Nathaniel invested $2,900 in an account paying an interest rate of 5.4% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 11 years?

Points of interval A (-1,-3) and (-2,-6)

Points of interval B is (1,1) and (2,-1)

How to find Piecewise function?

Determine which of the following intervals (or inequalities) the input belongs to before evaluating a piecewise function at any given input. The function specification for that specific interval can then simply be updated to reflect the new input.

[tex]f(x)=\left \{ {{3x, if x\leq -1} \atop {-2x+3, if 0 < x < 4}}\atop {2, if x\geq 4}\right.[/tex]

lets take 3x as Interval A

-2x+3 as interval B

and 2 as interval C

Now lets calculate the interval A

f(x)=3x

as x≤-1

∴f(-1) = 3(-1)

       =(-3)

∴ point is (-1,-3)

∴f(-2) = 3(-2)

       =(-6)

∴ point is (-2,-6)

Now lets calculate the interval B

f(x)=-2x+3

as 0<x<4

∴f(1) = -2(1)+3

       =-2+3

      =1

∴ point is (1,1)

∴f(2) = -2(2)+3

       =-4+3

       = -1

∴ point is (2,-1)

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The linear equation to represent the hours that Yuson has left to do after x days is 16 - 2x.

From the information, Yuson has to do Y hours of community service.

She works two hours every day, so service hours in x days = 2x

Remaining service hours after x days = y-2x

Also we have after 8 days , Yuson has completed half of her required community serivice. Therefore,

8 = y/2.

Cross multiply

y = 16

So the linear equation is 16-2x.

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Work Shown:

[tex]\text{x} = 0.\overline{63}[/tex]

x = 0.63636363...

100x = 63.63636363...

100x - x = (63.63636363...) - (0.63636363...)

99x = 63

x = 63/99

x = (7*9)/(11*9)

x = 7/11

This table shows a few fractions equivalent to 7/11

[tex]\begin{array}{|c|c|} \cline{1-2}\text{Multiply top} & \\ \text{and bottom by} & \text{Equivalent fraction}\\\cline{1-2}2 & 14/22\\\cline{1-2}3 & \boldsymbol{21/33}\\\cline{1-2}4 & \boldsymbol{28/44}\\\cline{1-2}5 & 35/55\\\cline{1-2}6 & 42/66\\\cline{1-2}\end{array}[/tex]

The terms in bold are the two answers

In other words, 7/11 = 21/33 when multiplying top and bottom by 3.

Also, 7/11 = 28/44 when multiplying top and bottom by 4.

To confirm those answers, use a calculator to find that

7/11 = 0.636363...

21/33 = 0.636363...

28/44 = 0.636363...

To rule out the non-answers, use the calculator to find that

14/21 = 0.667 approximately

7/12 = 0.5833 approximately

Answer:

can i have more info?

Step-by-step explanation:

The order of the quotient from smallest to largest is given as follows:

42.6/70, 426/70, 42.6/0.07, 42.6/0.07.

A quotient is given by the division of two terms a and b, that is:

a / b.

From this, we have that the dividend a and divisor b are inverse proportional, that is:

There are three divisions with the same term a, hence they are ordered, from smallest to largest, as follows:

42.6/70, 42.6/0.07, 42.6/0.07.

(the smallest the value of b, the largest the quotient).

The final quotient is:

426/70.

Dividing by 10 to have an equivalent value of a, we have that:

426/70 = 42.6/7.

Which is the second largest value of b, hence the second smallest quotient.

The problem is given by the image shown at the end of the answer.

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Answer:

200 miles

Step-by-step explanation:

if its 40 miles per hour then multiply 5 with 40 and you'll end up with 200 miles

Answer:

1000-400=600km

good luck i hope it helped, its all about reading the graph!

The probability that the sample standard deviations exceeds 3.5 hours more than 0.95 is 0.23 < 0.95 ..

The numbers of hours spent on watching television by a student in a weak before is normally distributed.

We have provide the following details, standard

deviations of sample ( Number of hours in weak) (σ) = 4.5 hours

sample size (n) = 30

we shall compute the mean and variance of sample .

The E of s squared is equal to 4.5 squared. The variance of S squared is equal to twice the square of sigma divided by 1, which is 30 minus 1, which is 28.6, 28.2817. The chi-square distribution here has 29 degrees of freedom, which equals 29 squared to 4.5 squared. We want to find probabilities greater than 90 because the standard deviation of our sample is greater than 3.5 hours. The probability that S squared is greater than 3.5 is The probability that chi-square with 29 degrees of freedom is greater than

17. 54321 is very high. This is the same as zero.

This is equal to 1 minus the probability that 29 degrees of freedom chi-square is greater than 51 points 5556, which is what we want for part B. we are given one Probability will be zero.

