You want to purchase a new car in 6 years and expect the car to cost $12,000. Your bank offers a plan with a guaranteed APR of 6.5% if you make regular monthly deposits. How
← much should you deposit each month to end up with $12,000 in 6 years?
T
You should invest $ each month
(Round the final answer to the nearest cent as needed. Round all intermediate values to seven decimal places as needed

Answer: 16

Step-by-step explanation:

there are 4 1/4 in 1 cup. so it'll be 4 cakes for each cup of oil you have. multiply the number of cakes that can be made per cup (4) by the number of cups you have (4)

(4) x (4) = 16

Answer: lower bound = 0.7404; upper bound = 0.8596

Step-by-step explanation:

The proportion p for this population:

p = \(\frac{240}{300}\)

p = 0.8

Confidence interval for proportion is calculated as:

p ± z-score.\(\sqrt{\frac{p(1-p)}{n} }\)

Z-score for a 99% confidence interval is: z = 2.58

Calculating:

0.8 ± 2.58.\(\sqrt{\frac{0.8(0.2)}{300} }\)

0.8 ± 2.58.\(\sqrt{0.00053}\)

0.8 ± 2.58(0.0231)

0.8 ± 0.0596

This means that the lower limit of this interval is 0.7404 and upper bound is 0.8596

Answer:

\(=13x+5\)

Step-by-step explanation:

\(\left(2x+9\right)+\left(11x-4\right)\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=2x+9+11x-4\\\mathrm{Group\:like\:terms}\\=2x+11x+9-4\\\mathrm{Add\:similar\:elements:}\:2x+11x=13x\\=13x+9-4\\\mathrm{Add/Subtract\:the\:numbers:}\:9-4=5\\=13x+5\)

Answer:

E(X) = 38.9346

Var(X) = 25.588

E(Y) = 38.25

Var(Y) = 26.1875

Step-by-step explanation:

Given - Four buses carrying 153 high school students arrive to Montreal. The buses carry, respectively, 36, 46, 32, and 39 students. One of the students is randomly selected.One of the 4 bus drivers is also randomly selected.

To find - Compute the expectations and variances of X and Y.

Proof -

Let us assume that,

X be The number of students that were on the bus carrying this randomly selected student.

Y denote the number of students on his bus.

Now,

E(X) =  \(\frac{36(36) + 46(46) + 32(32) + 39(39)}{153}\)

       = \(\frac{5957}{153}\)

       = 38.9346

⇒E(X) = 38.9346

Now,

E(Y) = \(\frac{36 + 46 + 32 + 39}{4}\)

      =  \(\frac{153}{4}\)

      = 38.25

⇒E(Y) = 38.25

Now,

Var(X) = \(\frac{36(36 - 38.9346)^{2} + 46(46 - 38.9346)^{2} + 32(32 - 38.9346)^{2} + 39(39 - 38.9346)^{2}}{153}\)

          = \(\frac{310.0276 + 2296.3144 + 1308.5091 + 0.1668}{153}\)

          = \(\frac{3915.0179}{153}\)

          = 25.588

⇒Var(X) = 25.588

Now,

Var(Y) = E(Y²) - [E(Y)]²

          = \(\frac{36^{2} + 46^{2} + 32^{2} + 39^{2} }{4} - (38.25)^{2}\)

          = \(\frac{5957}{4} - 1463.0625\)

          = 1489.25 - 1463.0625

          = 26.1875

⇒Var(Y) = 26.1875

Answer:

10.4

Step-by-step explanation:

√(5--5)²+(0-3)²

√100+9

√109=10.4

The set of factors used to factor the given trinomial are -4 and -4. Therefore, option C is the correct answer.

The given trinomial is x²-8x+16.

Factors of 16           Sum of factors

-1 and -16               -1+(-16)=-17

-2 and -8                  -2+(-8)=-10

-4 and -4                  -4+(-4)=-8

The set of factors would used to factor the trinomial are -4 and -4.

Therefore, option C is the correct answer.

To learn more about the factorisation of polynomial visit:

https://brainly.com/question/16789195.

