On moving day, Guyton needs to rent a truck. The length of the cargo space is , and the height is less than the width. The brochure indicates that the truck can hold . What are the dimensions of the cargo space

Answer:

Step-by-step explanation:

When the input is 4, the output of f(x) = x + 21 is f(4).

Substitute x = 4 to f(x):

f(4) = 4 + 21 = 25

Answer:

25

Step-by-step explanation:

We can find the output by plugging in 4 as x into the function:

f(x) = x + 21

f(4) = 4 + 21

f(4) = 25

Answer:

r=$14,400

The hotel should charge $120

Step-by-step explanation:

Revenue (r)= p * n

where,

p = price per item

n = number of items sold

A change in price leads to a change in number sold

A variable to measure the change in p and n needs to be introduced

Let the variable=x

Such that

p + x means a one dollar price increase

p - x means a one dollar price decrease

n + x means a one item number-sold increase

n - x means a one item number-sold decrease

for each $2 price increase (p + 2x) there are 3 fewer rooms are rented (n-3x)

know that at $60 per room, the hotel rents 210 rooms

r = (60 + 2x) * (210 - 3x)

=12,600-180x+420x-6x^2

=12,600+240x-6x^2

r=2100+40x-x^2

= -x^2 +40x+2100=0

Solve the quadratic equation

x= -b +or- √b^2-4ac / 2a

a= -1

b=40

c=2100

x= -b +or- √b^2-4ac / 2a

= -40 +or- √(40)^2 - (4)(-1)(2100) / (2)(-1)

= -40 +or- √1600-(-8400) / -2

= -40 +or- √ 1600+8400 / -2

= -40 +or- √10,000 / -2

= -40 +or- 100 / -2

x= -40+100/-2 OR -40-100/-2

=60/-2 OR -140/-2

= -30 OR 70

x=70

The quadratic equation has a maximum at x=70

p+2x

=60+2(30)

=60+60

=$120

r= (60 + 2x) * (210 - 3x)

={60+2(30)}*{(210-3(30)}

r=(60+60)*(210-90)

=120*120

=$14,400

Answer:

14.24%

Step-by-step explanation:

We have found that the yield to call (YTC) formula is:

YTC = [C + (F-P) / N] / [(F + P) / 2]

Where:

C = Periodic coupon amount = 95

P = Current Price = 980

F = Redemption amount = 1150

N = time left to redemption = 3

We replace:

YTC = [95 + (1150-980) / 3] / [(1150 + 980) / 2]

YTC = 0.1424

In other words, the yield to call (YTC) is equal to 14.24%

Answer:

It is a well formed formula

Step-by-step explanation:

1 - p,q,r are well formed formulas.

2 - [tex]p \ \lor \ q[/tex]  is a well formed formula as well.

3 - [tex]\neg r[/tex] is a well formula as well

4 - [tex](\ p \ \lor \ q) \ \land \ \neg r[/tex] is a well formula as well.

Answer:

x = 3/2

y = 2

z = 3/2

Step-by-step explanation:

There are multiple methods to solve these. Message me for the method you need to see step by step.

Answer:

Bigger size   / smaller size = 40

Step-by-step explanation:

Notice that we      

36 / (9/10)    =    30 / (3/4)   = 40

Therefore the proportion model would be

Bigger size   / smaller size = 40

Answer:

A. -9

Step-by-step explanation:

If one of the variables were negative than, it would not be able to equal 2/7.

