If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 28 inches, what diameter pizza will reward you with the largest slice

Answers

Answer 1

Answer:

The diameter that will reward with the largest pizza is 14 in

Step-by-step explanation:

The perimeter of a sector of a circle is:

P = 2r + l

l = rθ

P = 2r + rθ

P=28 inches

28=2r + rθ

28-2r=rθ

θ=(28-2r/r)

=(2*14 - 2*r)/r

=2(14-r)/r

Area of the sector of the circle is:

A = r²/2 * θ

A = r²/2 * 2(14 - r)/r

A = r² * (14 - r)/r

A = r(14 - r)

A = 14r - r²

For the maximum area:

A = 14r - r²

A' = 14 - 2r

Set A' = 0

14 - 2r = 0

14= 2r

r = 7 in

The diameter (D) of the circle is twice of the radius:

D = 2r = 2 * 7= 14 in

The maximum area is:

A = 14r - r²

r = 7 in

A = 14 * 7 - 7²

A = 98 - 49

A = 49 in²


Related Questions

Let f(x) = - 4x + 5. Find and simplify f(x + 2).

Answers

Answer:

-4x - 3.

Step-by-step explanation:

f(x) = -4x + 5.

f(x + 2) = -4(x + 2) + 5

= -4x - 8 + 5

= -4x - 3.

Hope this helps!

Answer:

f(x+2)=-4x-3

Step-by-step explanation:

We are given:

[tex]f(x)= -4x+5[/tex]

and asked to find f(x+2). Therefore, we must substitute x+2 for each x in the function.

[tex]f(x+2)=-4(x+2)+5[/tex]

Now, simplify. First, distribute the -4. Multiply each term inside the parentheses by -4.

[tex]f(x+2)=(-4*x)+(-4*2)+5\\f(x+2)=-4x+(-4*2)+5\\f(x+2)=-4x-8+5[/tex]

Next, combine like terms. There are 2 constants (terms without a variable) that can be added. Add -8 and 5.

[tex]f(x+2)=-4x(-8+5)\\f(x+2)=-4x-3[/tex]

f(x+2) is -4x-3.


The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 6. If there were 4508 no votes, what was the total
number of votes

Answers

Answer:

 total  number of votes was  8265.

Step-by-step explanation:

Ratio of yes to no votes = 5:6

we know by rule of indices that

a/b = a*x/b*x

let the no. of people who voted yes be 5x

the no. of people who voted no be 6x

Thus, total no of votes = 5x+6x= 11x

given that

If there were 4508 no votes

thus,

6x = 4508

x = 4508/6 = 751 1/3 = 751.33

Thus, total no. of votes = 11 x = 11* 751.33 = 8264.63

rounding it to next integral no. as no. of votes cannot be fraction or decimal

the total  number of votes was  8265.

What are the following fractions from least to greatest 3/8 5/8 4/8 2/8 7/8

Answers

Answer:

2/8, 3/8, 4/8, 5/8, 7/8. If there are more numbers I apologize, I see 2 boxes that say "obj" instead.

PLEASE HELP! You do not have to answer all questions but can someone explain to me on where I am even suppose to begin? I don't even know how to answer a single one of these questions.

Answers

Step-by-step explanation:

For problems 1 through 15, evaluate the function at the given x value.

1. f(5) = 2(5) − 1 = 9

2. f(3) = 3² − 3(3) − 1 = -1

3. f(0) = 2(0) + 5 = 5

So on and so forth.

Then, match each answer with the corresponding letter.

The answer to #1 was 9.  9 corresponds to the letter A.

The answer to #2 was -1.  -1 corresponds to the letter C.

The answer to #3 was 5.  5 corresponds to the letter P.

Finally, write each letter with its corresponding problem number.

So everywhere you see a 1, write A.

Everywhere you see a 2, write C.

Everywhere you see a 3, write P.

Continue until every blank has a letter and the problem is solved.

Answer:

For problems 1 through 15, evaluate the function at the given x value.

1. f(5) = 2(5) − 1 = 9

2. f(3) = 3² − 3(3) − 1 = -1

3. f(0) = 2(0) + 5 = 5

So on and so forth.

