Trevor is making payments on a car that costs 26,555 dollars. He makes 36 equal payments. If he rounds the equal payments up to the nearest whole dollar, about how much will he overpay after 36 months? Explain.

Answers

Answer 1

Answer:

$13 overpayment

Step-by-step explanation:

We can find the amount Trevor should pay each month by dividing the $26,555 by 36 months:

               ($26,555/(36 months)) = $737.64 per month

Since Trevor decide to round up to the nearest dollar, he will pay $738 each month.  That's an overpayment of $0.361 each month.

After 36 months of overpaying by $0.361 each month, Trevor will have overpaid:

  ($0.36/month)*(36 months) = $13 overpayment


Related Questions

The coordinates of the vertices of a rectangle are A (5, 3), B (5,-9), C (-1,-9), and D (-1, 3)​

Answers

72 square units is the area of rectangle when coordinates of the vertices of a rectangle are A (5, 3), B (5,-9), C (-1,-9), and D (-1, 3

What is Area of Rectangle?

The area of Rectangle is length times of width.

The coordinates of the vertices of a rectangle are A (5, 3), B (5,-9), C (-1,-9), and D (-1, 3)​

The distance from AB

Distance=√(x₂-x₁)²+(y₂-y₁)²

=√(5-5)²+(-9-3)²=√(-12)²=√144=12

The distance from BC

=√(-1-5)²+(-9+9)²=√36=6

Length is 12 units and width is 6 units

Area of rectangle=Length×Width

=12×6

=72 square units

Hence, 72 square units is the area of rectangle when coordinates of the vertices of a rectangle are A (5, 3), B (5,-9), C (-1,-9), and D (-1, 3)

To learn more on rectangles click:

https://brainly.com/question/20693059

#SPJ1

*URGENT* Sam has 2 part time jobs. At the grocery store, he earns $8/h and at the library, he earns $10/h. Before going on vacation, he would like to save $280. Determine the fewest number of hours he would need to work to reach his goal.

Answers

Unit rate is the quantity of an amount of something at a rate of one of another quantity.

The fewest number of hours he would need to work to reach his goal of $280 is 28 hours working in the library.

What is a unit rate?

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

Amount to earn = $280

Grocery store:

Earnings per hour = $8

1 hour = $8

Multiply 280/8 on both sides.

280/8 x 1 hour = $280

35 hours = $280

Library:

Earnings per hour = $10

1 hour = $10

Multiply 280/10 on both sides.

28 hours = $280

We see that,

Working in the Library would make $280 in fewer hours than working in the grocery store.

Thus,

The fewest number of hours he would need to work to reach his goal of $280 is 28 hours working in the library.

Learn more about unit rates here:

https://brainly.com/question/11258929

#SPJ1

Albert has $1,000 in an account. The interest rate is 5% compounded annually.
To the nearest cent, how much interest will he earn in 4 years?

Answers

Answer:

$215.50

Step-by-step explanation:

To calculate the amount of interest that Albert will earn on his account over the course of 4 years, we can use the formula for compound interest:

Interest = principal * (1 + rate/n)^(n*t) - principal

Where:

principal is the initial amount of money in the account ($1,000 in this case)

rate is the annual interest rate (5% in this case)

n is the number of times that interest is compounded per year (annually in this case, so n=1)

t is the number of years the money is invested (4 years in this case)

Plugging these values into the formula, we get:

Interest = $1,000 * (1 + 0.05/1)^(1*4) - $1,000

= $1,000 * (1.05)^4 - $1,000

= $1,000 * 1.2155 - $1,000

= $215.50

To the nearest cent, the interest Albert will earn in 4 years is $215.50.

y=px+q and y=rx+s are perpendicular and p=49|r| . Find the values of p and r

Answers

Answer:

[tex]r=-\frac{\sqrt{7}}{7} \implies p=\sqrt{7}[/tex]

Step-by-step explanation:

We know that [tex]pr=-1[/tex] and [tex]p=49|r|[/tex].

[tex]\frac{-1}{r}=49|r| \\ \\ \frac{1}{r^2}=49r^2 \\ \\ 1=49r^4 \\ \\ r^4=\frac{1}{49} \\ \\ r=-\frac{\sqrt{7}}{7} \implies p=\sqrt{7}[/tex]

A 5-pound bag of potatoes cost $4.65. How many pounds, p, can you buy for $8.37​

Answers

Answer:   You can buy a 9-pound bag for $8.37.

