From 1960 to 2010, a certain money stock measure was growing at the rate of approximately 43e(1/2)x billion dollars per decade, where x is the number of decades since 1950. Find the total increase in the money stock measure from 1960 to 2010. (Round your answer to the nearest billion dollars.)

Answer:

5 4/5

Step-by-step explanation:

29 ÷ 5 = 5

29 - 25 = 4

Since 5x5 is 25 and we have 4 as a remainder we put it over the original denominator 5.

I really hope this helps.

29/5 as a mixed number is 5 and 4/5.

To convert the indecorous bit29/5 into a mixed number.

First, divide the numerator( 29) by the denominator( 5) and express the result as a whole number and a bit.

Now, 29 divided by 5 equals 5 with a remainder of 4.

The quotient( 5) becomes the whole number part of the mixed number, and the remainder( 4) becomes the numerator of the bit part, while the denominator remains the same.

Thus, 29/5 as a mixed number is 5 and 4/5.

Learn more about Mixed Fraction here:

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Answer:

The principal amount is $10160

Step-by-step explanation:

Given; Simple interest, I = 7620

Rate, R = 6.25

Time, T = 12

Principal, P =?

The formula for simple interest, I is;

[tex]I = \frac{PRT}{100}[/tex]

Making P the subject of formula;

[tex]P = \frac{I100}{RT}[/tex]

[tex]P = \frac{7620 *100}{6.25*12}[/tex]

[tex]P = \frac{762000}{75}\\P = 10160[/tex]

Therefore, the principal amount is $10160

Answer:

10000

Step-by-step explanation:

If an amount of money, P, called the principal, is invested for a period of t years at an annual interest rate r, the amount of simple interest, I, earned is given by

I=PrtwhereIPrt=interest=principal=rate=time

The following information is given.

Irt=$7,620=0.0635=12 years

Substituting the given information into the simple interest formula and solving for P gives

7,6207,620=(P)(0.0635)(12)=0.762P

Dividing both sides by 0.762, we have

P=7,6200.762=10,000

Thus, the principal amount of the bond was $10,000.

Answer:

Solution,

____________________________

Men ------------------------------ Days

_____________________________

In case of indirect proportion,

4/6= 6/X

or, 6*X= 6*4 ( cross multiplication)

or, 6x= 24

or, 6x/6= 24/6 ( dividing both sides by 6)

Hope this helps...

Good luck on your assignment..

Answer:

[tex]\boxed{4 days}[/tex]

Step-by-step explanation:

M1 = 4

D1 = 6

M2 = 6

D2 = x (we've to find this)

Since,  it is an inverse proportion (more man takes less days for the work to complete and vice versa), so we'll write it in the form of

M1 : M2 = D2 : D1

4 : 6 = x : 6

Product of Means = Product of Extremes

=> 6x = 4*6

=> 6x = 24

Dividing both sides by 6

=> x = 4 days

Options :

(A.) y=558-273x (B.) y=264+142x (C.) y = 55.8 +2.79x (D.) y= -26.4-1.42x

Answer:

C.) ŷ = 2.79X + 55.8

Step-by-step explanation:

Given the data:

cost (x): 9 2 3 4 2 5 9 10

Number of products sold: 85 52 55 68 57 86 83 73

Using the online regression calculator to generate a linear regression plot of the given data: the model obtained is given below

ŷ = 2.79X + 55.8

With y being the predicted or dependent variable

Slope or gradient of the line = 2.79

X = the independent variable

55.8 = the intercept.

Answer:

Step-by-step explanation:

It doesn't always work to choose the largest possible square first.

a. 15 = 9 + 4 + 1 + 1 = 3² +2² +1² +1²

b. 24 = 16 + 4 + 4 = 4² +2² +2²

c. 33 = 25 + 4 + 4 = 5² +2² +2²

d. 624 = 484 +100 +36 +4 = 22² +10² +6² +2²

Answer:

Option B - There is at least some difference in the average times spent by the two groups in the mall.

Step-by-step explanation:

A null hypothesis is a hypothesis that states that there is no statistical significance between the two variables. Thus, It is usually the hypothesis that a researcher or experimenter will try to disprove or discredit. While an alternative hypothesis is one that states there is a statistically significant relationship between two variables.