Step-by-step explanation:

average age of 15 students of iub 11years if teacher is also included average age becomes 13 years how old is teachers

Answers

Answer: the teacher is 43

Step-by-step explanation: if you take 11 and multiply it by 15 you get 165 if you take 208 and divide it by 16 you get 13.

so basically you subtract 208 from 165 to get 43

Which of the following correctly shows the quotient of 80 divided by 5 ?

Answers

Answer:16

Step-by-step explanation:

Just divide 80 by 5 or skip count by fives.

What is the 50th term of the arithmetic sequence having u(subscript)1 = -2 and d = 5

Answers

Answer:

243

Step-by-step explanation:

The general term for this arithmetic sequence is:

a(n) = -2 + 5(n - 1).

Then a(50) = -2 + 5(49) =   243

Mrs. Simpson’s calculus class has an exam with an average score of 80 and standard deviation of 15. Assume that exam scores are normally distributed. If Mrs. Simpson decides to give an A grade to students who score in the top 20% of the class, what exam score is needed in order to get the A grade? (3pts)

Answers

Answer:

93 is the exam score needed in order to get the A grade in Mrs Simpson’s test

Step-by-step explanation:

Let x be the score that gives an A grade

Mathematically from the z-score formula, we know that;

z-score = x-mean/SD

From the question, x = ? , mean = 80 and SD = 15

Thus;

z-score = x-80/15

But in this question, we have the probability but we do not have the z-score

So we need the z-score that is equivalent to 20%

20% is same as 0.2

Using the standard normal distribution table, a probability of 0.2 corresponds to a z-score of 0.84

Thus, mathematically;

0.84 = x-80/15

x-80 = 15(0.84)

x-80 = 12.6

x = 80 + 12.6

x = 92.6 which is approximately 93

Suppose that 80% of all registered California voters favor banning the release of information from exit polls in presidential elections until after the polls in California close. A random sample of 25 registered California voters is selected.

Required:
a. Calculate the mean and standard deviation of the number of voters who favor the ban.
b. What is the probability that exactly 20 voters favor the ban?

Answers

Answer:

a. Mean = 20

Sd = 4

b. Probability of X = 20 = 0.1960

Step-by-step explanation:

we have

n = 25

p = 80% = 0.8

mean = np

= 0.8 * 25

= 20

standard deviation = √np(1-p)

= √25*0.8(1-0.8)

=√4

= 2

probability that exactly 20 favours ban

it follows a binomial distribution

= 25C20 × 0.8²⁰ × 0.2⁵

= 53130 × 0.01153 × 0.00032

= 0.1960

Probability of X = 20 = 0.1960

(21x-3)+21=23x+6 solve​

Answers

Answer:

False

Step-by-step explanation:

You Cnat solve it

Answer:

you cannot solve it

Step-by-step explanation:

false

Find the inverse of the following function.

Answers

Answer:

The inverse is 1/64 x^2 = y   x ≥ 0

Step-by-step explanation:

f(x) = 8 sqrt(x)

y = 8 sqrt(x)

Exchange x and y

x = 8 sqrt (y)

Solve for y

Divide each side by 8

1/8 x = sqrt(y)

Square each side

(1/8 x)^2 = (sqrt(y))^2

1/64 x^2 = y

The inverse is 1/64 x^2 = y   x ≥ 0

since x ≥0 in the original function

Answer:

[tex]\Huge \boxed{\mathrm{D}}[/tex]

Step-by-step explanation:

[tex]f(x)=8\sqrt{x}[/tex]

[tex]\sf Replace \ with \ y.[/tex]

[tex]y=8\sqrt{x}[/tex]

[tex]\sf Switch \ the \ variables.[/tex]

[tex]x= 8\sqrt{y}[/tex]

[tex]\sf Divide \ both \ sides \ of \ the \ equation \ by \ 8.[/tex]

[tex]\displaystyle \frac{x}{8} =\sqrt{y}[/tex]

[tex]\sf Square \ both \ sides \ of \ the \ equation.[/tex]

[tex]\displaystyle (\frac{x}{8} )^2 =y[/tex]

[tex]\displaystyle \frac{x^2 }{64} =y[/tex]

[tex]\displaystyle f^{-1}(x)=\frac{1}{64} x^2[/tex]