Step-by-step explanation:

[tex]\frac{5lbs}{4.65} =\frac{p}{8.37}[/tex]    

Then, we cross multiply, and we get:

5(8.37) = 4.65p

  41.85 = 4.65p   [We divided 4.65 by both sides]

         9 = p

should a test of statistical significance be conducted before or after computing d and interpreting its value?

Answers

Yes, a test of statistical significance be conducted before or after computing d and interpreting its value.

The p-value is an important phrase for hypothesis testing in the context of statistical significance of data.

The p-value is defined as a function of observed sample outcomes that is used to evaluate statistical hypotheses. Before running the test, a threshold value must be chosen.

The significance is a figure that represents the probability that the outcome of a study occurred entirely by chance. The statistical significance can be low or high. It does not always imply practical significance. When a researcher does not use language carefully in their experiment report, the significance may be misconstrued.

To learn more about test statistics

brainly.com/question/14128303

#SPJ4

Solve for X and y PLEASE GIVE FULL EXPLANATION HOW YOU GOT IT

Answers

Answer:

(1, -1)

Step-by-step explanation:

we isolate y in the first equation

2x+y=1

-2x.  -2x

y=1-2x

and now we fill y into second equation

4x-2(1-2x)=6

4x-2+4x=6

8x-2=6

   +2 +2

8x=8

/8 /8

x=1

and now to find y we insert x

2(1)+y=1

2+y=1

-2.   -2

y= -1

hopes this helps

the circle defined by the equation $(x 4)^2 (y-3)^2 = 9$ is moved horizontally until its center is on the line $x = 6.$ how many units to the right does the center of the circle move?

Answers

The center of the circle shifted 6 units to the right when it's center is on line x=6.

What is circle?

A circle is a spherical shape without boundaries or edges. A circle is a closed, curved object with two dimensions in geometry. Simply put, a circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve. A circle is made up of all points in the same plane that are equidistant from one another. Only the bordering points make up the circle. A circle can be compared to a hula hoop. The circle is only present at the border's points.

Here,

Centre of circle=(-4,3)

-4+6=2

New centre is (2,3).

When the circle's center is on line x=6, its center has moved 6 units to the right.

To know more about circle,

https://brainly.com/question/9635560

#SPJ4

emma wants to know if long distance relationships in college have a greater likelihood of ending than relationships that are not long distance. she creates a questionnaire and recruits 100 students from her school to complete the questionnaire so she can test her hypothesis. emma is:

Answers

Emma is asking an empirical question so that she she can test her hypothesis

What is a Empirical hypothesis?

Something empirical is something based on real evidence .

Evidence that is verifiable by observation as opposed to something that is true in theory or by some kind of reckoning or logic

A hypothesis is a theory that is put forward for further examination to see if it is correct. It is not a call but it is an explanation that fits the available evidence so , An empirical hypothesis is a theory that is based on real evidence and experience but that has not been proven yet

So, According to the question

Emma wants to know if long distance relationship in college have a greater likelihood of ending than a relationship that are not long distance and for that she creates a questionnaire and the crowds 100 student from our school to complete the questionnaire so she can test her hypothesis

Here, Emma is asking an empirical questions ( question about experience) and will conclude the test based on these 100 students experience and thoughts.

To know more about Hypothesis here

https://brainly.com/question/29576929

#SPJ4

braulio has $15 less than adam. together they have $153. write the system of equations that could be used to determine the amount of money braulio, b, and the amount of money adam, a, has each. how much does braulio make?

Answers

The amount of money with Adam and Braulio as per given system of equations is equal to $84 and $69.

As given in the question,

Let 'a' be the amount of money with Adam

And 'b' be the amount of money with Braulio

System of equations as per given given data:

b = a - 15___(1)

a + b = 153 ___(2)

Substitute the value of 'b' in (2) we get,

a + a -15 = 153

⇒2a = 153 + 15

⇒2a = 168

⇒ a = $84

Amount of money with Adam is $84

Amount of money with Braulio is b = 84 - 15

                                                          = $69

Therefore, the amount of money with Adam and Braulio is equal to $84 and $69.

Learn more about amount of money here

brainly.com/question/14509921

#SPJ4

Would you use SSS or SAS to prove the triangles​ congruent? If there is not enough information to prove the triangles by SSS or​ SAS, write​ "not enough​ information." Explain your answer.