Your integrand is missing some symbols. My best interpretation is the following integral:

[tex]I=\displaystyle\int\frac{x^4+18x^2+4}{x^5+30x^3+20x}\,\mathrm dx[/tex]

Decompose into partial fractions; we're looking for an expansion of the form

[tex]\dfrac{x^4+18x^2+4}{x^5+30x^3+20x}=\dfrac ax+\dfrac{bx^3+cx^2+dx+e}{x^4+30x^2+20}[/tex]

Now:

[tex]x^4+18x^2+4=a(x^4+30x^2+20)+(bx^3+cx^2+dx+e)x[/tex]

[tex]=(a+b)x^4+cx^3+(30a+d)x^2+ex+20a[/tex]

Matching up coefficients tells us that

[tex]\begin{cases}a+b=1\\c=0\\30a+d=18\\e=0\\20a=4\end{cases}\implies a=\dfrac15,b=\dfrac45,d=12[/tex]

so that

[tex]I=\displaystyle\frac15\int\frac{\mathrm dx}x+\frac45\int\frac{x^3+15x}{x^4+30x^2+20}\,\mathrm dx[/tex]

The integral is trivial:

[tex]\displaystyle\frac15\int\frac{\mathrm dx}x=\frac15\ln|x|+C[/tex]

For the second integral, notice that

[tex]\mathrm d(x^4+30x^2+20)=(4x^3+60x)\,\mathrm dx[/tex]

Distribute the 4 over the numerator, then substitute [tex]u=x^4+30x^2+20[/tex] and [tex]\mathrm du=(4x^3+60x)\,\mathrm dx[/tex]:

[tex]\displaystyle\frac15\int\frac{4x^3+60x}{x^4+30x^2+20}\,\mathrm dx=\frac15\int\frac{\mathrm du}u=\frac15\ln|u|+C=\frac15\ln(x^4+30x^2+20)+C[/tex]

So we have

[tex]I=\dfrac15\ln|x|+\dfrac15\ln(x^4+30x^2+20)+C[/tex]

and with some simplification,

[tex]I=\boxed{\ln\sqrt[5]{|x^5+30x^3+20x|}+C}[/tex]

Answer:  D. y = (x - 3)² + 2

Step-by-step explanation:

Inverse is when you swap the x's and y's and solve for y.

               y = [tex]\sqrt{x-2}[/tex] + 3

Swap:      x = [tex]\sqrt{y-2}[/tex] + 3

Solve:  x - 3 = [tex]\sqrt{y-2}[/tex]

           (x - 3)² = [tex](\sqrt{y-2})^2[/tex]

           (x - 3)² = y - 2

    (x - 3)² + 2 = y

Step-by-step explanation:

Hello there!!

no need to be panic we will help you, alright.

look solution in picture ok...

sorry for cutting in middle.

Hope it helps...

Complete Question

A committee has six members. There are three members that currently serve as the​ board's chairman comma vice chairman comma and treasurer . Each member is equally likely to serve in any of the positions. Three members are randomly selected and assigned to be the new chairman comma vice chairman comma and treasurer . What is the probability of randomly selecting the three members who currently hold the positions of chairman comma vice chairman comma and treasurer and reassigning them to their current​ positions?

The probability is ?

Answer:

The probability is [tex]P(3 ) = \frac{ 1 }{20 }[/tex]

Step-by-step explanation:

From the question we are told that

       The total number of members is  n = 6  

       The  number of member to be selected is  r =  3  

Generally the number of ways of selecting 3 members from 6  is mathematically evaluated as

          [tex]\left n } \atop {}} \right. C _r = \frac{n! }{(n-r ) ! r !}[/tex]

=>       [tex]\left 6 } \atop {}} \right. C _ 3 = \frac{6 ! }{(6-3) ! 3 !}[/tex]

=>        [tex]\left n } \atop {}} \right. C _r = \frac{6* 5* 4 * 3! }{3 ! 3*2 * 1}[/tex]

=>       [tex]\left n } \atop {}} \right. C _r = \frac{6* 5* 4 }{3 *2 * 1}[/tex]

=>        [tex]\left n } \atop {}} \right. C _r =20[/tex]

Now the number of ways of selecting the 3 members who currently hold the position is  n  = 1

  So the probability is mathematically represented as

                 [tex]p(k ) = \frac{ n }{\left n } \atop {}} \right. C _r }[/tex]

substituting values

                  [tex]P(3 ) = \frac{ 1 }{20 }[/tex]

Answer:

C. With 99% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.

Step-by-step explanation:

A confidence interval let us make an inference about a population parameter from a sample statistic. In this case, a sample proportion let us infere aout the population proportion with a certain degree of confidence.

