A man invests $ 16800 in savings plan that pays simple interest at a rate of 5% per annum. Find the Tim’s taken for his investment to grow to $18900

Given:

The limit problem is:

[tex]lim_{x\to -5}\dfrac{\dfrac{1}{5}+\dfrac{1}{x}}{10+2x}[/tex]

To find:

The value of the given limit problem.

Solution:

We have,

[tex]lim_{x\to -5}\dfrac{\dfrac{1}{5}+\dfrac{1}{x}}{10+2x}[/tex]

It can be written as:

[tex]=lim_{x\to -5}\dfrac{\dfrac{x+5}{5x}}{2(5+x)}[/tex]

[tex]=lim_{x\to -5}\dfrac{x+5}{5x}\times \dfrac{1}{2(5+x)}[/tex]

[tex]=lim_{x\to -5}\dfrac{1}{5x\times 2}[/tex]

[tex]=lim_{x\to -5}\dfrac{1}{10x}[/tex]

Applying limit, we get

[tex]lim_{x\to -5}\dfrac{1}{10x}=\dfrac{1}{10(-5)}[/tex]

[tex]lim_{x\to -5}\dfrac{1}{10x}=\dfrac{1}{-50}[/tex]

Therefore, the value of given limit problem is [tex]-\dfrac{1}{50}[/tex].

Answer:

36.7

Step-by-step explanation:

180 - 102.9 - 40.4= 36.7

The measure of the third angle of the given triangle after applying the angle sum property of a triangle is 36.7 degrees.

The measures of the two angles of a triangle are 102.9 and 40.4.

We need to find the measure of the third angle.

The angle sum property of a triangle states that the sum of all three interior angles of a triangle is 180 degrees.

If A, B, and C are the interior angles we have,

A + B + C = 180.

Consider the three interior angles to be A, B, and C.

We are given two angles 102.9 and 40.4.

Let  A = 102.9,  B = 40.4.

and C = angle to be measured.

Now,

Applying the angle sum property of a triangle.

We have,

A + B + C = 180

102.9 + 40.4 + C = 180

143.3 + C = 180

C = 180 - 143.3

C = 36.7 degrees.

After applying the angle sum property of a triangle we got the measure of the third angle as 36.7 degrees.

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Answer:

[tex]Pr = 0.059049[/tex]

Step-by-step explanation:

Given

[tex]p = 0.9[/tex] --- probability of scoring

Required

Probability that his first miss is his 6th shot

Let q represent the event that he did not score.

Using complement rule:

[tex]q = 1 - p = 1 - 0.9 = 0.1[/tex]

The event that his first miss is his 6th is represented as:

p p p p p q ---- That he scoress the first 5 attempts

So, the probability is:

[tex]Pr = p^5 * q[/tex]

[tex]Pr = 0.9^5 * 0.1[/tex]

[tex]Pr = 0.059049[/tex]

Answer:

2.56 * 10^11 L

Step-by-step explanation:

1 body has 40 L

Thus, the amount in 6.4 billion would be;

40 * 6.4 * 10^9

= 256 * 10^9

= 2.56 * 10^2 * 10^9

= 2.56 * 10^11 L

Answer:

Step-by-step explanation:

Solve using ratios:

Find x:

Answer:

1/3 fraction of whole paint is used by mark

Step-by-step explanation:

Mark used  1/2 out of 3/2 cans.

[tex]\frac{1}{2}[/tex] ÷ [tex]\frac{3}{2} = \frac{1}{2}*\frac{2}{3}=\frac{1}{3}[/tex]

Step-by-step explanation:

(1/2) / (1/3) = (1/2)(3/1) = 3/2 miles per hour = 1.5 miles per hour

Answer:

Step-by-step explanation:

to find the unit rate, which is what we are looking for, we have to divide the number of miles by the number of hours. Specifically:

[tex]\frac{\frac{1}{2} }{\frac{1}{3} }[/tex] and to work this out, we bring up the bottom fraction and flip it to multiply, giving us:

[tex]\frac{1}{2}[/tex] × [tex]\frac{3}{1}[/tex] which is [tex]\frac{3}{2}[/tex] miles per hour (which is the same thing as walking a mile and a half every hour). The choice you're looking for is the one that reflects 3/2 miles per hour. (I can't see which choice it is; they're too small!)

find the DB =[tex]\displaystyle\bf \sqrt{17^2-8^2} =15[/tex]  ; now find AD=AB-DB=21-15=6  .Then                AC=[tex]\displaystyle\bf \sqrt{AD^2+CD^2} =\sqrt{6^2+8^2} =10[/tex]  

Answer:

C

Step-by-step explanation:

Using Pythagoras' identity in both right triangles

To find BD

BD² + CD² = BC²

BD² + 8² = 17²

BD² + 64 = 289 ( subtract 64 from both sides )

BD² = 225 ( take the square root of both sides )

BD = [tex]\sqrt{225}[/tex] = 15

Then

AD = AB - BD = 21 - 15 = 6

To find AC

AC² = AD² + CD²

AC² = 6² + 8² = 36 + 64 = 100 ( take the square root of both sides )

AC = [tex]\sqrt{100}[/tex] = 10 → C

Answer:

4

−

4

+

8

2

+

8

Step-by-step explanation:

Answer:

Multiplication

Amount Tom earns per hour = $7

Step-by-step explanation:

Amount Jeff earns per hour = $14

Amount Tom earns per hour = 1/2 × $14

Note: 1/2 = 0.5

Amount Tom earns per hour = 1/2

× $14

= 0.5 × $14

= $7

Amount Tom earns per hour = $7

Answer:

160°

Step-by-step explanation:

Let one angle be x

Let second angle be 8x

Sum of supplementary angles = 180°

x+ 8x = 180°

9x = 180

x = 180/9 = 20

First angle= x= 20°

Second angle = 8x = 8*20 = 160°

The sum of the 15th square number and the 5th cube number is 350.

