1 If $5000 is put into a savings account that pays3.5% interest compounded monthly, how muchmoney, to the nearest ten cents, would be in thataccount after 6 years, assuming no money was addedor withdrawn?1) $5177.802) $5941.303) $6146.304) $6166.50 how to solve this?

The value of the car after 3 years is $79, 000

To determine the value, we have to use the formula;

Value = Initial value × (1 - Depreciation rate)ⁿ

Substitute the values given, we get;

Remaining value after 3 years = $100,000 × (1 - 0.10)³

Expand the bracket, we get;

Value after 3 years = $100,000 × (0.90)³

Find the cube value and substitute, we have;

Value after 3 years = $100,000 × 0.729

Multiply the values, we have;

Value after 3 years = $72,900

Learn more about depreciation at: https://brainly.com/question/1203926

#SPJ1

The surface area of the composite figure is 2005 in².

To find the surface area of the composite figure, we need to calculate the sum of the areas of its individual components.

Let's break down the figure into its different parts and calculate the surface area step by step:

Rectangular Prism: The rectangular prism has dimensions of 20 in, 11 in, and 5 in. The surface area of a rectangular prism can be found by adding the areas of its six faces. The total surface area of the rectangular prism is given by:

Surface Area of Rectangular Prism = 2lw + 2lh + 2wh

Plugging in the values, we have:

Surface Area of Rectangular Prism = 2(20)(11) + 2(20)(5) + 2(11)(5) = 440 + 200 + 110 = 750 in²

Rectangular Prism: Another rectangular prism has dimensions of 19 in, 12 in, and 12 in. Following the same process as above, we can calculate the surface area of this rectangular prism:

Surface Area of Rectangular Prism = 2lw + 2lh + 2wh

Plugging in the values, we have:

Surface Area of Rectangular Prism = 2(19)(12) + 2(19)(12) + 2(12)(12) = 456 + 456 + 288 = 1200 in²

Base: The base is a rectangle with dimensions 11 in and 5 in. The surface area of a rectangle is given by the formula:

Surface Area of Rectangle = lw

Plugging in the values, we have:

Surface Area of Rectangle = (11)(5) = 55 in²

Finally, to find the total surface area of the composite figure, we add the surface areas of the individual components:

Total Surface Area = Surface Area of Rectangular Prism + Surface Area of Rectangular Prism + Surface Area of Rectangle

Total Surface Area = 750 in² + 1200 in² + 55 in² = 2005 in²

For more ssuch questions on surface area visit:

https://brainly.com/question/16519513

#SPJ8

A line of best fit guides a line through a scatter plot of data points that best describes the association between those points.

A line of best fit guides a line through a scatter plot of data points that best describes the association between those points. Statisticians typically utilize the least squares approach to arrive at the geometric equation for the line, either through manual computations or regression analysis software.

A line of best fit can be approximately specified utilizing an eyeball the method by marking a straight line on a scatter plot so that the numeral of points above the line and below the line stands about equal (and the line passes via as many points as possible).

To learn more about line of best fit refer to;

https://brainly.com/question/1518824

#SPJ2

Answer:

111 mg (to the nearest whole number)

Step-by-step explanation:

1 lb = 0.45359237 kg

⇒ 49 lbs = 49 x 0.45359237 = 22.22602613... kg

If the medication is administered at 5 mg/kg/day then

22.22602613...  x 5 = 111.1301307 = 111 mg (to the nearest whole number)

The domain of the function above is [-2, 3].

The range of the function above is [-2.5, 2].

The intervals over which the function is increasing is [-2, 1.5] U [-2.5, 2].

The intervals over which the function is decreasing is [1.5, -2.5].

In Mathematics and Geometry, a domain refers to the set of all real numbers for which a particular function is defined.

Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph of this rational expression (function)   shown in the image attached below, we can reasonably and logically deduce the following domain and range:

Domain = [-2, 3] or -2 ≤ x ≤ 3.

Range = [-2.5, 2] or -2.5 ≤ y ≤ 2.

Additionally, the intervals over which the function is increases over the interval [-2, 1.5] and [-2.5, 2], while it decreases over the interval [1.5, -2.5].

In conclusion, the given function is not constant over any interval.

Read more on domain here: brainly.com/question/17003159

#SPJ1

A graph of the exponential function \(f(n)=37000(1.06)^n\) is shown in the image attached below.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x)=a(b)^x\)

Where:

Based on the information provided above, your salary can be modeled or represented by the following exponential function;

\(f(n)=37000(1.06)^n\)

Lastly, we would use an online graphing calculator to plot the given exponential function as shown in the graph attached below.