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#Complete question

The number of hours spent watching television by students in the week before final exams has a normal distribution with a standard deviation of 4.5 hours. A random sample of 30 students was taken.a. Is the probability more than 0.95 that the sample standard deviation exceeds 3.5 hours?b. Is the probability more than 0.95 that the sample standard deviation is less than 6 hours?

Answer:

The answer to your question could be either 3/2 (improper fraction), 1.5 (decimal), or 1 1/2 (mixed fraction).

Step-by-step explanation:

11/12 + 7/12 = 18/12

18/12 = 9/6

9/6 = 3/2

Answer:

y = 5x -2

Step-by-step explanation:

The 5 is the slope.  It is the change in y over the change in x.  As the x changes by 1, the y changes by 5.

The -2 is the y intercept.  This is at the point (0,-2)  The -2 is the y intercept.

Answer:

C

Step-by-step explanation:

Answer:

k=f(x)-ab^x-h

h=x-ln(f(x)/a-k/a)/ln(b)

a=f(x)/b^x-h - k/b^x-h

If $185.30 is withheld from each of Bob's paychecks, then his family's annual health insurance premium is $4817.80.

From the given information,

It was stated that the balance of the premium is deducted in equal amounts from Bob’s paycheck 26 times over the calendar year and $185.30 is withheld from each of Bob’s paychecks.

Therefore, the family’s annual health insurance premium will be calculated :

              = $185.30 × 26

              = $4,817.80

In conclusion, the correct option is $4,817.80.

therefore, his family's annual health insurance premium is $4817.80

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Answer: the slope is 1/4

Step-by-step explanation:

(2,0.5)    (4,1)

Use the formula for finding the slope:

        [tex]\boxed {The\ slope=\frac{y_2-y_1}{x_2-x_1} }[/tex]

[tex]x_1=2\ \ \ \ x_2=4\ \ \ \ y_1=0.5\ \ \ \ y_2=1\\[/tex]

Hence,

[tex]\displaystyle\\The\ slope=\frac{1-0.5}{4-2}\\\\The\ slope=\frac{0.5}{2}\\\\The\ slope=0.25\\\\The\ slope=\frac{1}{4}[/tex]

The equation of the lines passing the points and parallel to the equations ( 7,-3) , 3y = 12x + 5  (-5, -2), y + 3x = 10 is as follows:

The equation of a line can be represented in different form such as standard form, general form, slope intercept form and point slope form. Therefore, let's represent the line in slope intercept form.

The equation of a line in slope intercept form is as follows:

y = mx + b

where

Parallel line shave the same slope.

Hence,

( 7,-3) , 3y = 12x + 5

y = 4x + 5 / 3

slope is 4

The equation of the line is y = 4x + b. let's find the y-intercept using (7, -3).

-3 = 4(7) + b

b = -3 - 28

b = - 31

Hence, y = 4x  - 31

(-5, -2), y + 3x = 10

y = -3x + 10

slope = -3

Therefore, let's find y-intercept using (-5, -2)

-2 = -3(-5) + b

-2  = 15 + b

b = -2 -15

b = - 17

Therefore, y = -3x - 17.

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Number of cups of peanuts needed to make 49 cups of the mixed nuts snack is 21 cups

The ratio of cups of almonds to cups of peanuts in a mixed snack = 4 : 3

Number of of cups of almonds = 4x

Number of cups of peanuts = 3x

Total number of cups of mixed nuts snack = 49 cups

Then the equation will be

4x + 3x = 49

Add the like terms

7x = 49

x = 49 / 7

x = 7

Number of cups of almonds needed = 4x

= 4×7

= 28 cups

Number of cups of peanuts needed = 3x

= 3×7

= 21 cups

Hence, number of cups of peanuts needed to make 49 cups of the mixed nuts snack is 21 cups

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The turning point of the parabola is the point (2, - 9).

Quadratic equations represents parabolae and the vertex of the parabola represents the turning point as the slope of the curve changes its sign, from positive to negative or viceversa. The vertex can be derived by the vertex form of the equation of the parabola:

y - k = C · (x - h)²

Where:

Since the quadratic equation has two real coefficients, we need the location of two points on Cartesian plane to find one solution. First, create the system of linear equations:

b = - 5                                      (1)

5 · a + b = - 25                        (2)

Second, substitute b in (2) and clear a:

5 · a - 5 = - 25

5 · a = - 20

a = - 4

Third, write the quadratic equation:

y = x² - 4 · x - 5

Fourth, transform the equation into vertex form by completing the square:

y + 9 = x² - 4 · x + 4

y + 9 = (x - 2)²

Fifth, write the vertex of the parabola:

(h, k) = (2, - 9)

The point (2, - 9) represents the turning point of the parabola.