A. Triangle UTZ = Triangle -------------- (SAS)
B. Triangle UTZ = Triangle --------------( SSS)
c.The two triangles are not necessarily congruent. There is not enough information.

Answers

Answer:

B. [tex]\triangle UVZ \cong \triangle YVX[/tex] (SSS)

From the given image, we can say that the congruency postulate is that; Triangle UTZ ≅ Triangle YVX by SSS

How to identify congruent triangles?

There are 6 main triangle congruency postulates namely;

1. SSS which means the three corresponding sides of both triangles are congruent.

2. SAS which means that 2 corresponding sides and the included corresponding angle are congruent.

3. ASA which means that 2 corresponding angles and the included corresponding side are congruent.

4. AAS which means that 2 corresponding angles and the non-included corresponding angle are congruent.

5. Hypotenuse-Leg Congruence Theorem which states that If the hypotenuse and leg in one right triangle are congruent to the hypotenuse and leg in another right triangle, then the two triangles are congruent.

From the given image of both triangles, we can see that all three corresponding sides are congruent to each other which indicates SSS Congruency postulate.

Read more about Triangle Congruency Postulate at; https://brainly.com/question/28039171

#SPJ1

Can a triangle be formed with side lengths 4, 8, 11? Explain. No, because 11 − 8 < 4 Yes, because 11 − 4 < 8 No, because 4 + 8 > 11 Yes, because 4 + 8 > 11

Answers

A triangle can be formed with side lengths 4, 8, 11. Yes, because 4 + 8 > 11

How to illustrate the triangle?

According to the Triangle Inequality Theorem, the largest side cannot be greater than the sum of the other two sides. The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the remaining side.

If the sum of any two sides is greater than the sum of the third, then the difference of any two sides is less than the sum of the third. The sum of any two sides must be greater than the sum of the third. The longest side in a triangle is the side opposite a larger angle.

Learn more about triangles on:

https://brainly.com/question/17335144

#SPJ1

Ashley collected 25 responses to a survey and used a two-tailed test to establish a significance level of 0.02 and calculate a 98% confidence interval.Using the t-table (located in the tutorial), what is the critical t-value used for calculating a 98% confidence interval with 24 degrees of freedom? Answer choices are rounded to the thousandths place.
Tutor's Assistant: The Advanced Math Tutor can help you get an A on your homework or ace your next test. Is there anything else the Advanced Math Tutor should be aware of?
Ashley collected 25 responses to a survey and used a two-tailed test to establish a significance level of 0.02 and calculate a 98% confidence interval.Using the t-table (located in the tutorial), what is the critical t-value used for calculating a 98% confidence interval with 24 degrees of freedom? Answer choices are rounded to the thousandths place.

Answers

The critical t-value used for calculating a 98% confidence interval with 24 degrees of freedom is a.) 2.492

How to get the value?

It should be noted that in order yoo find the critical t-value for a 98% confidence interval with 24 degrees of freedom, you will need to use a t-table to look up the value in the t-distribution.

In this situation, the t-distribution is a probability distribution that is used to estimate population parameters when the sample size is small and the population standard deviation is unknown.

In a two-tailed test, the critical t-value is the value that is exceeded by the test statistic with a probability of 0.02 in each tail of the distribution. Here, the critical t-value is 2.492. The correct option is A.

Learn more about confidence interval on:

https://brainly.com/question/15712887

#SPJ1

Using the t-table (located in the tutorial), what is the critical t-value used for calculating a 98% confidence interval with 24 degrees of freedom? Answer choices are rounded to the thousandths place.

a.) 2.492

b.) 1.311

c.) 1.699

d.) 2.045

Create a fraction (and state the decimal number) that is exactly halfway between
15/24 and 1/8.
§. Show all of your thinking. Represent your answer as
fraction and decimal.

Answers

Answer:

Step-by-step explanation:

?

For a recipe, Val uses 4 cups of sugar for each cup of flour. How many cups of flour does Val need when he uses 1 cup of sugar?
Which one is correct

1/4
1/2
4
1

Answers

Answer:

1/4

Step-by-step explanation:

4 : 1 = 1 : x

x = 1 · 1 / 4

x = 1/4

How do I multiply a 1x2 matrix by a 2x3 matrix?