Find x. A. 3√3 B. 3 C. 2√3/3 D. √63

Answers

Answer:

[tex]\huge\boxed{\sf x = 3\sqrt{3}}[/tex]

Step-by-step explanation:

Cos 30 = Adjacent / Hypotenuse

Where Adjacent = x , Hypotenuse = 6

[tex]\frac{\sqrt{3} }{2}[/tex] = x / 6

x = [tex]\frac{\sqrt{3} }{2}[/tex]  * 6

[tex]\sf x = 3\sqrt{3}[/tex]

What is the exact distance from (−1, 4) to (6, −2)? square root of 80. units square root of 82. units square root of 85. units square root of 89. units

Answers

Answer:

[tex]\sqrt{85}[/tex].

Step-by-step explanation:

[tex]x[/tex]-coordinates:

First point: [tex]-1[/tex].Second point: [tex]6[/tex].Difference: [tex]|-1 - 6| = |-7| = 7[/tex].

[tex]y[/tex]-coordinates:

First point: [tex]4[/tex].Second point: [tex]-2[/tex].Difference: [tex]|4 - (-2)| = |6| = 6[/tex].

Refer to the diagram attached. Consider these two points as the two end points of the hypotenuse of a right triangle. The lengths of the two legs are equal to:

the difference between the two [tex]x[/tex]-coordinates, [tex]7[/tex], and the difference between the two [tex]y[/tex]-coordinates, [tex]6[/tex].

Apply Pythagorean Theorem to find the length of the hypotenuse (which is equal to the distance between the two points in question.)

[tex]\begin{aligned}\text{Hypotenuse} &= \sqrt{(\text{First Leg})^2 + (\text{Second Leg})^2} \\ &= \sqrt{7^2 + 6^2} \\ &= \sqrt{85}\end{aligned}[/tex].

Answer:

C

Step-by-step explanation:

Find the slope of the line through the points (-4, 6) and (8,4).

I need help on this

Answers

Start with the slope formula.

m = y2-y1/x2 - x1

We take the second y minus the first y

over the second x minus the first x.

So we have 4 - 6/8 - -4.

This simplifies to -2/12 which reduces to -1/6.

A person standing close to the edge on top of a 96-foot building throws a ball vertically upward. The quadratic function h = − 16 t 2 + 116 t + 96 models the ball's height above the ground, h , in feet, t seconds after it was thrown. a) What is the maximum height of the ball? b) How many seconds does it take until the ball hits the ground?

Answers

Answer:  a)  306.25 feet   b) 8 s

Step-by-step explanation:

Actually we have to find the function' s  h(t)  maximum meaning.

To do that we have to find the corresponding t - let call it t max

As known t max= (t1+t2)/2 where t1 and t2 are the roots of quadratic equation' s  

Lets find the roots t1 and t2

-16*t^2+116*t+96=0   divide by 4 each side of the equation

-4*t^2 +29*t+24=0

D=29^2+24*4*4=1225 =35^2

t1=(-29-35)/(-8)=8

t2=(-29+35)/(-8)=-6/8=-3/4=-0.75

t max=  (8+(-0.75))= 7,25/2=3.625 s

h max= -16*t max ^2+116*t +96= -16*3.625^2+116*3.625+96=306.25 feet

b) t2=8s is the time when the ball hits the ground.

Answer:

  a) 306.25 ft

  b) 8 seconds

Step-by-step explanation:

a) The time at the maximum height is found from the equation for the axis of symmetry:

  ax^2 +bx +c   has axis of symmetry at x=-b/(2a)

For the given equation, the t-value at the vertex is ...

  t = -116/(2(-16)) = 3.625 . . . seconds

At that time, the height is ...

  h = (-16(3.625) +116)(3.625) +96 = (58)(3.625) +96 = 306.25

The maximum height is 306.25 feet.

__

b) The ball will hit the ground when h=0. From the vertex values in the first part, we know we can rewrite the equation in vertex form as ...

  h(t) = -16(t -3.625)^2 +306.25

This will be 0 when ...

  0 = -16(t -3.625)^2 +306.25

  (t -3.625)^2 = 306.25/16

  t = 3.625 +√19.140625 = 3.625 +4.375 = 8

The ball will hit the ground after 8 seconds.