#SPJ1

Answer:

The answer is -5. To do this you first draw your number line and label it from +7 to -10. You then count from from seven till the 11th number which in this case it's -5

Answer:

Step-by-step explanation:

183,883,72

Answer:

18388372

Step-by-step explanation:

1 )Use the algorithm method.

      3 2 1 7

×              5      7      1      6

        1      1       1      4                      

        1      9      3      0     2            

        3 2  1  7 0

  2 1  1     4  

  2 2 5    1       9      0     0

1  1     3

1  6 0 8   5       0      0     0

      1  1    1

1  8 3 8   8       3       7     2

2 )Therefore, 3217 × 5716 = 18388372.

18388372

Answer:

Step-by-step explanation:

Therefore after rewrite the expression we get 1/33 = 27.

Define negative exponent?

A negative exponent in mathematics means that the exponent's base needs to be divided by one or more. For instance, the equivalent of the mathematical expression 3-2 is:

1 / (3²) = 1/9

We can use the rule: to rewrite 1/3-3 without an exponent.

a⁻ⁿ = 1/aⁿ

where n is a positive integer and an is a non-zero number.

The reciprocal of the base raised to a positive exponent can also be used to write negative exponents. For instance:

3⁻ = (1/3²) = 1/9

In scientific notation, where numbers are written as powers of 10, negative exponents are frequently utilized

When we change this rule's 3-3 to:

3⁻³ = 1/3³

As a result, 1/3-3 can now be written as:

1/3⁻³ = 1/(1/3³)

= 1/(1/27)

= 27

To know more about negative exponent visit:

brainly.com/question/29009712

#SPJ1

The values of the two integers are -43 and -143.

Let the value of the smaller integer be "x".

Since, the sum of two integers is -186.

Smaller integer + Larger integer = -186

x + ( 3x - 14 ) = -186

Solve for x

x + 3x - 14 = -186

4x - 14 = -186

4x = -186 + 14

4x = -172

x = -172/4

x = -43

Hence;

The smaller integer = x = -43

The largere integer = 3x - 14 = 3(-43) - 14 = -143.

Learn to solve more equations here: brainly.com/question/14686792

#SPJ1

Answer:

\(\dfrac{5e^2}{2}\)

Step-by-step explanation:

Differentiation is an algebraic process that finds the slope of a curve. At a point, the slope of a curve is the same as the slope of the tangent line to the curve at that point. Therefore, to find the slope of the line tangent to the given function, differentiate the given function.

Given function:

\(y=x^2\ln(2x)\)

Differentiate the given function using the product rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let\;$u=x^2}\)\(\textsf{Let\;$u=x^2$}\implies \dfrac{\text{d}u}{\text{d}x}=2x\)

\(\textsf{Let\;$v=\ln(2x)$}\implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{2}{2x}=\dfrac{1}{x}\)

Input the values into the product rule to differentiate the function:

\(\begin{aligned}\dfrac{\text{d}y}{\text{d}x}&=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}\\\\&=x^2 \cdot \dfrac{1}{x}+\ln(2x) \cdot 2x\\\\&=x+2x\ln(2x)\end{aligned}\)

To find the slope of the tangent line at x = e²/2, substitute x = e²/2 into the differentiated function:

\(\begin{aligned}x=\dfrac{e^2}{2}\implies \dfrac{\text{d}y}{\text{d}x}&=\dfrac{e^2}{2}+2\left(\dfrac{e^2}{2}\right)\ln\left(2 \cdot \dfrac{e^2}{2}\right)\\\\&=\dfrac{e^2}{2}+e^2\ln\left(e^2\right)\\\\&=\dfrac{e^2}{2}+2e^2\\\\&=\dfrac{5e^2}{2}\end{aligned}\)

Therefore, the slope of the line tangent to the graph of y = x²ln(2x) at the point where x = e²/2 is:

\(\boxed{\dfrac{5e^2}{2}}\)

\(\huge\text{Hey there!}\)

\(\large\text{7.06}\times\large\text{1,000 - 1,976}\div\large\text{100}\\\large\text{7.06}\times\large\text{1,000 = \boxed{\bf 7,060}}\\\large\text{7,060 - 1,976}\div\large\text{100}\\\large\text{1,976}\div\large\text{100 = 494}\div\large\text{25 = \boxed{\bf 19.76}}\\\large\text{7,060 - 19.76}\\\mathsf{= \boxed{\bf \ Answer: \dfrac{17,6006}{25}\ or\ 7,040.24}}\leftarrow\large\text{either of those choices should}\\\large\text{work because they are both equivalent to each other }\)