Answers

Matrix multiplication, also known as matrix product and the multiplication of two matrices, produces a single matrix. It is a type of binary operation. If A and B are the two matrices, then the product of the two matrices A and B are denoted by: X = AB.

The multiplication is done by adding the elements obtained by multiplying each element of the lines of the first matrix times the elements of the columns of the second matrix (Line× Column).

[tex]A=\left[\begin{array}{ccc}1&2\\\end{array}\right] _{1*2} \\B= \left[\begin{array}{ccc}4&5&6\\7&8&9\end{array}\right] _{2*3}[/tex]

2=2 yes it is possible to multiply

1*3= order of the resulting matrix

(line*column)

[tex]A*B=\left[\begin{array}{ccc}4+14&5+16&6+18\\\end{array}\right] _{1*3}[/tex]

[tex]A*B=\left[\begin{array}{ccc}18&21&24\\\end{array}\right] _{1*3}[/tex]

To learn more about matrices visit: brainly.com/question/11367104

#SPJ4

What is the value of n - 7 when n = 14

Answers

Answer: 7

Step-by-step explanation:

We substitute n for 14 to get the equation 14-7, which equals 7.

Construct the simplest polynomial with integer coefficients with the given roots:
3i, -2,2,0

Answers

The simplest polynomial with the given roots will be equal to x⁴ + 5x² - 36.

What is a Polynomial?

A polynomial is a mathematical expression that solely uses the operations of addition, subtraction, multiplication, and raising non-negative integers to power, together with uncertainty and coefficients. x² + 4x + 7 is an illustration of a single indeterminate x polynomial.

The total of terms with the pattern [tex]kx^n[/tex] forms a polynomial. Where n is indeed a positive number and k is any number. For instance, the polynomial 3x + 2x - 5 exists.

As per the given information in the question,

The given roots are 3i, -2, 2

As we know that if 3i is a root then -3i is also a root.

Then, the factored form of this polynomial will be:

p(x) = (x - 3i)(x + 3i)(x + 2)(x - 2)

= (x - (3i)²) (x² -2x + 2x - 4)

It will become: (x² + 9)(x² - 4)

It can be further expanded,

x⁴ - 4x² + 9x² - 36

x⁴ + 5x² - 36

To know more about Polynomial:

https://brainly.com/question/11536910

#SPJ1

In an analysis of variance problem if SST = 120 and SSTR-80, then SSE is
a. 200
b. 40
c. 80
d. 120

Answers

The value of SSE (sum squared error) is 40 in the given analysis of the variance problem if SST = 120 and SSR = 80. Option b is correct.

How to find SSE in an analysis of variance problems with the SST and SSR values?

Here the words SSE means Sum Squared Error, SST means Sum of Squares Total and SSR means Sum of Square Regression.

In the SSE accuracy measure, errors are squared and then added. It is used when the data points are similar in magnitude.

The formula is SST = SSR + SSE ⇒ SSE = SST - SSR

Calculation:

The given values of the analysis of the variance problem are

SST = 120; SSR = 80

Then, the value of SSE = SST - SSR = 120 - 80 = 40

So, option b is correct.

Learn more about the sum squared error here:

https://brainly.com/question/28046641

#SPJ1

if f(x) = , what is f(7.6)? 3 3.5 3.8 4

Answers

The solution of the given greatest integer function is found as 3.5.

Explain the term greatest integer function?The largest integer function is one that yields an integer that is closest to the specified real value. Additionally known as the step function. The closest integer is used to round off the input using the biggest integer function.

We have to compute;

f(x) = 1/2[x]

Given what we have; f(7.6).

Enter x = 7.6 in the function provided;

f(7.6) = 1/2[7.6]

As ,the value (7.6) --> 7.0 (greatest integer function)

f(7.6) = 7/2

f(7.6) =  7/2

f(7.6) = 3.5

Thus, the solution of the given greatest integer function is found as 3.5.

To know more about the function, here

https://brainly.com/question/11624077

#SPJ4

The correct question is-

If f(x) = 1/2[x], what is f(7.6)?

3

3.5

3.8

4

Steven uses a ladder to change the bulb in the floodlight on the front of the house because it is 15 feet above the ground. Stephen needs to place the end of the ladder 8 feet away from the house so that it does not crush the flowers in the flower bed.

How tall must the ladder be to reach the height of the floodlight?