With this confidence interval, we are 99% confident that the polpulation proportion falls within this interval. This means that there is 99% chances of having the population proportion within this interval.

To estimate the population proportion of adults who do not believe in UFO's we should have to construct another confidence interval with the proportion (1-p), but this parameter can not be estimated from the confidence interval for p.

Answer:

147

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The equation of the line that is parallel to the given line and has an x-intercept of -3 is y= 2/3x + 2.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

We have a graph.

So, slope of line in graph is

= (-1-1)/ (0.-3)

= -2/ (-3)

= 2/3

and, we know that two parallel line have same slope.

so, the slope of parallel line is 2/3 and the x intercept is -3.

So, the Equation line is y= 2/3 x  + b

0 = 2/3 (-3) +b

b= 2

Thus, the required equation is y= 2/3x + 2.

Learn more about Slope here:

https://brainly.com/question/2863474

#SPJ5

Answer:

  (T, C, J) = (in dollars)

     (10000, 10000, 0),

     (15000, 4915.97, 84.03),

     (18181.82, 1680.67, 137.51)

Step-by-step explanation:

There are a number of ways to approach this question. We have chosen an approach that determines the investments required to achieve interest rate targets.

__

For an overall interest rate of I, the proportion that must be invested at rate I1 < I < I2 is ...

  proportion at I1 = (I2 -I)/(I2 -I1)

Similarly, the proportion that must be invested at I2 is what's left over. It can be computed similarly:

  proportion at I2 = (I -I1)/(I2 -I1)

__

We want an overall interest rate of $2000/$20000 = 10%.

Given available interest rates of 9%, 11%, and 130%, we need to have investments at a rate lower than 10% and at a rate higher than 10%.

If we use only the options for 9% and 11% (no junk bonds), then we can compute ...

  proportion at 9% = (11 -10)/(11 -9) = 1/2

  proportion at 11% = (10 -9)/(11 -9) = 1/2

1st Option:

  $10,000 in treasury bills; $10,000 in corporate bonds

__

Suppose we want to achieve a 13% return on our investments at 11% and 130%. Then the proportion invested at 9% will use this value for I2:

  proportion at 9% = (13 -10)/(13 -9) = 3/4

Of the remaining 1/4 of the money, we can achieve a 13% return by mixing the investments like this:

  proportion at 11% = (130 -13)/(130 -11) = 117/119

  proportion at 130% = (13 -11)/(130 -11) = 2/119

2nd option:

  $20,000 × 3/4 = $15,000 in treasury bills

  $5000 × 117/119 = $4,915.97 in corporate bonds

  The remaining amount, $84.03 in junk bonds

__

Let's suppose we want a 20% return on our investment in junk bonds and corporate bonds. Then the proportion of the money invested at 9% will be ...

  proportion at 9% = (20 -10)/(20 -9) = 10/11

And the proportion at 11% will be ...

  proportion at 11% = (130 -20)/(130 -11) = 110/119 . . . (of the remaining 1/11 of the funds)

3rd option:

  $20,000 × 10/11 = $18,181.82 in treasury bills

  $1,818.18 × 110/119 = $1,680.67 in corporate bonds

  The remaining amount, $137.51 in junk bonds

_____

Additional comment

The most that could be invested in Junk Bonds is $165.29. If the remainder is invested in Treasury Bills, then the overall return will be $2000. (You could consider this to be a 4th option.)

