An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The equation

2000007 350 represents the situation, where t is the number of years the money has been invested. About how long has the

money been invested? Use a calculator and round your answer to the nearest whole number

5 years

7 years

19 years

22 years

Answer: $400

Step-by-step explanation:

Discount = 15%

The original price/value of an item is always 100%

So selling price (%) = original price - discount = 100%-15% = 85%

We got selling price as 85%

This implies that 85% = 340

Let's find 1% first, then 100%

1% = 340÷85 = 4

100% = 4 × 100 = $400

The usual (normal/original) price is $400

Juan sold a bicycle at a discount of 15% if the selling price was $340 then the usual price of the bicycle was $400.

percentage, a relative value indicating hundredth parts of any quantity.

Let's represent the usual price of the bicycle by P.

Since Juan sold the bicycle at a discount of 15%, the selling price (S) would be 85% of the usual price (P).

We can express this relationship as an equation:

S = 0.85P

We also know that the selling price of the bicycle was $340.

Substituting S = $340 into the equation above, we get:

$340 = 0.85P

To find P, we can solve for it:

P = $340 / 0.85

P = $400

Therefore, the usual price of the bicycle was $400.

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No, the inference is not valid because it excluded those who were not online and so did not see the poll.

To improve the poll, the news show could have conducted it in a more representative manner by surveying a larger sample of people from a variety of backgrounds

The poll's results may have been influenced by various factors, including but not limited to the order in which the comedians were presented, the demographics of the respondents, and the fact that it was conducted online, possibly excluding those without internet access. Overall, the poll's representative accuracy is questionable.

To enhance the accuracy of the survey, the broadcast could have implemented a more inclusive method by polling a wider range of individuals from diverse backgrounds. An alternate method for conducting the poll would have been by personal or telephonic means, enabling individuals without internet connectivity to participate.

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The slope of the line passing through points A and B is 1/3.

The formula for the slope of a line to find the slope passing through points A and B. The formula is:

slope = (change in y) / (change in x)

Let's label the coordinates of point A as (x₁, y₁) and the coordinates of point B as (x₂, y₂).

Then, substitute the values and calculate the slope:

slope = (y₂ - y₁) / (x₂ - x₁)

slope = (3 - 2) / (3 - 0)

slope = 1 / 3

Therefore, the slope of the line passing through points A and B is 1/3.

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Answer:

62%

Step-by-step explanation:

31/50 is also equal to 62/100 (if we multiply the numerator and denominator by 2). 62/100 is 62%.

Answer:

62%

Step-by-step explanation:

31/50=0.62.

0.62 as a percent would be 62%

The correct transformation is Horizontal Compression, Left 1 , Up 2.

What is transformation?

An operation that manipulates a polygon or other two-dimensional object on a plane or coordinate system is known as a transformation.

The shape in two dimensions before any alteration is known as a pre-image or inverse image. The shape after transformation is the image.

Given: \(f(x)=\sqrt{3x+3} +2\)

The parent function of given function is square root function.

\(f(x)=\sqrt{x}\)

Shift 1 unit left

\(f(x)=\sqrt{(x+1)}\)

Horizontal Compression

\(f(x)=\sqrt{3(x+1)}\)

Vertical up by 2 units

\(f(x)=\sqrt{3x+3}+2\)

Hence, the parent function \(f(x)=\sqrt{x}\), horizontally shrink by a factor of 3 , shift 1 unit to the left, shift 2 units upwards.

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Question: Given the function,\(f(x)=\sqrt{3x+3} +2\), choose the correct transformation(s).

Answer:

y=2/15

Step-by-step explanation:

8+(6/y)=53

We move all terms to the left:

8+(6/y)-(53)=0

Domain of the equation: y)!=0

y!=0/1

y!=0

We add all the numbers together, and all the variables

(+6/y)+8-53=0

We add all the numbers together, and all the variables

(+6/y)-45=0

We get rid of parentheses

6/y-45=0

We multiply all the terms by the denominator

-45*y+6=0

We add all the numbers together, and all the variables

-45y+6=0

We move all terms containing y to the left, all other terms to the right

-45y=-6

y=-6/-45

y=2/15

hope this helps.

Answer:

165

Step-by-step explanation:

divide calories by grams to find COP and then multiply that by 42.6 to get 165 calories

Answer:

b. 5 meters

Step-by-step explanation:

1 meter = 1000 millimeters

5 meter = 5000 millimeters

Which is longer 5 meters or 400 millimeters?

5000 > 400

So, the answer is b. 5 meters.

x and y are the variables.

In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation are called variables. Commonly used variables are X, Y, and Z.