(IGNORE MY ANSWER I DIDNT MEAN TO CLICK ON IT)

Answers

Answer:

17 feet

Step-by-step explanation:

We can use the Pythagorean therom, since the triangle has a 90 degree angle:

         8^2 + 15^2 = x^2

         64  +  225 = x^2

          x^2 = 289

           x = 17 feet

See the attached worksheet.

The function y = - 16t2 + 248 models the height y in feet of a stone t seconds after it is dropped from the edge of a vertical cliff.
What is the original height of the stone before it is dropped?
How long will it take the stone to hit the ground? Round to the nearest hundredth of a second.

Answers

The height of the stone before it is dropped is 4.64 feet, and the time taken to hit the ground is 3.94 seconds.

What is function?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.

Given:

The function y =  - 16t² + 248

Calculate the value of t when f(t) = 0.

0 = -16t² + 248

t² = = 248 / 16 = 15.5

t = √15.5 ≈ 3.94  Seconds

Calculate the height at t = 3.94

y = -16 × 3.9² + 248

y = -243.36 + 248

y = 4.64 feet

Therefore, the height of the stone before it is dropped is 4.64 feet, and the time taken to hit the ground is 3.94 seconds.

To know more about function:

https://brainly.com/question/5975436

#SPJ1

Kevin ate 2/5 of a pie. Su yung ate 3/10 of the pie. how much of the pie did Kevin and Su Yang eat together

Answers

The total amount of pie Kevin and Su Yung ate together is 7/10 of the pie

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total amount of pie Kevin and Su Yung ate be = A

Now , the equation will be

The amount of pie Kevin ate = 2/5 of the total pie

And ,

The amount of pie Su Yung ate = 3/10 of the total pie

So , the equation is

Total amount of pie Kevin and Su Yung ate = amount of pie Kevin ate + amount of pie Su Yung ate

Substituting the values in the equation , we get

Total amount of pie Kevin and Su Yung ate A = 2/5 + 3/10

Total amount of pie Kevin and Su Yung ate A = ( 4 + 3 ) / 10

Total amount of pie Kevin and Su Yung ate A = 7 / 10 of the total pie

Therefore , the value of A is 7/10

Hence ,

The total amount of pie Kevin and Su Yung ate together is 7/10 of the pie

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

convert this rational number to its decimal form and round to the nearest thousandth 1/4

Answers

The given rational number 1/4 in the decimal form is 0.25 which is to the nearest thousandths.

What is decimal form?

We shall represent this as 1.5 pizzas in decimal form.

In this case, the dot stands in for the decimal point, the number before the dot, in this case, "1," represents one entire pizza, and the number after the decimal point, or the fractional component, represents the other half of the pizza.

So, we have the rational number:

1/4

Convert to decimal as follows:

1/4 = 0.25

Rounding off to the nearest thousandth: 0.2500 ⇒ 0.25

Therefore, the given rational number 1/4 in the decimal form is 0.25 which is to the nearest thousandths.

Know more about decimal form here:

https://brainly.com/question/17834668

#SPJ4

Which of the following is the axiom of congruence 2 points SSS SAS ASA SSA?

Answers

Two triangles are said to be congruent if their sides (S) and angles (A) are the same. SAS, ASA, SSS, and RHS serve as the triangle's congruence criteria. A triangle's congruency is not determined by SSA.

What does a math congruent mean?

Congruent refers to objects that are precisely the same size and shape. Even after the forms have been flipped, turned, or rotated, the shape and size ought to remain constant.

                   Draw two circles with the same radius, for instance, then cut them out and stack them.

How are three congruent?

An equilateral triangle is one that has all three of its sides be in line with one another. We add a slash mark to the sides that are congruent. An equilateral triangle's angles are 60°.

Learn more about Congruent

brainly.com/question/12413243

#SPJ4

the operations manager of a manufacturer of television remote controls wants to determine which batteries last the longest in his product. he took a random sample of his remote controls and tested two brands of batteries. the number of minutes of continuous use before the batteries failed for each brand are given in battery.xlsx . if significance level is 10%, is there statistical evidence of a difference in longevity between the two batteries?

Answers

There is no sufficient evidence to support the claim that there is a difference in the longevity of the two brands of batteries , as the null hypothesis failed to be rejected.