\(\large\text{Good luck on your assignment and enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

The probability that all three number cubes will land on an odd number is 1/8

From the question, we have the following parameters that can be used in our computation:

Number of cubes = 3

Sections on each cube = 6

Odd sections on each cube = 3

This means that

P(Odd) = Odd sections/Total sections

So, we have the following representation

P(Odd) = 3/6

Simplify

P(Odd) = 1/2

For the three cubes, we have

P(All odd) = P(Odd)^Number of cubes

Substitute the known values in the above equation, so, we have the following representation

P(All odd) = (1/2)³

Evaluate

P(All odd) = 1/8

Hence, the probability is 1/8

Read more about probability at

brainly.com/question/251701

#SPJ1

Answer: 1/8

    ;

 ; l       .

                        .

      /.         ;      

      .

Answer:

Amadi: 20 years old

Chima : 4 years old

The graph of the function y = 5|x - 4| is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

Read more about functions at

brainly.com/question/2456547

#SPJ1

Answer:

Step-by-step explanation:

Based on the information provided, the residual plot makes sense based on the scatter plot.

In the given scatter plot, the points are plotted with horsepower on the x-axis and observed MPG (miles per gallon) on the y-axis. The scatter plot shows the relationship between horsepower and MPG for the motorcycles.

The residual plot, on the other hand, shows the differences between the observed MPG values and the predicted MPG values based on the regression line or model. Residuals represent the vertical distances between the observed data points and the regression line.

Looking at the residual plot, we can see that the residuals are scattered randomly around the zero line. Some residuals are positive, while others are negative, indicating that the observed MPG values deviate both above and below the predicted MPG values.

Given this information, option A is the correct answer: "The random residual plot makes sense because the scatter plot appears to have a linear relationship." The scatter plot does not necessarily suggest a positive or negative relationship between horsepower and MPG. It simply shows the general trend or pattern. The random distribution of residuals in the residual plot indicates that the regression model is capturing the relationship adequately, and the variations or deviations from the regression line are random, which is expected in a good regression model.

The residual plot created by Jorge does make sense as it reflects the negative relationship between horsepower and miles per gallon present in the original scatter plot. As the horsepower increases, the miles per gallon decreases which is depicted accurately in the residual plot made.

The best answer for this is B. The random residual plot makes sense because the scatter plot appears to have a negative relationship. A residual plot is a graph that is used to examine the goodness of fit in regression and ANOVA analysis. It is the differences between the observed and predicted values of data. The points in a residual plot are randomly dispersed around a horizontal axis if the corresponding regression model is appropriate for the data.

In this case, the scatter plot demonstrates a negative relationship between the horsepower of motorcycles and miles per gallon. As the horsepower increases, the miles per gallon decrease. This negative relationship is reflected in the pattern of residuals, which fluctuates around the zero line on the y-axis of the residual plot. Consequently, the random distribution of residuals on Jorge's plot does make sense given the scatter plot data.

https://brainly.com/question/34130523

#SPJ2

Answer:

The new mean of the sample is 15

Step-by-step explanation:

Given;

number of sample, n =10

initial mean of the sample, M = 5

initial total score of the sample = 5 x 10 = 50

If each score is multiplied by 3, the new score = 3 x 50 = 150

The new mean = new score / number of sample

The new mean = 150 / 10

The new mean = 15

Therefore, the new mean of the sample is 15

Answer:

The number is 43

Step-by-step explanation:

The difference between 131 and 2x (I'm rewriting it algebraically) is 45. So we need to find x. We do that by doing this equation

131 - 45 = 86

So since 86 is what 2x equals, we divide it by 2 to get x

86 ÷ 2 = 43

So x = 43

The limits of the function for this problem are given as follows:

In this problem, we are given the graph of the function, hence the limit is given by the value of the function as the function approaches x = a, not the actual numeric value of the function at x = a.

At x = -2, we have that:

As the lateral limits are equal, lim x -> -2 f(x) = 3.

