0.100

8                                                   7                   7/60 = 0.116

9                                                   4                   4/60 = 0.066

10                                                 5                   5/60 = 0.083

Total                                            59                 59/60 = 0.983

For the Tally section, I believe you just fill in tally marks corresponding to the frequency. One of the observations in the table is 0, which is not a column in the frequency table.

Answer:

23

Step-by-step explanation:

5 x 3 = 15

4 x 2 = 8

15 + 8

= 23

Answer:

Dimensions of tank:

⇒ Volume of each tank = width × length × height

                                       = 8.75 × 8.75 × 23

                                       = 1760.9375 in³

Given:

mass = density × volume

⇒ mass of hot coffee = 5.8 oz/in³ × 1760.9375 in³

                                     = 10213.44 oz (nearest hundredth)

⇒ mass of cold coffee = 3.5 oz/in³ × 1760.9375 in³

                                      = 6163.28 oz (nearest hundredth)

Convert the masses of the tanks from ounces to pounds

1 lb = 16 oz

⇒ mass of hot coffee tank = 10213.44 ÷ 16

                                            = 638.34 lb (nearest hundredth)

⇒ mass of cold coffee tank = 6163.28 ÷ 16

                                             = 385.21 lb (nearest hundredth)

If the table can hold a maximum of 800 lb:

hot coffee:  800 lb ÷ 638.34 lb = 1.25 (nearest hundredth)

cold coffee:  800 lb ÷ 385.21  lb = 2.08 (nearest hundredth)

Therefore, either:

can be placed on a table which can support a maximum weight of 800 lb

Answer:

answers

Step-by-step explanation:

125000 Submit Answer.

Answer:

12763

Step-by-step explanation:

Based on the given conditions, formulate: 

10000 x ( 5%+1)⁵

Evaluate the equation/expression: 12762.81563

Find the closest integer: 12763

Answer: 36

Step-by-step explanation:

If there are 30 new crayons, all you have to do is subtract the 24 new crayons Angie added, thus being six new crayons. Multiply this by 6 to get 36.

Answer:

Step-by-step explanation:

Solve the equation in steps below

Correct choice is B

Answer:

The slope is 4/3

Step-by-step explanation:

The solution is in the image

The null hypothesis is that the mean mass of vitamin c per tablet does not differ from 297 milligrams

The alternative hypothesis is that the mean mass of vitamin c per tablet differs from 297 milligrams.

The null hypothesis usually states that there is no relationship between the population parameters. It is known as the true hypothesis. The alternative hypothesis states that there is a relationship between the population parameters.

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The simpliication of the expression is:

[tex]\frac{3 + 5x}{\sqrt{96}*x - \sqrt{x} }[/tex]

We have the expression:

[tex]\frac{3 + 5\sqrt{x^2} }{4\sqrt{6x^2} - \sqrt{x} }[/tex]

Remember two things:

[tex]\sqrt{x^2} = x\\\\\sqrt{A*B} = \sqrt{A} *\sqrt{B}[/tex]

So we can rewrite the expression as:

[tex]\frac{3 + 5\sqrt{x^2} }{4\sqrt{6x^2} - \sqrt{x} }\\\\\frac{3 + 5x}{\sqrt{96}x - \sqrt{x} }[/tex]

And we can't simplify the equation anymore than that, so we stop there.

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Answer:

for $5 plan if he rents 47 dvd it will pay 47% as one DVS cost 1 $ .

Step-by-step explanation:

3 yards 5 feet 6 inches X 7 is 33.833333 yards. The correct option is K- none of these.

First step

One yard is 36 inches hence:

3 yards 6 inches=(36 inches×3)+6 inches

3 yards 6 inches=108 inches+6 inches

3 yards 6 inches=114 inches

Second step

5 Feet to inches=5 ft×12

5 feet to inches=60 inches

Third step

Yards=[(114 inches+60 inches)×7]/ 36 inches

Yards=(174 inches×7)/ 36 inches

Yards=1,218 /36 inches

Yards=33.833333

Therefore the correct option is K- none of these.

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spanish 45 kilis la respuesta seria que los yolander son 53kilos

Step-by-step explanation:

b is the answer y=50+12x/x

As we can get the information

the registration fee is fixed, but the dues is

increased with the Month.

so the average monthly cost

answer y=50+12x/x

Answer:

If the angle degree and size of triangle are similar or same, it is depicted as congruent.

Answer:

44ft^2

Step-by-step explanation:

Break the shape into 3 rectangles, two 3 by 2's and one 4 by 8. (Get 4 by subtracting 3 from 7 for the left and right most side)

3 x 2 = 6 ft^2

since there's two rectangles you end up 6 + 6 so you get 12 ft^2

then 4 x 8 = 32 ft^2

add 32 and 12, get 44 ft^2

Answer:

108

Step-by-step explanation:

x and 2/3 x are linear pair angles.

Sum of linear pair angles is 180.

x + 2/3 x = 180

3x/3 + 2x/3 = 180

( 3x + 2x )/3 = 180

5x/3 = 180

Cross multiply,

5x = 180 * 3

Divide 5 on both sides,

x = ( 180 * 3 )/5

  = 36 * 3

x = 108

Answer:

  π = C/(2r)

Step-by-step explanation:

The equation that relates the circumference of a circle to the radius is ...

  C = 2πr

__

We can divide both sides of the equation by 2r to get an expression for π.

  [tex]C=2\pi r\\\\\dfrac{C}{2r}=\dfrac{2\pi r}{2r}\\\\\boxed{\pi=\dfrac{C}{2r}}[/tex]