So the mean and standard deviation for the sample of battery 1 is :

M(1)=  106+ 111+ 109+ 105/4 =107.75

standard deviation (1)=r√(x(i)-M/(n-1)=root(22.75/3)=2.754

Similarly, for the second  battery, the mean and   standard deviation  is

M(2)= 125 +103+ 121+ 118/4=116.75

S(2)=√(276.75/3)=√(92.25)=9.605

Here the hypothesis test for the difference between populations means, here the claim is that the longevity of the two brands of batteries differs.So the alternative and null hypotheses are:

H(0)= μ1-μ2=0

H(1)=μ1-μ2 ≠0

Here the  significance level is 0.05(α), The difference between sample means is M(d)=107.75- 116.75=-9 .Now the  estimated standard error of the difference between the means is :

s(Md)=√(2.754²+9.605²/4)=4.996, Now the test static will be, t=-9-0/4.996=-1.8014 and the degree of freedom is 4+4-2=6 .Here  the test is two-tailed  with  degrees of freedom of  the test static is -1.8014, so the P-value for the  test is : 2.P(t< -1.8014)=0.122

Here the P-value (0.122) is greater than the significance level so the effect is insignificant, and the null hypothesis failed to be rejected.

To know more about the hypothesis refer to the  link brainly.com/question/28920252

#SPJ4

the operations manager of a manufacturer of television remote controls wants to determine which batteries last the longest in his product. he took a random sample of his remote controls and tested two brands of batteries. the number of minutes of continuous use before the batteries failed for each brand is given in battery.xlsx. if the significance level is 10%, is there statistical evidence of a difference in longevity between the two batteries?

The sample data for each battery is:

Battery 1: 106 111 109 105

Battery 2: 125 103 121 118

How do you use the binomial series to expand (1−x)^1/3?

Answers

The binomial series is used to expand a binomial expression of the form (a + b)^n, where 'a' and 'b' are constants and 'n' is a positive integer. In this case, we are expanding (1-x)^1/3.

Step 1: Rewrite the expression using the binomial theorem. We can rewrite (1-x)^1/3 as (1 + (-x))^1/3.

Step 2: Use the binomial theorem to expand the expression.

The binomial theorem states that (a + b)^n

= nC0*a^n + nC1*a^(n-1)*b + nC2*a^(n-2)*b^2 + ... + nCn*b^n.

Since 'n' is a 1/3 in this case, we can rewrite the expression as

(1 + (-x))^1/3

= 1C0*1^1/3 + 1C1*1^(1/3-1)*(-x) + 1C2*1^(1/3-2)*(-x)^2 + ...

Step 3: Substitute the values. We can substitute the values into the expression to get (1 + (-x))^1/3

= 1 + (-x) + (-x)^2 + ...

Step 4: Simplify the expression. The expression simplifies to

(1 - x + x^2 - x^3 + ...).

Learn more about binomial theorem at : https://brainly.com/question/27813780

#SPJ4

Complete the series 1,1,4,12,__

Answers

Hi how are you call 112 you will get nice

a special window has the shape of a rectangle surmounted by an equilateral triangle. see the figure. if the perimeter of the window is 16 feet, what dimensions will admit the most light?

Answers

A triangle whose sides are all equal is called an equilateral triangle and its area is given by A=[tex]\frac{\sqrt{3} }{4}[/tex] [tex]x^{2}[/tex], where x is the side of the triangle.

The area of a rectangle is found by using the formula

A=lw, where l is the length and w is the width.

The given figure can be split into two shapes: a rectangle and an equilateral triangle as shown in the diagram. Let l be the length of the rectangle.

Add all of the sides of the window and equate their result to 16. Then solve for l.

x + x + l + x + l = 16

3x + 2l = 16

2l = 16 - 3x

l = [tex]\frac{16-3x}{2}[/tex]

The total area of the window will be the sum of the area of the equilateral triangle ABE and the area of rectangle BCDE.

A = [tex]\frac{\sqrt{3} }{4}[/tex][tex]x^{2}[/tex] + lx

Subsitute  [tex]\frac{16-3x}{2}[/tex] for l into the obtained equation and simplify.

A =[tex]\frac{\sqrt{3} }{4}[/tex][tex]x^{2}[/tex] + ( [tex]\frac{16-3x}{2}[/tex])x

A = [tex]\frac{\sqrt{3} }{4} x^{2}[/tex] + 8x - [tex]\frac{3}{2} x^{2}[/tex]

Differentiate the obtained equation with respect to x and equate the first derivative to 0 to calculate the critical point x .