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The qualified student loan interest deduction in 2021 is $37500.

Adjusted gross income is an individual's total gross income less specific deductions in the United States income tax system. It is used to compute taxable income, which is AGI minus personal exemption and itemized deduction allowances. AGI is more important than gross income for most individual tax purposes.

AGI is calculated by taking your gross income and subtracting certain "above the line" deductions. 401(k) contributions, health savings account contributions, and educator expenses are common examples of deductions

As per Law, a maximum of $2,500 will be allowed to be deducted from the Income. Thus the following would be the solution.

Income of Sally Morris = $40,000

Less: Qualified student loan interest $2,500

Modified Adjusted Gross Income $37,500

The deduction is $37500.

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Answer:

third and last, can't promise that's right

The zero of the function lie between 2.5 and 3.0 and between 4.0 and 4.5

The given question is incomplete the complete question is

x      2.0    2.8    2.5    1.1    3.0   –0.8

f(x)    3.5   –1.2    4.0  –0.3  4.5     0.7

For the given table of values for a polynomial function, where must the zeros of the function lie?

A. between 2.0 and 2.5 and between 4.0 and 4.5

B. between 2.5 and 3.0 and between 4.0 and 4.5

C. between 2.0 and 2.5 and between 3.5 and 4.0

D. between 2.5 and 3.0 and between 3.5 and 4.0

answer : If a function is continuous and you have points on opposite sides of the x-axis, there must be a zero-crossing between those points. As evidenced by the table and graph,...

(3.0, 4.0) and (3.5, -0.2) 

are points on the x-axis on opposite sides. As a result, between x=3.0 and x=3.5, there must be a zero crossing.

In the same way,...

 (4.0, -0.8) and (4.5, 0.1) 

are points on the x-axis on opposite sides. As a result, between x=4.0 and x=4.5, there must be a zero-crossing.

The correct answer option includes both of these possible zero crossings.

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Answer:

3 inches

Step-by-step explanation:

Let's call the heights H1 thru H4.

So we have

H1/H2 = 24/5

H2/H3 = 1/12

Therefore if we multiply these, we have

H1/H3 = 2/5

Finally we are given

H1/H4 = 16/1.

By logic we can see that H3 is the tallest.

Thus if H3 = 10 feet, H1 = 4 feet

And from that,

H2 = 1/12 (10 feet) = 5/6 feet = 10 inches

and finally

H4 = 1/16(H1) = 1/16(4 feet) = 1/4 foot =

3 inches

Answer:

3 inches

Step-by-step explanation:

Let's call the heights H1 - H4

Here, we have

H1/H2 = 24/5

H2/H3 = 1/12

And so, we have

H1/H3 = 2/5

Finally

H1/H4 = 16/1.

Thus if H3 = 10 feet, H1 = 4 feet

And from that,

H2 = 1/12 (10 feet) = 5/6 feet = 10 inches

And last,

H4 = 1/16(H1) = 1/16(4 feet) = 1/4 foot = 3 inches

Answer:

4x+x+x+90=360

6x+90=360

6x=270

x=45

good luck!

4x+x+x+90=360

6x+90=360

6x=270

x=45

A box plot is used to study the distribution and level of a set of a set of numbers. A box plot is made up of two lines and a box. The two lines are known as whiskers.

The end of the first whisker represents the minimum number. The minimum number is the smallest number in the dataset.  The end of the second whisker represents the maximum number. The maximum number is the largest number in the dataset.

The first line to the left represents the lower (first) quartile. The second line on the box represents the median. The third line on the box represents the upper (third) quartile.

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Answer:

$7.50

Step-by-step explanation:

Answer:-2/5

Step-by-step explanation: due to them being negative we are using the simple thing of which number is closer to zero. -2/5 is closer which means that is it greater. -2/5 would be ahead on number line if you need a visualization

Answer:

-3/8

Step-by-step explanation:

1) Work out the options you are given

2) Find which one is greater

As the numbers are decimal the 'seemingly greater number' might actually be the smaller one.

To find out which decimal is greater you can easily plot them into a number line.

The number that is further to the left is smaller and the number closer to the right is higher!

If we were to plot the numbers one a number line the -0.375 would be closer to the right meaning it is greater.

HINTS:

To make it easier to divide minus numbers, at first completely forget about the minus (you can plug it back in at the end).

For example, if you were given -2/5 get rid of the minus to get 2/5 and from this we can easily figure out 2 ÷ 5 which would give us 0.4.

At the point where you have your final number you can add the - back in making it -0.4

Hope this helps, have a great day!

Answer: $1.92

Step-by-step explanation:

This is the correct answer. Have a good day