Hey! Your rational number would be \(\sqrt{4}\)

Let the number of children attended be c;

Let the number of adults attended be a;

and let the number of students that attended be s;

Then;

But there are half as many adults as there are children, then;

By substituting equation 3 in equation 1 and equation 2, we have;

Solving equation 4 and equation 5 simultaneously, we have;

Then, we substitute the value of a and s in equation 1 to get the value of c;

154 children attended

74 students attended

77 adults attended.

Answer:

a) Total number of ways can the letters of the word MINUTES be arranged in a row = 5040

b) Total number of ways in which M and I must remain next to each other =  1440

Step-by-step explanation:

To find - Refer to the solution to Exercise 9.3.11 to answer the following

              questions.

             (a) How many ways can the letters of the word MINUTES

                   be arranged in a row?

             (b) How many ways can the letters of the word MINUTES

                   be arranged in a row if M and I must remain next to each

                   other as either MI or IM?

Proof -

a)

Given that , the word is - MINUTES

We can see that all the words are different.

So, Total number of ways they can arrange in a row = 7!

                                                                                  = 7×6×5×4×3×2×1

                                                                                  = 5040

⇒Total number of ways can the letters of the word MINUTES be arranged in a row = 5040

b)

Given word is - MINUTES

Given that , M and I must remain next to each other

So, treat them as 1 word

If IM appears then

Total number of words = 6

So, they can arrange in 6! ways

Also,

MI appears then

Total number of words = 6

So, they can arrange in 6! ways

∴ we get

Total number of ways in which M and I must remain next to each other = 6! + 6! = 720 + 720 = 1440

⇒Total number of ways in which M and I must remain next to each other =  1440

Answer:

  y = 2^-x

Step-by-step explanation:

The graph appears to be a decaying function with a horizontal asymptote of 0. This matches an exponential function with a negative exponent.

  y = a·b^-x

The y-intercept is 1, so the function multiplier is 1.

The value at x=-1 is 2, so the base of the exponent could be 2. (at x=-2, the value is 4, confirming this choice)

The function appears to be ...

  y = 2^-x

Answer:

C. F(x) = 1/(x+7)(x-3)

Step-by-step explanation:

How do I solve this ?

Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

Answer: There is a small relationship between IQ an productivity.

Step-by-step explanation:

Given: The correlation between employee IQ and productivity in a factory is .12.

Null hypothesis : There is no relationship between employee IQ and productivity.

Alternative hypothesis : There is relationship

between employee IQ and productivity.

Since, p < .01 , where 0.01 is the significance level.

So, we reject the null hypothesis.

That means, there is a relationship between employeeIQ and productivity.

Since correlation coefficient is near to 0, so it represent weak correlation.

Conclusion: There is a small relationship between IQ an productivity.

Answer:

3x²-2x+1=?

3(4²)-2(4)+1=?

3(16)-8+1=?

48-8+1=?

40+1=41

The values of x for which f(x) = 7 are x = 61 and x = 21.

To find the values of x for which f(x) = 7, we can set up the equation and solve for x.

The given function is f(x) = 0.5|x - 41| - 3.

Setting f(x) equal to 7, we have:

0.5|x - 41| - 3 = 7.

First, let's isolate the absolute value term:

0.5|x - 41| = 7 + 3.

0.5|x - 41| = 10.

To remove the absolute value, we can consider two cases:

Case: (x - 41) is positive or zero:

0.5(x - 41) = 10.

Multiplying both sides by 2 to get rid of the fraction:

x - 41 = 20.

Adding 41 to both sides:

x = 61.

So x = 61 is a solution for this case.

Case: (x - 41) is negative:

0.5(-x + 41) = 10.

Multiplying both sides by 2:

-x + 41 = 20.

Subtracting 41 from both sides:

-x = -21.

Multiplying both sides by -1 to solve for x:

x = 21.

So x = 21 is a solution for this case.

Therefore, the values of x for which f(x) = 7 are x = 61 and x = 21.

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Answer:

the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis is;

\(\frac{\pi }{2} [e^2 - 1 ]\)  or 10.036

Step-by-step explanation:

Given the data in the question;

y = \(y = e^{(x - 1 )\), y = 0, x = 1, x = 2.

Now, using the integration capabilities of a graphing utility

y = \(y = e_2}^{(x - 1 )_\), y = 0

Volume = \(\pi \int\limits^2_1 ( e^{x-1)^2} - (0)^2 dx\)

Volume = \(\pi \int\limits^2_1 ( e^{x-1)^2 dx\)

Volume = \(\pi \int\limits^2_1 e^{2x-2}dx\)

Volume = \(\frac{\pi }{e^2} \int\limits^2_1 e^{2x}dx\)

Volume = \(\frac{\pi }{e^2} [\frac{e^{2x}}{2}]^2_1\)

Volume = \(\frac{\pi }{2e^2} [e^4 - e^2 ]\)  

Volume = \(\frac{\pi }{2} [e^2 - 1 ]\)  or 10.036

Therefore, the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis is;

\(\frac{\pi }{2} [e^2 - 1 ]\)  or 10.036

Answer:

1:

Step-by-step explanation:

The x-intercepts of the given equation 4x^2-12x+4 is -3/2

What is Quadratic equation ?