[tex]\frac{dA}{dx}[/tex] = [tex]\frac{\sqrt{3} }{4}[/tex] (2x) + 8 - [tex]\frac{3}{2}[/tex] (2x)

0 = [tex]\frac{\sqrt{3} }{2}[/tex] x - 3x + 8

x (3 - [tex]\frac{\sqrt{3} }{2}[/tex]) = 8

x = [tex]\frac{16}{6-\sqrt{3} }[/tex]≈3.74887

Again, differentiate the equation

[tex]\frac{dA}{dx}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex]x - 3x + 8  with respect to x.

[tex]\frac{d^{2}A }{dx^{2} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] - 3

The value of the second derivative is [tex]\frac{\sqrt{3} }{2}[/tex]−3, which is negative. This implies that the area will be maximum at the critical point.

Subsitute x = 3.74887 into the equation

l = [tex]\frac{16-3x}{2}[/tex] and simplify

l = [tex]\frac{16-(3)(.74887)}{2}[/tex] ≈ 2.3767

The maximum light will enter through the window when the triangular portion will have the side length of 3.74887 feet and the dimensions of the rectangular portion will be 3.74887-ft-by-2.3767-ft.

Learn more about surmounted related word problems by:

https://brainly.com/question/27547781

#SPJ4

Avery had $25.27 in her wallet. If she bought lunch with 10.75% dollars from her wallet, how much money did she have in her wallet after lunch?

Answers

Answer:

$22.55

Step-by-step explanation:

Not 100% sure but you can double check...