Now, applying these definitions to the question, we can see that;

Null Hypothesis is;

H0; There is no difference in the average times spent by the two groups in the mall

While the alternative hypothesis is;

Ha; There is at least some difference in the average times spent by the two groups in the mall

Thus, correct answer is option B

Answer:

It is option b

Step-by-step explanation:

Answer:

  -0.4

Step-by-step explanation:

Since x=4 is not a critical point, you can simply evaluate the function. You can do this in your head.

  (2√4 -6)/(9 -4) = (2·2 -6)/5 = -2/5 = -0.4

Answer:

The product of 5/ 12 and –420 should have been the value of x.

Answer: D

Step-by-step explanation:

Took the test

Answer:

(a) 2 white & 1 red ball = 42 ways

(b) All 3 white balls =  4 ways

(c) All 3 red balls = 35 ways

Step-by-step explanation:

An urn contains 4 white balls and 7 red balls. Three balls are selected.

In how many ways can the 3 balls be drawn from a total of 11 ​balls:

​(a) If 2 balls are white and 1 is​ red?

The 2 white balls can be selected in ⁴C₂ ways

The 1 red ball can be selected in ⁷C₁ ways

2 white & 1 red ball = ⁴C₂ × ⁷C₁

2 white & 1 red ball = 6 × 7

2 white & 1 red ball = 42 ways

​(b) If all 3 balls are​ white?

The 3 white balls can be selected in ⁴C₃ ways

The 0 red ball can be selected in ⁷C₀ ways

All 3 white balls = ⁴C₃ × ⁷C₀

All 3 white balls =  4 × 1

All 3 white balls =  4 ways

​(c) If all 3 balls are​ red?

The 3 red balls can be selected in ⁷C₃ ways

The 0 white ball can be selected in ⁴C₀ ways

All 3 red balls = ⁷C₃ × ⁴C₀

All 3 red balls = 35 × 1

All 3 red balls = 35 ways

Answer:

The number of possible combinations of sports and instrument that Anja can select is 12.

Step-by-step explanation:

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

[tex]{n\choose k}=\frac{n!}{k!\cdot(n-k)!}[/tex]

It is said that Anja can choose one sport to play and one instrument to learn using the list below:

Sports: softball, basketball, tennis, or swimming

Instruments: guitar, piano, or clarinet​.

There 4 options for sports and 3 for an instrument.

Compute the number of ways to select one sport to play as follows:

[tex]n (S)={4\choose 1}=\frac{4!}{1!\cdot(4-1)!}=\frac{4!}{3!}=\frac{4\times3!}{3!}=4[/tex]

Compute the number of ways to select one instrument to learn as follows:

[tex]n(I)={3\choose 1}=\frac{3!}{1!\cdot(3-1)!}=\frac{3!}{2!}=\frac{3\times2!}{2!}=3[/tex]

Compute the number of possible combinations of sports and instrument that Anja can select as follows:

Total number of possible combinations = n (S) × n (I)

                                                                  [tex]=4\times 3\\=12[/tex]

Thus, the number of possible combinations of sports and instrument that Anja can select is 12.

Answer:

12

Step-by-step explanation:

Answer:

Hope this helps you

Answer: 136

Step-by-step explanation:

An= A1+(n-1)d

A1=16, d=8, and n=16

A16= 16 +(16-1)(8)

A16= 16(15)(8)

A16= 16+120

A16=136

Hey there! :)

Answer:

f(16) = 136 seats.

Step-by-step explanation:

This situation can be expressed as an explicit function where 'n' is the row number.

The question also states that the number of seats increases by 8. Use this in the equation:

f(n) = 16 + 8(n-1)

Solve for the number of seats in the 16th row by plugging in 16 for n:

f(16) = 16 + 8(16-1)

f(16) = 16 + 8(15)

f(16) = 16 + 120

f(16) = 136 seats.