A highway department executive claims that the number of fatal accidents which occur in her state does not vary from month to month. The results of a study of 140 fatal accidents were recorded. Is there enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month? Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Fatal Accidents 8 15 9 8 13 6 17 15 10 9 18 12

Answers

Answer:

There is enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month, as the Variance is 14 and the Standard Deviation = 4 approximately.

There is a high degree of variability in the mean of the population as explained by the Variance and the Standard Deviation.

Step-by-step explanation:

Month       No. of              Mean       Squared

           Fatal Accidents  Deviation   Difference

Jan          8                       -4                  16

Feb        15                        3                   9

Mar         9                       -3                   9

Apr         8                       -4                  16

May       13                        1                    1

Jun         6                      -6                 36

Jul         17                       5                 25

Aug       15                       3                   9

Sep       10                      -2                   4

Oct        9                       -3                   9

Nov    18                          6                 36

Dec    12                          0                   0

Total 140                                         170

Mean = 140/12 = 12    Mean of squared deviation (Variance) = 170/12 = 14.16667

Standard deviation = square root of variance = 3.76386 = 4

The fatal accidents' Variance is a measure of how spread out the fatal accident data set is. It is calculated as the average squared deviation of the number of each month's accident from the mean of the fatal accident data set.  It also shows how variable the data varies from the mean of approximately 12.

The fatal accidents' Standard Deviation is the square root of the variance, and a useful measure of variability when the distribution is normal or approximately normal.

Simplify 3m2 (−6m3 )

Answers

Answer:

3m2(-6m3)

since it's a term you have to multiply it by the number in bracket

6m(-6m3)

6m(-18m)

-108m²

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 53.9 for a sample of size 24 and standard deviation 5.6. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 90% confidence level). Assume the data is from a normally distributed population. Enter your answer as a tri-linear inequality accurate to three decimal places.

_______ < μ < _________ please teach using calculator method

Answers

Answer:

The  estimate is

             [tex]52.02 < \mu < 55.78[/tex]

Step-by-step explanation:

From the question we are told that

    The sample mean is [tex]\ = x = 53.9[/tex]

     The sample size is  n =  24

      The standard deviation is  [tex]\sigma = 5.6[/tex]

 

Given that the confidence level is  90% the level of significance is mathematically represented as

           [tex]\alpha = 100 - 90[/tex]

            [tex]\alpha = 10 \%[/tex]

            [tex]\alpha = 0.10[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table.The value is  

           [tex]Z_{\frac{\alpha }{2} } =Z_{\frac{0.10 }{2} } = 1.645[/tex]

The reason we are obtaining critical value of    [tex]\frac{\alpha }{2}[/tex] instead of    [tex]\alpha[/tex] is because    [tex]\alpha[/tex]

represents the area under the normal curve where the confidence level interval (  [tex]1 - \alpha[/tex] ) did not cover which include both the left and right tail while  

[tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the margin of error

NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)

Generally the margin of error is mathematically represented as

          [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{ \sqrt{n} }[/tex]

substituting values

         [tex]E = 1.645 * \frac{5.6 }{ \sqrt{24} }[/tex]

          [tex]E = 1.880[/tex]

The  estimate of how much the drug will lower a typical patient's systolic blood pressure(using a 90% confidence level) is mathematically represented as

         [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

         [tex]53.9 - 1.880 < \mu < 53.9 + 1.880[/tex]

         [tex]52.02 < \mu < 55.78[/tex]

Test the age of the participants (AGE1) against the null hypothesis H0 = 34. Use a one-sample t-test. How would you report the results?

Answers

Answer:

t = -1.862, df = 399, p > 0.05

Step-by-step explanation:

The null hypothesis is the statement which is test for its validity. The decision to accept or reject the null hypothesis is based on the test statistics value. In the given question the null hypothesis is H0 = 34. There is one sample t-test for the testing of null hypothesis. The null hypothesis will be same for each type of one sample t-test. The null hypothesis assumes that the difference between the true mean and comparison value is zero.