The 15th square number will be:

15² = 15 × 15

= 225

The 5th cube number will be:

5³ = 5 × 5 × 5

= 125

The sum of the numbers will be:

225 + 125

= 350

Therefore, we get that, the sum of the 15th square number and the 5th cube number is 350.

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Answer:

Step-by-step explanation:

x : 100 = 7740 : 98 000 000

x = (7740 * 100)/98 000 000

x = 0.007898 %

A percentage is a hundredth of a number      Then                                                    [tex]\displaystyle\bf \frac{7740}{98\cdot10^6} \cdot100=\frac{387}{49000} \approx 0,00789\%[/tex]                                                      

Answer:

The answer is C 100πcm^3

Answer:

5 3 3 2 2

Step-by-step explanation:

180

90 2

45 2 2

15 3 2 2

5 3 3 2 2

Answer:

180 = 5 × 3² × 2²

Step-by-step explanation:

Starting with 180, the prime factors are in bold

180 = 90 × 2

      = 45 × 2 × 2

      = 15 × 3 × 2 × 2

      = 5 × 3 × 3 × 2 × 2

Then

180 = 5 × 3 × 3 × 2 × 2 = 5 × 3² × 2²

Answer:

(- 1, - 1 )

Step-by-step explanation:

Given the 2 equations

x = 4y + 3 → (1)

2x + y = - 3 → (2)

Substitute x = 4y + 3 into (2)

2(4y + 3) + y = - 3 ← distribute parenthesis and simplify left side

8y + 6 + y = - 3

9y + 6 = - 3 ( subtract 6 from both sides )

9y = - 9 ( divide both sides by 9 )

y = - 1

Substitute y = - 1 into (1) for corresponding value of x

x = 4(- 1) + 3 = - 4 + 3 = - 1

solution is (- 1, - 1 )

Answer:

A.

Step-by-step explanation:

4y = 12x + 16

3x = y - 4

=>

y = 3x + 4

using that in the first equation

4(3x+4) = 12x + 16

12x + 16 = 12x + 16

=> both lines/equations are identical, so they have infinitely many solutions.

Answer:

x = 6 units

Step-by-step explanation:

For θ = 30°, Perpendicular is 3. Hypotenuse is x.

We can use trigonometry to find x.

[tex]\sin(30)=\dfrac{P}{H}[/tex]

[tex]\sin(30)=\dfrac{3}{x}\\\\x=\dfrac{3}{\sin(30)}\\\\x=6[/tex]

So, the value of x is equal to 6 units.

Answer:

56 different outfits

Step-by-step explanation:

Answer: 3172

Step-by-step explanation:

Answer:

The triangles are similar.

Step-by-step explanation:

They are similar because they have the same angles. They may be the same size, but it would be best to refer to whatever definition you were given.

The correct descriptions from the list accurately describe the relationship between QRS and TUV is,

⇒ Similar

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

Two triangles are shown in figure.

Here, All the corresponding angles are same in both triangles.

And, The ratio of their corresponding sides are,

In triangle TUV;

⇒ 90 / 108 = 30 / 36

In triangle QRS;

⇒ 30 / 36

Hence, The correct descriptions from the list accurately describe the relationship between QRS and TUV is,

⇒ Similar

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Answer:

mean value of female = 10.000

standard deviation of female = 1.604

mean value of male = 10.000

standard deviation of male = 2.449

Step-by-step explanation:

Given:

n=8 females

n=8 males

The objective is to find the mean and deviation and also based on the mean and the standard deviation have to describe the differences in intelligence scores for males and females

Solution:

The mean and the standard deviation are found by using MINITAB

The MINITAB procedure is explained as follows,

Step 1

choosing start > Basic statistics > Display Descriptive Statistics

Step 2

In variables supposed to enter the columns Female and Male

Step 3

Here choosing option statistics and select Mean and standard deviation

Step 4

Finally clicking OK

MINITAB output is as follows,

variable Mean standard deviation

Female 10.000 1.604

Male 10.000 2.449

b)

From the MINITAB output the mean are same for females and males.

Here the standard deviation of females is less than the standard deviation of males. That is the male scores are more variable when compared to female scores.

Answer:

20 Lines

Step-by-step explanation:

According to the Question,

Now,  the total pairs of points which can be formed is 9

And, the line passing through 2 such points 9c2 = 9! / (2! x 7!) = 9x4 ⇒ 36

Here, We have overcounted all of the lines which pass through three points.

And, each line that passes through three points will have been counted 3c2 = 3! / 2! ⇒ 3 times

Now, the sides of the square consist of 3 points. We have counted each side thrice, so 4*2 are repeated.