At x = 1, we have that:

As the lateral limits are different, the lim x -> 1 f(x) does not exist.

At x = 4, we have that:

As the lateral limits are equal, lim x -> 4 f(x) = -3.

More can be learned about lateral limits at https://brainly.com/question/26103899

#SPJ1

Answer:

36

Step-by-step explanation:

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

8y + 16

Step 02:

factor:

8y + 16 = 8 (y + 2)

The answer is:

8 (y + 2)

The function is f(x) = x³ − 4x² + 2.

The slope of a line or straight object is the ratio of how much amount of rise occurs in correspondence to the increment in the run.

As,

Slope = rise/ run

Given:.

f(x) = x³ − 4x² + 2

As a line passing through the same point that f(x) passes through at x = 3 with a slope equal to the limit.

Then the slope of the function is given by the differentiation.

slope= d/dx [f(x)]

slope= d/dx  ( x³ − 4x² + 2)

slope=  3x² - 8x

slope= 3* 3* 3 -8*3

slope= 27-24

slope= 3

Learn more about the slope here:

brainly.com/question/2503591

#SPJ2

The computation of the increased in salary is $500.

Here, we have,

Explanation:

Data provided in the question

Salary for the first year = $50,000

CPI increase during the year = 4%

Overstated inflation = 1% i.e. 5%

The computation of the increased in salary is shown below:

= Salary of the first year × inflation rate - salary of the first year × CPI increase during the year

= $50,000 × 5% - $50,000 × 4%

= $2,500 - $2,000

= $500

Hence, The computation of the increased in salary is $500.

To learn more on percentage click:

brainly.com/question/13450942

#SPJ1

complete question:

Mark's wage contract specifies a $50,000 salary for the first year, and specifies a salary increase equal to the percentage increase in the CPI during the second year. The increase in the CPI during the year was 4.0%. If the CPI overstates inflation by 1.0% (that is, the actual price increase was 3% and not 4%), at the end of the first year Mark's salary increased by $________ more than it would have without the upward bias.

The money account is doubled at an interest rate of 5.2 % compunded quarterly, that is, under the model of compound interest in a time period of about 3.5 years.

The compound interest takes into account the change of money deposited in time in contrast with the simple interest, which only takes the initial amount of money into account. Please notice that four quarters equals a year.

The compound interest formula is described below:

C = C' · (1 + r/100)ⁿ     (1)

Where:

If we know that C = 2 · C' and r = 5.2, then the doubling time is:

n = /㏒ C/C'/㏒ (1 + r/100)

n = ㏒ 2/㏒ 1.052

n ≈ 13.674

The money account is doubled at an interest rate of 5.2 % compunded quarterly, that is, under the model of compound interest in a time period of about 3.5 years. \(\blacksquare\)

To learn more on compound interests, we kindly invite to check this verified question: https://brainly.com/question/14295570

Answer:

51

Step-by-step explanation:

Answer:

In 1997, the baseball card would be worth $7.46 + $2.52 = $9.98.

In 1998, the baseball card would be worth $9.98 + $2.52 = $12.50.

In 1999, the baseball card would be worth $12.50 + $2.52 = $15.02.

Step-by-step explanation:

In this problem, we are given the value of a baseball card in 1996, which is $7.46. We are also told that the value of the card increases by $2.52 each year since then. This means that in 1997, the value of the card increased by $2.52 compared to its value in 1996, so the value in 1997 would be $7.46 + $2.52 = $9.98. Similarly, in 1998, the value of the card increased by another $2.52 from its value in 1997, so the value in 1998 would be $9.98 + $2.52 = $12.50. In 1999, the value of the card increased by another $2.52 from its value in 1998, so the value in 1999 would be $12.50 + $2.52 = $15.02.

Answer:

66

Step-by-step explanation:

the difference of 54 and 32 is 54 - 32 = 22

the difference of 8 and 5 is 8 - 5 = 3

then

22 × 3 = 66

Answer:

\(\huge\colorbox{blue}{A}\huge\colorbox{orange}{N}\huge\colorbox{gray}{S}\huge\colorbox{red}{W}\huge\colorbox{yellow}{E}\huge\colorbox{purple}{R}\)

hitsss