An Uber driver provides service in city A and city B only dropping off passengers and immediately picking up a new one at the same spot. He finds the following Markov dependence. For each trip, if the driver is in city A, the probability that he has to drive passengers to city B is 0.25. If he is in city B, the probability that he has to drive passengers to city A is 0.45. Required:a. What is the 1-step transition matrix? b. Suppose he is in city B, what is the probability he will be in city A after two trips? c. After many trips between the two cities, what is the probability he will be in city B?

Answers

Answer:

a.  1-step transition matrix is be expressed as:

[tex]P= \left[\begin{array}{cc}0.75&0.25\\0.45&0.55\\\end{array}\right][/tex]

b. The probability that he will be in City A after two trips given that he is in City B  = 0.585

c. After many trips, the probability that he will be in city B = 0.3571

Step-by-step explanation:

Given that:

For each trip, if the driver is in city A, the probability that he has to drive passengers to city B is 0.25

If he is in city B, the probability that he has to drive passengers to city A is 0.45.

The objectives are to calculate the following :

a. What is the 1-step transition matrix?

To  determine the 1 -step transition matrix

Let the State ∝ and State β denotes the Uber Driver providing service in City A and City B respectively.

∴  The transition probability from state ∝ to state β is 0.25.

The transition probability from state ∝ to state ∝ is 1- 0.25 = 0.75

The transition probability from state β to state ∝ is 0.45. The transition probability from state β to state β is 1 - 0.45 = 0.55

Hence; 1-step transition matrix is be expressed as:

[tex]P= \left[\begin{array}{cc}0.75&0.25\\0.45&0.55\\\end{array}\right][/tex]

b. Suppose he is in city B, what is the probability he will be in city A after two trips?

Consider [tex]Y_n[/tex] = ∝ or β  to represent the Uber driver is in City A or City B respectively.

∴ The probability that he will be in City A after two trips given that he is in City B

=[tex]P(Y_0 = 2, Y_2 = 1 , Y_3 = 1) + P(Y_0 = 2, Y_2 = 2 , Y_3 = 1)[/tex]

= 0.45 × 0.75 + 0.55 × 0.45

= 0.3375 + 0.2475

= 0.585

c. After many trips between the two cities, what is the probability he will be in city B?

Assuming that Ф = [ p  q ] to represent the long run proportion of time that Uber driver is in City A or City B respectively.

Then, ФP = Ф  , also  p+q = 1  , q = 1 - p  and p = 1 - q

[tex][ p\ \ \ q ] = \left[\begin{array}{cc}0.75&0.25\\0.45&0.55\\\end{array}\right] [ p\ \ \ q ][/tex]

0.75p + 0.45q = q

-0.25p + 0.45q = 0

since p = 1- q

-0.25(1 - q) + 0.45q = 0    

-0.25 + 0.25 q + 0.45q = 0

0.7q = 0.25

q = [tex]\dfrac{0.25} {0.7 }[/tex]

q =  0.3571

After many trips, the probability that he will be in city B = 0.3571

A waiter earns $11.00 an hour and approximately 10% of what he serves in a shift. If he works a 6 hour shift and takes $425 in orders, his total earnings for the six hours would be:


Answers

Answer:

108.50

Step-by-step explanation:

First find the wages

11* 6 = 66 dollars

Then figure the commission

10% of 425

.10 * 425

42.5

Add the two amounts together

42.5+66

108.50

HELP ASAP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

Option (B)

Step-by-step explanation:

The given expression is,

[tex]\sqrt{22x^6}\div\sqrt{11x^4}[/tex]

We can rewrite this expression as,

[tex]\frac{\sqrt{22x^6}}{\sqrt{11x^4} }[/tex]

Solving it further,

[tex]\frac{\sqrt{22x^6}}{\sqrt{11x^4} }=\frac{\sqrt{22(x^3)^2} }{\sqrt{11(x^2)^2} }[/tex] [Since [tex]x^3\times x^3=x^6[/tex] and [tex]x^{2}\times x^{2}=x^4[/tex]]

         [tex]=\sqrt{\frac{22(x^3)^2}{11(x^2)^2} }[/tex] [Since [tex]\frac{\sqrt{a} }{\sqrt{b} }=\sqrt{\frac{a}{b} }[/tex]]

         [tex]=\frac{x^3}{x^2}\sqrt{\frac{22}{11} }[/tex]

         [tex]=x\sqrt{2}[/tex]

Therefore, quotient will be x√2.