Answer:

B. 3.19b + 4.59m = 137.24

3.49b + 4.39m = $140.04

Step-by-step explanation:

A B

Bread $3.19 $3.49

Milk $4.59 $4.39

Sue paid $137.24 in supermarket A

Sue paid $140.04 in supermarket B

Let

Price of bread A=$3.19

Price of bread B=$3.49

Price of milk A=$4.59

Price of milk B=$4.39

Quantity of Bread=b

Quantity of Milk=m

Pb=price of bread

Pm=price of milk

Qb=Quantity of bread

Qm=Quantity of milk

For each supermarket

Supermarket A Equation

PbQb + PmQm =$137.24

3.19b+ 4.59m = 137.24

Supermarket B Equation

PbQb + PmQm=$140.04

3.49b + 4.39m = $140.04

Combining both equations

3.19b + 4.59m = 137.24

3.49b + 4.39m = $140.04

Answer:

  [tex]\boxed{2144}[/tex]

Step-by-step explanation:

The sum can be found by adding the parts:

  [tex]\sum\limits_{n=1}^{32}{(4n+1)}=4\sum\limits_{n=1}^{32}{n}+\sum\limits_{n=1}^{32}{1}=4\cdot\dfrac{32\cdot 33}{2}+32\\\\= 2112+32=\boxed{2144}[/tex]

__

The sum of numbers 1 to n is n(n+1)/2.

An exponential has the base at the bottom, or the lower portion. Think of "basement" to help remember this. The exponent is the number up top, so 12 is the exponent.

Answer:

The person above me is correct ( :

Step-by-step explanation:

B

Answer:

5

Step-by-step explanation:

We know that we have to add all numbers then divide it by how many numbers there are. So, 10 + 6 + 9 + 2 + 0 + 3 = 30.  30/6 = 5.  

Answer:

x

Step-by-step explanation:

f(x)=2x+5

Input: x

Output: f(x)

For i.e:

Input: 1

Output: f(1) = 2(1) + 5 = 2 + 5 = 7

Answer:

27 in²

Step-by-step explanation:

area of triangle (whole) = 1/2 x base x height

                                       = 1/2 x 10 x 6

                                       = 30 in²

area of small triangle = 1/2 x base x height

                                   = 1/2 x 3 x 2

                                   = 3 in²

area of shaded region = 30 in² - 3 in²

                                     = 27 in²

Answer: A. [tex]d=\sqrt{(190-7t)^2+(130-4t)^2}[/tex]

B. Minimum distance between them  = 18.61 feet.

C. After 28.76 seconds Sven and Rudyard are closest.

Step-by-step explanation:

A) Let (0,0) be the intersection point.

Then, Initial Location of Sven (0,190).

Speed of Sven = 7 feet per second

Then, position of Sven after t seconds = (0,190-7t)  [speed = distance x time]

Similarly, Initial position of Rudyard= (130,0)

Speed of Rudyard = 4 feet per second

Position after t seconds = (130-4t,0)

Distance d between Sven and Rudyard t seconds after they start walking:

[tex]d=\sqrt{(190-7t)^2+(130-4t)^2}[/tex]

B) Let [tex]d(t)=\sqrt{(190-7t)^2+(130-4t)^2}\\[/tex]

[tex]d'(t)=2(190-7t)(-7)+(2)(130-4t)(-4)\\\\=130t-3700[/tex]

Put d'(t)=0

[tex]130t-3700=0\\\\\Rightarrow\ t=\dfrac{3700}{130}\approx28.46\ sec[/tex]

Minimum distance :

[tex]d(28.46)=\sqrt{(190-7(28.46))^2+(130-4(28.46))^2}\\\\=\sqrt{346.154}\approx18.61\ feet[/tex]

Hence, the minimum distance between them  = 18.61 feet.

c) After 28.76 seconds Sven and Rudyard are closest.

Answer:

Step-by-step explanation:

Given that :

A web page is accessed at an average of 20 times an hour.

Therefore:

a. he rate parameter λ of the distribution of the time until the first hit = 20

b.  What is the expected time between hits?

Let consider E(Y) to be the expected time between the hits; Then :

E(Y) = 1/λ

E(Y) = 1/20

E(Y) = 0.05 hours

E(Y) = 3 minutes

(c.)  What is the probability that there will be less than 5 hits in the first hour?