In conclusion, the rate of change of this exponential function is equal to 1.06.

Read more on a graph here: brainly.com/question/4546414

#SPJ1

Answer:

blue

Step-by-step explanation:

Answer:

the blue one

Step-by-step explanation:

The fabric  has a cost per yard of $6 per yard

From the question, the given parameters are:

Yards of fabric = 2 1/2 yards

Cost of the fabric = $15

The cost per yard of the fabric is then calculated as

Cost per yard = Cost of the fabric/Yards of fabric

Substitute the known values in the above equation

So, we have

Cost per yard = 15/(2 1/2)

Evaluate the quotient

So, we have

Cost per yard = 6

Hence, the cost per yard is $6 per yard

Read more about rates at

https://brainly.com/question/12652779

#SPJ1

Answer:

\( \sqrt{89} \)

Step-by-step explanation:

\( \sqrt{ {(7 - 12)}^{2} + {(1 - ( - 7))}^{2} } \)

\( \sqrt{ {( - 5)}^{2} + {8}^{2} } \)

\( \sqrt{25 + 64} \)

\( \sqrt{89} \)

a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

For more questions on algebraic fraction:

https://brainly.com/question/11875858

#SPJ8

Using the Central Limit Theorem, it is found that the sampling distribution of the sample proportion of the 50 questions on which you get the correct is approximately normal, with mean of 0.7 and standard error of 0.0648.

It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1 - p)}{n}}\), as long as \(np \geq 10\) and \(n(1 - p) \geq 10\).

In this problem, we have that p = 0.7, n = 50, hence the mean and the standard deviation are given as follows:

\(\mu = p = 0.7\)

\(s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.7(0.3)}{50}} = 0.0648\)

More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213

Answer:

So 1/4th cup would be 97.5 calories

1 whole cup would make 390 calories so then just divide that by 4 and you have 97.5

Answer:

Step-by-step explanation:

Part A:

The value of f(3) represents the height of the ball after its 3rd bounce.

From the graph, we can see that the point corresponding to the 3rd bounce has a height of 4 feet.

Therefore, the correct answer is B. After 3 bounces, the height of the ball is 4 feet.

Part B:

The given function represents the height of the ball after each bounce. Since the ball is bouncing, its height will always be greater than zero.

The graph shows that the function has an asymptote at y = 0, which means that the height of the ball will approach zero as it bounces. However, this does not mean that the ball will never have a height of zero. The ball will eventually stop bouncing and come to rest on the ground, which corresponds to a height of zero.

Therefore, the correct answer is C. We agree that a possible range for the given function is y > 0.

To calculate your bi-weekly paycheck, follow these steps:

Step 1: Calculate the gross earnings:

Multiply the number of hours worked per week by the hourly rate.

20 hours/week * $9.00/hour = $180.00/week

Step 2: Calculate the total earnings for two weeks:

Multiply the weekly earnings by the number of weeks in a bi-weekly pay period.

$180.00/week * 2 weeks = $360.00

Step 3: Calculate the deductions:

Calculate each deduction separately and subtract them from the gross earnings.

Federal Income Tax: $360.00 * 11.9% = $42.84

State Income Tax: $360.00 * 3.6% = $12.96

F.I.C.A: $360.00 * 7.65% = $27.54

Professional Dues: Amount varies depending on the specific dues.

Total Deductions: $42.84 + $12.96 + $27.54 + Professional Dues

Step 4: Calculate the net earnings:

Subtract the total deductions from the gross earnings.

Net Earnings = Gross Earnings - Total Deductions

Once you have the net earnings, you can determine if it is sufficient to cover your monthly car insurance bill of $200. If your bi-weekly net earnings are greater than or equal to $200, you will be able to pay your car insurance bill.

It is important to note that these calculations are based on the information provided, and actual tax rates and deductions may vary depending on your specific circumstances and location.

Additionally, professional dues may differ depending on your profession. It is recommended to consult with a tax professional or payroll department for precise calculations.

For  more such questions on gross earning.

https://brainly.com/question/29206567

#SPJ8

Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

For similar question on surveyed.

https://brainly.com/question/14610641  

#SPJ8

The coordinates of point B are (-3, 17).

The given equation is M = I₁ + I₂ = 31 + 32.

Now let's substitute in our given values:

(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)

We will now set up two equations to solve for our two unknowns, x₂ and y₂:

Equation 1: (-5 + x₂) / 2 = -4

Multiply both sides by 2:

-5 + x₂ = -8

Add 5 to both sides:

x₂ = -3

This gives us the x-coordinate of point B.