Option (B) will be the correct option.

To which number sets of numbers does the number 3.567...belong?

Answers

Answer:

It's irrational number
Answer: irrational number set, real number set

If the decimal digits do not repeat in some known pattern, then the number is irrational. We cannot write it as a ratio or fraction of two integers. If it did have a pattern, then we can use algebra to find the fractional representation of that number. Based on what is shown, it looks like there is no pattern so that's why the value is irrational. The number is also a real number as this is the case with any number you'll encounter unless you're dealing with complex numbers (but your teacher may not have introduced that topic yet).

The difference between teenage female and male depression rates estimated from two samples is 0.07. The estimated standard error of the sampling distribution is 0.03. What is the 95% confidence interval

Answers

Answer:

The 95%  confidence interval is  [tex]0.0112 < \mu_m - \mu_f < 0.1288[/tex]

Step-by-step explanation:

From  the question we are told that  

      The  sample  mean difference is  [tex]\= x_m - \= x_f = 0.07[/tex]

       The  standard error  is  SE  =  0.03

Given that the confidence interval is  95% then the level of significance is mathematically evaluated as

               [tex]\alpha = 100 - 95[/tex]

               [tex]\alpha = 5\%[/tex]

               [tex]\alpha =0.05[/tex]

Next  we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is  [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

         [tex]E = Z_{\frac{ \alpha }{2} } * SE[/tex]

substituting values

         [tex]E = 1.96 * 0.03[/tex]

         [tex]E = 0.0588[/tex]

The 95% confidence interval  is mathematically represented as

      [tex](\= x_m - \= x_f ) - E < \mu_m - \mu_f <(\= x_m - \= x_f ) + E[/tex]

substituting values

     [tex]0.07 - 0.0588 < \mu_m - \mu_f <0.07 + 0.0588[/tex]

    [tex]0.0112 < \mu_m - \mu_f < 0.1288[/tex]

     

The difference between teenage female and male depression rates are given. The 95% percent confidence interval can be obtained using mean and standard error relation.

The confidence interval is (0.0016 , 0.1584).

Given:

The depression rates is [tex]0.07[/tex].

The standard error of sampling distribution is [tex]0.03[/tex].

The critical value [tex]z=1.96[/tex]

Write the relation for mean and standard error.

[tex]\mu\pm z_{\rm critical}+\rm standard\: error[/tex]

Substitute the value.

[tex]0.07\pm 1.96\times 0.03=(0.1288,\:0.0112)[/tex]

Therefore, the upper and lower boundary is [tex](0.1288,\:0.0112)[/tex]. Thus, The confidence interval is (0.0016 , 0.1584).

Learn more mean and standard error here:

https://brainly.com/question/20215215

a family spent $93 at a carnival.
*they spent $18 on tickets and $30 on food. they spent the rest of the money on games.

which equation can be used to to find "g", the amount of money used on games.

Answers

Answer: 93-(18+30)=g

93-48=g

45=g

Step-by-step explanation: yup

The answer is 93-18-30-g=0 or 18+30+g=93

How many times does 1/4 go into 3/8

Answers

Answer:

3/2

Step-by-step explanation:

3/8 ÷ 1/4

Copy dot flip

3/8 * 4/1

12/8

Divide top and bottom by 4

3/2

Charlie needs a $275,000 mortgage and he'd like to pay it off in 30 years. He is considering two banks. Bank A: 3.5% with monthly payments of $1234.87 Bank B: 4% with monthly payments of $1312.89 Charlie doesn't think a 0.5% difference is that much. What is the difference between these two bank loans with total interest paid over the life of the loan?

Answers

Answer:

Difference in interest= $41,250

Step-by-step explanation:

To calculate the interest paid on each bank loan we use the following formula

Interest = Principal * Rate * Time

For Bank A

Interest = 275,000 * 0.035 * 30

Interest = $288,750

For Bank B

Interest = 275,000 * 0.04 * 30

Interest = $330,000

Therefore

Difference in interest= 330,000 - 288,750

Difference in interest= $41,250

Therefore if the mortgage is taken from Bank B he will pay an extra $41,250 on the loan.