Let consider X which follows Poisson Distribution; Then,

P(X<5) [tex]\sim[/tex] G(∝=5,  λ = 20)

For 5 hits ; the expected time will be :

Let 5 hits be X

E(X) = ∝/λ

E(X) = 5/20

E(X) =1/4

E(X) = 0.25 hour

E(X) = 15 minutes

From above ; we will see that  it took 15 minutes to get 5 hits; then

[tex]P(\tau \geq 0.25) = \int\limits^{\alpha}_{0.25} \dfrac{\lambda^{\alpha}}{\ulcorner^{\alpha}} t^{a\pha-1} \ e^{-\lambda t} \, dt[/tex]

[tex]P(\tau \geq 0.25) = \int\limits^{5}_{0.25} \dfrac{20^{5}}{\ulcorner^{5}} t^{5-1} \ e^{-20 t} \, dt[/tex]

[tex]\mathbf{P(\tau \geq 0.25) =0.4405}[/tex]

Answer:

~820.8$

Step-by-step explanation:

The total money (M) after 18 years could be calculated by:

M = principal x (1 + rate)^time

with

principal = 400$

rate = 4% compounded monthly = 0.04/12

time = 18 years = 18 x 12 = 216 months (because of compounded monthly rate)

=> M = 400 x (1 + 0.04/12)^216 = ~820.8$

Answer:

AC (b)

Step-by-step explanation:

Since 10 is half of 20, you have to find the variable closest to the middle. Which in this case, is C. So, your awnser is B. (AC)

Answer:

[tex]\boxed{\sf C}[/tex]

Step-by-step explanation:

The whole segment is [tex]\sf \sqrt {20}[/tex], we can see that AD is approximately 75% of the segment AE.

[tex]75\%*\sqrt{20} = 3.354102[/tex]

[tex]\sqrt{10}= 3.162278[/tex]

AC is almost half of AE.

[tex]\frac{\sqrt{20} }{2} = 2.2360679775[/tex]

[tex]\sqrt{10} = 3.16227766017[/tex]

It isn’t close to the option C.

Answer:

Hey there!

Jimmy has 15-7, or 8 apples left.

Hope this helps :)

Answer:

8/5

Step-by-step explanation:

w = k / √x

4 = k / √4

k = 8

w = 8 / √x

w = 8 / √25

w = 8/5

Answer:

AC2  =  AB2 + BC2     --->     AC2  =  122 + 52     --->   AC  =  13

AD / AB  =  AB / AC     --->     AD / 12  =  12 / 13     --->     AD  =  144/13

DC  =  AC - AD     --->   DC  =  13 - 144/13     --->     DC  =  25/13

AD / DB  =  DB / DC     --->   DB2  =  AD · DC     --->     DB2  =  (144/13) · (25/13)  --->     DB  =  60/13

DB is the geometric mean of AD and DC.

Step-by-step explanation:

Answer:

(i) 520

(ii) 2

Step-by-step explanation:

(i) x³ + y³

Plug x as 2, and y as 8.

(2)³ + (8)³

Solve for exponents.

8 + 512

Add.

= 520

(ii) ∛y

Plug y as 8.

∛(8)

Solve for cube root.

= 2

Answer:

( i ) 520

( ii ) 2

Step-by-step explanation:

We can find this solution by plugging in known values -

If x = 2, y = 8

x³+y³ = ( 2 )³ + ( 8 )³ = 8 + 512

= 520

Know let us move on to the second half -

We only need one part of this information now, y = 8. If so,

∛y = ∛8

2 x 2 x 2 = 8 - and thus 2 should be our solution for this portion.

Answer:

speed=3.33m/s

Step-by-step explanation:

speed= distance÷time

3.33 m/s

length = ?

Answer:

Length  : 50m

Speed   : 5 m  /  s

im sorry if im too late :'(