Quadratic equation can be defined as the equation in which it is in the form of ax^2+bx+c = 0

where c is a constant.

Given equation ,

y = 4x^2+12x+4

so we have to find the x-intercept , make y = 0

and we have to solve for the given quadratic equation

so,

we get

4x^2+12x+4 = 0

(2x)^2 + 9 + 12x = 0

(2x+3)^2 = 0

x = -3/2

There is double root unique intercept or tangent at  x  = -3/2

Therefore, The x-intercepts of the given equation 4x^2-12x+4 is -3/2

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Answer:

Step-by-step explanation:

Ronald's walking speed is 3 miles per hour, and he walks for 2 hours, so he covers 3 * 2 = 6 miles. In the next hour, he runs at a speed of 6 miles per hour, covering an additional 6 miles. Therefore, Ronald traveled a total of 6 + 6 = 12 miles.

Answer:

Step-by-step explanation:

What are the other colors?

if there are two colors ( red and another color ) then the probability of the pointer landing on red will be 1/2

similarly if there are 3 colors ( red and two other colors) then the probability of the pointer landing on red will be 1/3 ....

depends on how many colors are there

Answer:

Answer:

8/12

Step-by-step explanation:

Answer:

Using the slope-intercept form, the y-intercept is 7

Step-by-step explanation:

Answer: y=7-3x/2      3x/2 is seen as a fraction

Step-by-step explanation:

Move all the terms that don’t contain y to the right and then solve

Answer:

  660 in²

Step-by-step explanation:

The area of this figure looks like it is best computed by subtracting the areas of the empty corners from the area of the "bounding box."

The overall dimensions of the figure are ...

  horizontal: 31 in + 10 in = 41 in

  vertical: 13 in + 7 in = 20 in

Then the area of the bounding box is ...

  A = LW = (41 in)(20 in) = 820 in²

__

The area of the upper left empty space is ...

  A = (6 in)(5 in) = 30 in²

The area of the lower right empty space is ...

  A = (10 in)(13 in) = 130 in²

Then the area of the figure is ...

  total shaded area = (820 -30 -130) in² = 660 in²

__

Additional comment

The formula for the area of a rectangle is ...

  A = LW . . . . . . where L is the length, and W is the width

Solution:

Draw the whole rectangle.

Refer to image~

Subtract the area of the unshaded region from the rectangle's area.

Answer:

Yes

Yes

No

Step-by-step explanation:

Given value x = -2;

    Problem, is the expression a positive number ?

A. -2(x - 2)

  if x = -2

     -2(-2 - 2)

     = -2 (-4)

     = 8

Yes

B.  -3x(5 - 4x)

   if x = -2

     -3 x -2(5  - 4(-2))

    = 6 (5 + 8)

     = 6 x 13

     = 78

Yes

C. x + 6x

if x = -2

    -2 + 6(-2)

   = -2 - 12

   = - 14

No

2. The transformations are given as follows:

3. The transformations are given as follows:

For item 2, the transformations in this problem are given as follows:

For item 3, the transformations are given as follows:

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Answer:

a

The 95% confidence interval is   \(0.5753<  p <0.62474\)  

b

 This 95% confidence interval tell us that there 95% confidence that the true proportion of adults in the US that now believe life imprisonment is a better approach for punishing murder lies within the interval

c

 The margin of error is   \(E =    0.02474 \)  

d

 The confidence interval becomes wider

Step-by-step explanation:

From the question we are told that

   The sample size is  n = 1506

    The sample proportion is  \(\^ p = 0.60\)

From the question we are told the confidence level is  95% , hence the level of significance is    

      \(\alpha = (100 - 95 ) \%\)

=>   \(\alpha = 0.05\)

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } =  1.96\)

Generally the margin of error is mathematically represented as  

     \(E =  Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } \)

=>   \(E =    1.96 * \sqrt{\frac{0.60 (1- 0.60)}{1506} } \)    

=>   \(E =    0.02474 \)  

Generally 95% confidence interval is mathematically represented as  

      \(\^ p -E <  p <  \^ p +E\)

=>   \(0.60 - 0.02474 <  p <0.60 + 0.02474\)  

=>   \(0.5753<  p <0.62474\)  

This 95% confidence interval tell us that there 95% confidence that the true proportion of adults in the US that now believe life imprisonment is a better approach for punishing murder lies within the interval

Generally the level of confidence varies directly with the critical value of \(\frac{\alpha }{2}\) and this in turn varies directly with the margin of error which when sample proportion is constant it determines the width of the confidence interval so when the level of confidence increases the confidence interval becomes wider