The 0.5% difference in rates has a large impact over the 30 year term loan

Divide write the quotient in lowest term 1 1/3 divided by 1 3/4

Answers

Answer:

7/3  or 2 1/3

Step-by-step explanation:

1 1/3 ÷ 1  3/4

Change to improper fractions

(3*1+1)/3 ÷ (4*1+3)/4

4/3 ÷ 7/4

Copy dot flip

4/3 * 7/4

Rewriting

4/4 * 7/3

7/3

As a mixed number

2 1/3

Answer:

11/3÷13/4

11/3×4/13

44/39=

1.1282

When you enter the Texas Turnpike, they give you a ticket showing the time and place of your entry. When you exit, you turn in this ticket and they use it to figure your toll. Because they know the distance between toll stations, they can also use it to check your average speed against the turnpike limit of 65 mph. On your trip, heavy snow limits your speed to 40 mph for the first 120 mi. At what average speed can you drive for the remaining 300 mi without having your ticket prove that you broke the speed limit?

Answers

Answer:

87 mph

Step-by-step explanation:

Total distance needed is 120 mi + 300 mi and that is 420 mi.

Driving at 65 mph means that it would take

420 / 65 hours to reach his destination.

6.46 hours .

at the first phase, he drove at 40 mph for 120 mi, this means that it took him

120 / 40 hours to complete the journey.

3 hours.

the total time needed for the whole journey is 6.46 hours, and he already spent 3 hours in the first phase. To keep up with the 6.46 hours required, in the second phase, he has to drive at a speed of

6.46 - 3 hours = 3.46 hours.

300 mi / 3.46 hours => 86.71 mph approximately 87 mph

Therefore, he needs to drive at not more than 87 mph to keep up with the journey while not breaking his speed limit

Select the function that represents a parabola with zeros at x = –2 and x = 4, and y-intercept (0,–16). A ƒ(x) = x2 + 2x – 8 B ƒ(x) = 2x2 + 4x – 16 C ƒ(x) = x2 – 2x – 8 D ƒ(x) = 2x2 – 4x – 16

Answers

Answer:

D. [tex]f(x) = 2\cdot x^{2}-4\cdot x -16[/tex]

Step-by-step explanation:

Any parabola is modelled by a second-order polynomial, whose standard form is:

[tex]y = a\cdot x^{2}+b\cdot x + c[/tex]

Where:

[tex]x[/tex] - Independent variable, dimensionless.

[tex]y[/tex] - Dependent variable, dimensionless.

[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Coefficients, dimensionless.

In addition, a system of three linear equations is constructed by using all known inputs:

(-2, 0)

[tex]4\cdot a -2\cdot b + c = 0[/tex] (Eq. 1)

(4, 0)

[tex]16\cdot a + 4\cdot b +c = 0[/tex] (Eq. 2)

(0,-16)

[tex]c = -16[/tex] (Eq. 3)

Then,

[tex]4\cdot a - 2\cdot b = 16[/tex] (Eq. 4)

[tex]16\cdot a + 4\cdot b = 16[/tex] (Eq. 5)

(Eq. 3 in Eqs. 1 - 2)

[tex]a - 0.5\cdot b = 4[/tex] By Eq. 4 (Eq. 4b)

[tex]a = 4 + 0.5\cdot b[/tex]

Then,

[tex]16\cdot (4+0.5\cdot b) + 4\cdot b = 16[/tex] (Eq. 4b in Eq. 5)

[tex]64 + 12\cdot b = 16[/tex]

[tex]12\cdot b = -48[/tex]

[tex]b = -4[/tex]

The remaining coeffcient is:

[tex]a = 4 + 0.5\cdot b[/tex]

[tex]a = 4 + 0.5\cdot (-4)[/tex]

[tex]a = 2[/tex]

The function that represents a parabola with zeroes at x = -2 and x = 4 and y-intercept (0,16) is [tex]f(x) = 2\cdot x^{2}-4\cdot x -16[/tex]. Thus, the right answer is D.

Answer:

D ƒ(x) = 2x2 – 4x – 16

Step-by-step explanation:

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