Answer:

32.38 square m

Step-by-step explanation:

Diameter of semicircle = 5 m

Hence, radius = 5/2 = 2.5 m

Area of figure = Area of rectangle - 2 times area of one semicircle

[tex] = l \times b - 2 \times \frac{1}{2} \pi {r}^{2} \\ \\ = 10.4 \times 5 - \pi {r}^{2} \\ = 52 - 3.14 \times {(2.5)}^{2} \\ = 52 - 3.14 \times 6.25 \\ = 52 - 19.625 \\ = 32.375 \\ \approx 32.38 \: {m}^{2} \\ [/tex]

Answer:

5 1/4

Step-by-step explanation:

5 is the whole number so we up it aside.

Then we are left with 25/100,when we simplify that 25 into 25 is 1.

25 into 100 is 4 times.

Therefore we are left with 1/4.

I hope this helps :)

Answer:

5 1/4 because 1/4=25 and not only that u could do 5 25/100 and simplfy and u get 5 1/4

Step-by-step explanation:

Answer:

x = -2.47, 0.47

Step-by-step explanation:

Easiest and quickest way to do this is to graph the quadratic and analyze for x-intercepts.

Alternatively, we have to use the Quadratic Formula because we cannot factor the expression.

Answer:

2

Step-by-step explanation:

Answer:

I hope it will help you....

Answer:

1. V = 15.95 (to 2 decimal places)

2. V = 107.23 (to 2 decimal places)

3. V = 560.25 (to 2 decimal places)

Step-by-step explanation:

1. y = ln 5x, y = 2, y = 3, x = 0; about the y-axis

Find volume using the disk method.

First find inverse of y=ln(5x)

5x = exp(y)

x(y)=exp(y)/5

Width of each strip = dy

length of each strip = x(y)

volume of each disk by rotation of strip about y=axis

dV = 2*pi*x(y)dy

total volume  

V = integral (dV) for y=2 to 3

= integral (2*pi*e^y/5) for y=2 to 3

= 2*pi*(e^y/5) for y=2 to 3

= 2pi(e^3-e^2)/5

= 15.95 (to 2 decimal places)

2. y2 = 2x, x = 2y; about the y-axis

Find point of intersection between  

solve y^2/2 = 2y  =>  y=4, x=2y=8, therefore

intersection is at (8,4), which is the upper integration limit

Using the disk method again

Volume of each disk

dV(y) = pi((2y)^2-(y^2/2)^2)dy

Total volume of solid  

V = integral(pi((2y)^2-(y^2/2)^2)dy) for y=0 to 4

= pi (4y^3/3 - y^5/20)  for y = 0,4

= pi (256/3 - 1024/20)

= 512pi/15

= 107.23 (to 2 decimal places)

3. y = x, y = 0, x = 2, x = 7; about x = 1

Use the shell method.

volume of each shell formed by roatation of a vertical strip about the axis of rotation (x=1)

dV = 2*pi*(x-1)*(y*dx)

Total volume of rotation

V = integral(2*pi*(x-1)*y dx for x=2 to 7

= 535pi/3

= 560.25 (to 2 decimal places)

=============================================================

How I got that answer:

We have gone from 54 websites to 793 websites. This is a change of 793-54 = 739 new websites. This is over a timespan of 2004-1995 = 9 years.

Since we have 739 new websites over the course of 9 years, this means the rate of change is 739/9 = 82.1111... where the '1's go on forever. Rounding to the nearest whole number gets us roughly 82 websites a year.

----------

You could use the slope formula to get the job done. This is because the slope represents the rise over run

slope = rise/run

The rise is how much the number of websites have gone up or down. The run is the amount of time that has passed by. So slope = rise/run = 739/9 = 82.111...

In a more written out way, the steps would be

slope = rise/run

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

slope = (793 - 54)/(2004 - 1995)

slope = 739/9

slope = 82.111....

Answer:

0

Step-by-step explanation:

y = 3 × 6x

0 = 3 × 6x

0 = 18x

18x = 0

x = 0

Hope this helps! :)

Answer:

  5√3 ft/s

Step-by-step explanation:

Let h represent the horizontal distance of the kite from the person. Let s represent the string length. Then the Pythagorean theorem tells us ...

  s^2 = 100^2 + h^2

  2s·ds/dt = 0 + 2h·dh/dt

  ds/dt = (h/s)·dh/dt

So, we need to know the horizontal distance when s=200.