Other Questions
1. all of the following are true about intensive parenting except: a. it is emotionally absorbing b. it is labor-intensive c. it allows the parent great flexibility with time d. it is financially expensive group of answer choices Which certification can help you enhance your job prospects in the role of a computer programmer?; Is an associate degree enough for web development?; Can you be a computer programmer with an associate's degree?; Do all jobs that involve the web require a computer science degree? what is the preliminary treatment in a municipal wastewater treatment plant? preliminary treatment includes wastewater screening and . there is change in wastewater quality after the treatment. two users a and b have the following privileges: a can read and write a file f, and read, write, and execute a service program p. b can only read f and execute p. an intruder has managed to perform one of the violations: (i) guess a's password. (ii) guess b's password. (iii) place a passive wiretap on a's terminal line and intercept all data communication, except for the password, which is protected through encryption. (iv) place an active wiretap on a's terminal line, which allows the interception of all communication, except the password, but also allows insertion of arbitrary new messages into the communication stream. (a) for each of the 4 violations, (i) through (iv), describe a simple scenario, if one exists, that would lead to each of the following violations: information disclosure. information modification or destruction. unauthorized use of services. denial of service. daily backups are completed at the abd company location, and only a weekly backup is maintained at another network location. which of the following disaster recovery strategies is abd using? answer hot spare cold site hot site warm site if b is an integer how would you represent the next 6 even integers scientists discovered that the enhancer associated with hair color has a binding site for a particular transcription factor. one of the binding sites has the sequence cactaag and is associated with dark hair, and the other form of the binding site has the nearly identical sequence cgctaag. how could these two nearly identical enhancer binding sites lead to different rates of initiating transcription of the regulated gene? PLEASE HELP ITS A TIMED QUESTION Evaluate 5-4 and 5-2 Jackie Revez purchased a new home in Riverside Park. The purchase price was $210,000, and she put down 30%. Her mortgage is 10 1/2% for 30 years. What is the outstanding balance of her loan after the first month? (Round your answer to the nearest cent.) On July 1, 2020, Cheyenne Corporation purchased Young Company by paying $256,300 cash and issuing a $100,000 note payable to Steve Young. At July 1, 2020, the balance sheet of Young Company was as follows. Cash $50,100 Accounts payable $205,000 Accounts receivable 89,900 Stockholders equity 242,900 Inventory 109,000 $447,900 Land 40,200 Buildings (net) 76,000 Equipment (net) 70,900 Trademarks 11,800 $447,900 The recorded amounts all approximate current values except for land (fair value of $63,400), inventory (fair value of $125,600), and trademarks (fair value of $16,000). Collapse question part (a) Partially correct answer. Your answer is partially correct. Try again. Prepare the July 1 entry for Cheyenne Corporation to record the purchase. (Credit account titles are automatically indented when amount is entered. Do not indent manually. If no entry is required, select "No Entry" for the account titles and enter 0 for the amounts.) Account Titles and Explanation Debit Credit enter an account titleenter an account titleEntry field with correct answer Cash enter a debit amountenter a debit amountEntry field with correct answer 50,100 enter a credit amountenter a credit amountEntry field with correct answer enter an account titleenter an account titleEntry field with correct answer Accounts Receivable enter a debit amountenter a debit amountEntry field with correct answer 89,900 enter a credit amountenter a credit amountEntry field with correct answer enter an account titleenter an account titleEntry field with correct answer Inventory enter a debit amountenter a debit amountEntry field with correct answer 125,600 enter a credit amountenter a credit amountEntry field with correct answer enter an account titleenter an account titleEntry field with correct answer Land enter a debit amountenter a debit amountEntry field with correct answer 63,400 enter a credit amountenter a credit amountEntry field with correct answer enter an account titleenter an account titleEntry field with correct answer Buildings enter a debit amountenter a debit amountEntry field with correct answer 76,000 enter a credit amountenter a credit amountEntry field with correct answer enter an account titleenter an account titleEntry field with correct answer Equipment enter a debit amountenter a debit amountEntry field with correct answer 70,900 enter a credit amountenter a credit amountEntry field with correct answer enter an account titleenter an account titleEntry field with correct answer Trademarks enter a debit amountenter a debit amountEntry field with correct answer 16,000 enter a credit amountenter a credit amountEntry field with correct answer enter an account titleenter an account titleEntry field with correct answer Goodwill enter a debit amountenter a debit amountEntry field with incorrect answer now contains modified data enter a credit amountenter a credit amountEntry field with correct answer enter an account titleenter an account titleEntry field with correct answer Accounts Payable enter a debit amountenter a debit amountEntry field with correct answer enter a credit amountenter a credit amountEntry field with correct answer 205,000 enter an account titleenter an account titleEntry field with correct answer Cash enter a debit amountenter a debit amountEntry field with correct answer enter a credit amountenter a credit amountEntry field with correct answer 256,300 enter an account titleenter an account titleEntry field with correct answer Notes Payable enter a debit amountenter a debit amountEntry field with correct answer enter a credit amountenter a credit amountEntry field with correct answer 100,000 QUESTION 12 A voucher is usually supported by a. a supplier's invoice b. a purchase order c. a receiving report d. all of theseQUESTION 13 The bank reconciliation a. is part of the internal control system b.is for information purposes only c. is sent to the bank for verification d. should be prepared by an employee who records cash transactions Which property justifies the step?2x +3 = -5x -17x + 3 = -1A. distrubutive propertyB. addition property of equalityc. commutative propertyD. subtraction property of equality Write the formula of each of the following ions or compounds.(a) pentaaquachlorochromium(III) chloride(b) tetraamminedinitrorhodium(III) bromide(c) dichlorobis(ethylenediamine)ruthenium(III)(d) diaquatetrachlororhodate(III)(e) triamminetribromoplatinum(IV) what is considered the hallmark of children who are securely attached to their mothers? explain how the proteins coded by the recombinant dna plasmid initiated in this exercise could be synthesized using bacteria cells. Which statement best reflects the solution(s) of the equation? 1/x+1/x3=x2/x3a. There is only one solution: x = 1. The solution x = 3 is an extraneous solution.b. There are two solutions: x = 1 and x = 3.c. There is only one solution: x = 3. The solution x = 1 is an extraneous solution.d. There is only one solution: x = 1. The solution x = 0 is an extraneous solution. After making content decisions and designing the site, the next step in the process of developing a website is connecting to the Internet by placing the required computer files on a serverT/F the of the brain allows you to become aware of pain coldness a light touch A nurse is assessing the newborn of a client who took a selective serotonin reuptake inhibitor (SSRI) during pregnancy. Which of the following manifestations should the nurse identify as an indication of withdrawal from an SSRI?Expected clinical manifestation associated with fetal exposure to SSRIs include irritability, agitation, tremors, diarrhea, and vomiting. These manifestations typically last 2 days.TachypneaHypoglycemiaLow birth weight The social enterprise serves which of the following purposes?a. Welfare servicesb. Social causesc. Public servicesd. Charitable causes