Equation 2: (-5 + 2 + y₂) / 2 = 7

Simplify:

(-3 + y₂) / 2 = 7

Multiply both sides by 2:

-3 + y₂ = 14

Add 3 to both sides:

y₂ = 17

This gives us the y-coordinate of point B.

Therefore, the coordinates of point B are (-3, 17).

For more such questions on coordinates

https://brainly.com/question/29660530

#SPJ8

Applying the congruent chords theorem, the value of x is: 7.

Length of segment LP is: 6 units.

In geometry, a chord is defined as the line segment that joins two points on the circumference of a circle.

In a circle, if two chords are congruent, then they are equidistant from the center of a circle, according to the congruent chords theorem.

In the circle given, chords JK = LM = 12 units. This means both chords are congruent, therefore, they are equidistant from the center of the circle S.

According to the congruent chords theorem, NS = PS, thus:

8 = 2x - 6

8 + 6 = 2x

14 = 2x

Divide both sides by 2

14/2 = 2x/2

7 = x

x = 7

LP = 1/2(12)

LP = 6 units.

In summary, applying the congruent chords theorem, the value of x is: 7.

Length of segment LP is: 6 units.

Learn more about the congruent chords theorem on:

https://brainly.com/question/7511582

#SPJ1

Answer:

Because If we tried to define scalar multiplication we would run into problems.  No there are not any special accommodations.

Step-by-step explanation:

Our negative number means that the government owes you $413.75. We would have to pay the government money if it weren't a negative number.

In order to pay for general government services, goods, and activities, local, state, and federal governments must collect mandated payments or charges from citizens and corporations.

Since ancient times, paying taxes to governments or officials has been a fundamental aspect of civilization.

So, to address this issue, utilize the Single column.

You must first calculate her taxes before deducting the tax credit.

She earns $17,000 in taxable income. She now falls into the 15% category.

The amount owed on the first 9275 dollars that are subject to the tax must first be determined.

.10 * 9275 =  927.50

The remainder of her debt, which is in the 15% range, must then be collected.

.15 * (17000 - 9275) = 1158.75

Add up all of our taxes on the money, then deduct our tax credit of $2500.

(927.50 + 1158.75) -  2500

(2086.25) -  2500 = -413.75

Therefore, our negative number means that the government owes you $413.75. We would have to pay the government money if it weren't a negative number.

Know more about tax here:

https://brainly.com/question/25783927

#SPJ1

Answer:

Explanation:

The point-slope form of an equation is given by

where (x0, y0) is a point on the line and m is the slope.

A line that is parallel to y = -3/2 x +1 has the same slope, namely -3/2; therefore, we know that our equation must look like

where (y0, x0) is a point hitherto unknown.

Furthermore, we also know that the line passes through the point (-4, 2) and therefore, we set (x0, y0) = (-4, 2) - this gives

which is our equation in point-slope form. However, we are asked to convert it into the standard form.

Expanding out the right-hand side gives

adding 3/2 x to both sides gives

Finally, adding 2 to both sides gives

which is our answer!

Answer:

Θ ≈ 26.4°

Step-by-step explanation:

using the sine ratio in the right triangle

sinΘ = \(\frac{opposite}{hypotenuse}\) = \(\frac{40}{90}\) = \(\frac{4}{9}\) , then

Θ = \(sin^{-1}\) ( \(\frac{4}{9}\) ) ≈ 26.4° ( to 1 decimal place )

Check the picture below.

\(\sin(\theta )=\cfrac{\stackrel{opposite}{40}}{\underset{hypotenuse}{90}}\implies \sin(\theta )=\cfrac{4}{9}\implies \theta =\sin^{-1}\left( \cfrac{4}{9} \right)\implies \theta \approx 26.4^o\)

Make sure your calculator is in Degree mode.

Answer:

3(2x+5)

Step-by-step explanation:

Since the GCF of 6 and 15 is 3, you should take out the 3 from both parts of the equation.

Answer:

0.053

Step-by-step explanation:

This is a geometric distribution problem.

I'm geometric distribution problem,

E(X) = 1/p

Where;

E(X) is expected value and p is probability of success

Thus;

1/p = 12.5

p = 1/12.5

p = 0.08

Now, to find the probability that the sixth person tested is the first one with high blood pressure, we will use the probability formula in geometric distribution which is;

P(X = k) = qⁿ•p

q = 1 - p

q = 1 - 0.08

q = 0.92

Thus;probability that the sixth person tested is the first one with high blood pressure will be expressed as;

P(X > 5) = (0.92^(5)) × 0.08

P(X > 5) = 0.053

Answer:

I'm pretty sure it's a.....