  200^2 = 100^2 + h^2

  40000 -10000 = h^2

  h = 100√3

Substituting known values into the equation for ds/dt, we have ...

  ds/dt = (100√3)/(200)(10 ft/s) = 5√3 ft/s

The string must be let out at 5√3 ft/s when it is already 200 ft long.

Answer:

This Statement is True.

Check Explanation for why it is true.

Step-by-step explanation:

The sampling distribution of sample means arises when random samples are drawn from the population distribution and their respective means are computed and put together to form a distribution. Hence, the curve of this sampling distribution of sample means will show how the sample means are distributed. Hence, this statement is true.

Hope this Helps!!!

Answer:

[tex] n = (\frac{2.326*1.7}{0.3})^2= 173.73[/tex]

And the value for n rounded up would be n = 174

Step-by-step explanation:

We have the following info given:

[tex] s= 1.7[/tex] previous estimation for the deviation

[tex] ME=0.03[/tex] the margin of error desired

[tex] Conf =0.98[/tex] represent the confidence

The Margin of error is given by:

[tex] ME = z_{\alpha/2} \frac{\sigma}{\sqrt{n}}[/tex]

If we solve for the value of n we got:

[tex] n= (\frac{z*\sigma}{ME})^2[/tex]

For this problem we know that the confidence is 98% so then the significance level would be [tex]\alpha=0.02[/tex] and the critical value would be:

[tex] z_{\alpha/2}= 2.326[/tex]

And replacing we got:

[tex] n = (\frac{2.326*1.7}{0.3})^2= 173.73[/tex]

And the value for n rounded up would be n = 174

Answer:

12 boys

Step-by-step explanation:

From the above question:

Number of boys = 3

Number of girls = 2

Boys: Girls

3:2

Let :

a = boys

b = girls

Hence, a : b = 3 : 2

a/b = 3/2  

Cross Multiply

2a = 3b .......... Equation 1

a = 3b/2

If four more girls join the class, there will be the same number of boys and girls

Hence,

a: b + 4 = 3 : 3

a/b + 4 = 3/3

Cross Multiply

3a = 3(b + 4)

3a = 3b + 12 ........ Equation (2)

From Equation 1: a = 3b/2

Substitute 3b/2 for a in Equation 2 we have:

3a = 3b + 12 .........Equation 2

3(3b/2) = 3b + 12

9b/2 = 3b + 12

Cross Multiply

9b = 2(3b + 12)

9b= 6b + 24

9b - 6b = 24

3b = 24

b = 8

Substitute 8 for b in Equation 1

a = 3b/2

a = 3 × 8/2

a = 24/2

a = 12

Therefore, the number of boys in the class is 12

Answer:

Step-by-step explanation:

[tex]\frac{14}{x} =14/x[/tex]

Thus, we can multiply both sides by x to get 14=0.  Because 14 does not equal 0, the equation has no solutions.  A value of x that makes the equation false is 541, which makes the simplified equation turn into 14=0.

Another value of x that makes the equation false is 7, which makes the simplified equation turn into 14=0.

Hope it helps <3

Replace x with 2 and solve:

2^2 + 4(2) = 4 + 8 = 12

Replace x with 3 and solve:

3^2 + 4(3) = 9 + 12 = 21

The difference between the two answers is : 21 -12 = 9

The difference between the two inputs is 3-2 = 1

The rate of change is the change in the answers I’ve the change in the inputs:

Rate of change = 9/1 = 9

Answer:

Step-by-step explanation:

A=pi*r^2

A=3.14*4.2^2

A=3.14*17.64

A=55.3896

A≈55.39 units ^2

Answer:

55.42

Step-by-step explanation:

So since we know that how you calculate a circle's area is the formula -->

π (r)^2 (r is radius), We can simply just plug all the numbers in -->

3.14 (4.2)^2 => 4.2 squared is 17.64 => 3.14 (17.64) = around 55.417 but since we want to round it to the nearest hundred, we get 55.42

Hope this helps!

Answer:

She can cut 122 pieces.

Step-by-step explanation:

She has 3 pieces of ribbon that are 25 yds long. In total, she has 75 yds, which is equal to 2700 in. Erika needs 22 in. pieces, so just divide 2700 by 22 to get your number.

2700/22 ≈ 122.72

Answer:

2.5 mg

Step-by-step explanation:

.5 x 5 = 2.5