The answer is A

Step-by-step explanation:

common sense

Answer:

a) ( 76.20, 83.80)

b) ( 76.47, 83.53)

Step-by-step explanation:

a)

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = 80

Standard deviation r = 15

Number of samples n = 60

Confidence interval = 95%

z(at 95% confidence) = 1.96

Substituting the values we have;

80 +/-1.96(15/√60)

80+/-1.96(1.936491673103)

80+/- 3.80

= ( 76.20, 83.80)

Therefore at 95% confidence interval = ( 76.20, 83.80)

b)

Mean x = 80

Standard deviation r = 15

Number of samples n = 120

Confidence interval = 99%

z(at 99% confidence) = 2.58

Substituting the values we have;

80 +/-2.58(15/√120)

80+/-2.58(1.369306393762)

80+/- 3.53

= ( 76.47, 83.53)

Therefore at 99% confidence interval = ( 76.47, 83.53)

The type of sytudy that we have here is the observational study.

In an observational study, the researcher observes and analyzes data from individuals without actively intervening or manipulating any variables.

In this case, the researcher is observing and comparing the health outcomes of two groups of individuals: those who have eaten a vegan diet for the past five years and those who have not.

The participants are not randomly assigned to the groups, and the researcher does not actively control or manipulate the diet of the individuals.

Read more on observational study here:https://brainly.com/question/4758113

#SPJ1

Answer:

Option (4)

Step-by-step explanation:

From the table attached,

Ratio of spores in day 2 and day 1 = \(\frac{400}{200}\)

                                                         = 2

Ratio of spores in day 3 and day 2 = \(\frac{800}{400}\)

                                                          = 2

There is a common ratio of 2 in each successive to the previous term of the Mold spores.

Therefore, spores are growing exponentially.

Let the function representing exponential function is,

y = a(b)ˣ

Here, y = Number of spores after time 'x'

x = Number of days

a and b are the constants.

On day 1,

x = 1

y = 200

By substituting these values in the exponential function,

200 = a(b)¹

ab = 200 -------(1)

On day 2,

x = 2

y = 400

400 = a(b)² -------(2)

Divide equation 2 by equation 1,

\(\frac{400}{200}=\frac{ab^{2} }{ab}\)

b = 2

By substituting the value of b in equation (1),

a(2) = 200

a = 100

Therefore, equation of the function will be,

y = 100(2)ˣ

Option (4) will be the answer.

According to the information, the result of these mathematical operations are: 200,005.81, 0.50, -5,795, 12,711.

To solve the different mathematical operations we have several alternatives. However, the easiest is to use a calculator to help us find the solution more quickly.

In the case of multiplication, we must understand that an operation in which a number is repeated several times and added and that would be the result, for example:

5 * 5 = 25

5 + 5 + 5 + 5 + 5 = 25

In the case of division, it is when a number is divided into another in equal parts, for example:

15 / 5 = 3

that is to say that there are 3 sets of 5 units each.

A subtraction is an operation in which we remove some units from a number, for example:

10 - 2 = 8

In this case, we subtract 2 units from the 10 and a number 8 remains.

An addition is the opposite of subtraction, in this we increase the value of a number by adding another value, for example:

10 + 10 = 20

In this case we added 10 units and the result was 20.

Then, the answers of the operations would be:

Learn more about operations in: https://brainly.com/question/29949119

#SPJ1

The total cost of the pita bread and hummus dips will be $305.00.

To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:

Cost of pita bread:

Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates

Cost of each crate = $15.00

Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00

Cost of hummus dips:

Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes

Cost of each box = $20.00

Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00

Therefore, the expressions Toula can use to determine the costs are:

Cost of pita bread = 3 crates × $15.00/crate

Cost of hummus dips = 13 boxes × $20.00/box

The total cost will be the sum of the costs of pita bread and hummus dips:

Total cost = Cost of pita bread + Cost of hummus dips

Total cost = $45.00 + $260.00

Total cost = $305.00

Therefore, the total cost of the pita bread and hummus dips will be $305.00.

for such more question on cost

https://brainly.com/question/8993267

#SPJ8

We will investigate how to represent an equation given in a general form given:

To represent the above equation in the required form:

We will manipulate the terms of the given form by performing basic algebraic operators. We will start off with solving the parenthesis ( ) on the right hand side of the " = " sign:

We will then put all the variable terms involving " x and y" on left hand side of the " = " sign and cosntants on the other side:

The equation is expressed in the required form above with the values of integers: