Answer:
30
Step-by-step explanation:
You can try the answer choices to see what works.
15·10 ≠ 750
25·20 ≠ 750
30·25 = 750 . . . . the larger number is 30
50·45 ≠ 750
Answer:
The value of the greater number is 30.
Step-by-step explanation:
We need to find the values of x that satisfy the equation :
[tex]x(x-5)=750[/tex]
Working with the equation ⇒
[tex]x(x-5)=750[/tex]
[tex]x^{2}-5x=750[/tex]
[tex]x^{2}-5x-750=0[/tex]
Given an equation with the form
[tex]ax^{2}+bx+c=0[/tex]
We can use the quadratic equation to find the values of x
[tex]x1=\frac{-b+\sqrt{b^{2}-4ac}}{2a}[/tex] and
[tex]x2=\frac{-b-\sqrt{b^{2}-4ac}}{2a}[/tex]
With [tex]a=1\\b=-5\\c=-750[/tex] we replace in the equations of x1 and x2 ⇒
[tex]x1=\frac{-(-5)+\sqrt{(-5)^{2}-4.(1).(-750)}}{2.(1)}=30[/tex]
[tex]x1=30[/tex] is a solution of the equation [tex]x^{2}-5x-750=0[/tex]
Now for x2 ⇒
[tex]x2=\frac{-(-5)-\sqrt{(-5)^{2}-4.(1).(-750)}}{2.(1)}=-25[/tex]
[tex]x2=-25[/tex] is a solution of the equation [tex]x^{2}-5x-750=0[/tex]
Given that both numbers are positive ⇒
[tex]x>0[/tex] and [tex](x-5)>0\\x>5[/tex]
Therefore, x2 is not a possible value for the greater number
The greater number is [tex]x1=30[/tex]
A box contains 13 transistors, 4 of which are defective. If 4 are selected at random, find the probability that a. All are defective. b. None are defective.
The probability that all selected transistors are defective is approximately 0.0014, while the probability that none of the selected transistors are defective is 0.1762.
Given:
Transistors = 13
Defective = 4
a. The number of ways to choose 4 defective transistors from the 4 available = [tex]^4C_4[/tex]
= [tex]\dfrac{4!}{4! 0!}[/tex]
= 1
and, the total number of ways to choose 4 transistors from the 13 available
[tex]^{13}C_4= \dfrac{13!}{4! * (13-4)!}[/tex]
= [tex]\dfrac{(13 * 12 * 11 * 10)}{(4 * 3 * 2 * 1)}[/tex]
= 715
Therefore, the probability of selecting all defective transistors is:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 1 / 715
= 0.0014
b. The number of ways to choose 4 non-defective transistors from the 9 available is
[tex]^{9}C_4= \dfrac{9!}{4! * (9-4)!}[/tex]
= [tex]\dfrac{(9 * 8* 7* 6)}{(4 * 3 * 2 * 1)}[/tex]
= 126
So, the probability of selecting none defective transistors is:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 126 / 715
= 0.1762
Learn more about Probability here:
https://brainly.com/question/32117953
#SPJ12
Final answer:
The probabilities are calculated using combinations: the probability all selected transistors are defective is 1/C(13,4) or 0.13%, and the probability none are defective is C(9,4)/C(13,4) = 17.6%.
Explanation:
The student's question about probabilities can be answered using combinations and the basic principles of probability. We need to calculate the probability that out of 13 transistors, all 4 selected are defective, and then the probability that none are defective.
Probability All Are Defective
To find the probability that all 4 transistors selected are defective, we calculate the number of ways to pick 4 defective ones out of 4 (which is 1 way, since we only have 4 defective ones), and divide it by the number of ways to pick any 4 out of 13. Using combinations, we calculate:
Probability(all defective) = C(4,4) / C(13,4) = 0.13%.
Probability None Are Defective
To find the probability that none of the 4 selected transistors are defective, we calculate the number of ways to pick 4 non-defective ones out of 9 (since 13 total minus 4 defective leaves 9 non-defective), and divide it by the number of ways to pick any 4 out of 13:
Probability(none defective) = C(9,4) / C(13,4) = 17.6%
When visiting his parents, Tyler drives at an average speed of 42 km/h through urban areas and at an average speed of 105 km/h on the motorway. His journey usually takes him 2.5 hours. One day when there is fog, he sets off 1 hour early and only manages to drive at an average speed of 28 km/h in the urban areas and 60 km/h on the motorway. He arrives 30 minutes late. What was the total distance that Tyler travelled?
Answer:
168 km
Step-by-step explanation:
Let x represent the distance Tyler drives at the slower speed, and let y represent the distance at the higher speed. Using time = distance/speed, we can write equations for the total travel time:
x/42 +y/105 = 2.5
x/28 +y/60 = 4.0 . . . . . 1.5 hours more than the usual 2.5 hours
Multiplying the first equation by 210, we have ...
5x +2y = 525
Multiplying the second equation by 420, we get ...
15x +7y = 1680
Subtracting 3 times the first of these equations from the second, we have ...
(15x +7y) -3(5x +2y) = (1680) -3(525)
y = 105
Putting this into the very first equation, we get ...
x/42 + 105/105 = 2.5
x/42 = 1.5 . . . . . . subtract 1
x = 63 . . . . . . . . .multiply by 42.
The total distance to Tyler's parents' house is ...
63 km + 105 km = 168 km
Tyler's total travel distance is approximately 168 km.
Calculating Total Distance Traveled
To determine the total distance Tyler traveled, let du be the distance through urban areas and dm be the distance on the motorway.
→ The total distance is:
[tex]D = d_u + d_m[/tex]
First, using the normal journey:
→ Urban Area:
Speed = 42 km/h
Time = [tex]t_u[/tex] / 42,
→ Motorway:
Speed = 105 km/h
Time = [tex]t_m[/tex] / 105,
→ Total time for normal journey:
→ [tex]t_u/42 + t_m/105 = 2.5\ hours[/tex]
We have:
→ [tex]d_u[/tex] = 42 * [tex]t_u[/tex]
→ [tex]d_m[/tex] = 105 * [tex]t_m[/tex]
When there is fog:
→ Urban Area:
Speed = 28 km/h
Time = [tex]t__uf}[/tex] / 28
→ Motorway:
Speed = 60 km/h
Time = [tex]t_{um[/tex] / 60
Total time for foggy journey:
→ [tex]t_{uf[/tex] /28 + [tex]t_{mf[/tex] /60
Given that he leaves 1 hour early and arrives 30 minutes late, the total journey time in foggy conditions is:
→ 2.5+1+0.5=4 hours
Thus,
→ [tex]t_{uf[/tex] /28 + [tex]t_{mf[/tex] /60 = 4
Solving the Equations
We now have two equations:
→ [tex]t_u/42 + t_m/105 = 2.5\ hours[/tex]
→ [tex]t_{uf}\ /\ 28\ + t_{mf} \ /\ 60 = 4 hours[/tex]
Let's solve these equations step-by-step.
First, let's multiply the first equation by 210 (the least common multiple of 42 and 105):
→ [tex]210(t_u/42 + t_m/105) = 210*2.5[/tex]
→ [tex]5t_u+2t_m=525[/tex] (eq. 1)
Next, let's multiply the second equation by 420 (the least common multiple of 28 and 60):
→ [tex]420( t_u/28+ t_m /60)=420*4[/tex]
→ [tex]15t_u +7t_m =1680[/tex] (eq. 2)
We now solve these two linear equations:
→ [tex]5t_u+2t_m=525[/tex]
→ [tex]15t_u +7t_m =1680[/tex]
First, let's solve Equation 1 for [tex]t_m[/tex] in terms of [tex]t_u[/tex]:
→ [tex]d_m=(525-5d_u)/2[/tex]
Substitute this expression into Equation 2:
→ [tex]15t_u+7((525-5d_u)/2)=1680[/tex]
Multiply through by 2 to clear the fraction:
→ [tex]30t_u +7(525-5t_u )=3360[/tex]
→ [tex]30t_u +3675-35t_u =3360[/tex]
→ [tex]-5t_ u +3675=3360[/tex]
→ [tex]-5t_u=3360-3675[/tex]
→ [tex]-5t _u=-315[/tex]
→ [tex]t_u=63[/tex]
Now substitute [tex]t_u=63[/tex] back into Equation 1 to find [tex]t_m[/tex]:
→ [tex]5(63)+2t_m =525[/tex]
→ [tex]315+2t_m =525[/tex]
→ [tex]2t_m =210[/tex]
→ [tex]t_m=105[/tex]
Thus, the total distance Tyler travels is:
[tex]= t _u +t_m[/tex]
[tex]=63+105[/tex]
[tex]=168\ kilometers[/tex]
What is the sum of an 8-term geometric series if the first term is -11, the last term is 859,375, and the common ratio is -5?
A. -143,231
B. -36,047
C. 144,177
D. 716,144
Answer:
D.
Step-by-step explanation:
You could find the 8 terms and then add them up.
Let's do that.
Luckily we have the common ratio which is -5. Common ratio means it is telling us what we are multiplying over and over to get the next term.
The first term is -11.
The second term is -5(-11)=55.
The third term is -5(55)=-275.
The fourth term is -5(-275)=1375.
The fifth term is -5(1375)=-6875.
The sixth term is -5(-6875)=34375.
The seventh terms is -5(34375)=-171875.
The eighth term is -5(-171875)=859375.
We get add these now. (That is what sum means.)
-11+55+-275+1375+-6875+34375+-171875+859375
=716144 which is choice D.
Now there is also a formula.
If you have a geometric series, where each term of the series is in the form [tex]a_1 \cdot r^{n-1}[/tex], then you can use the following formula to compute it's sum (if it is finite):
[tex]a_1\cdot \frac{1-r^{n}}{1-r}}[/tex]
where [tex]a_1[/tex] is the first term and [tex]r[/tex] is the common ratio. n is the number of terms you are adding.
We have all of those. Let's plug them in:
[tex]a_1=-11[/tex], [tex]r=-5[/tex], and [tex]n=8[/tex]
[tex]-11 \cdot \frac{1-(-5)^{8}}{1-(-5)}[/tex]
[tex]-11\cdot \frac{1-(-5)^{8}}{6}[/tex]
[tex]-11 \cdot \frac{1-390625)}{6}[/tex]
[tex]-11 \cdot \frac{-390624}{6}[/tex]
[tex]-11 \cdot -65104[/tex]
[tex]716144[/tex]
Either way you go, you should get the same answer.
Final answer:
The sum of the 8-term geometric series with the given first term and common ratio is calculated using the geometric series sum formula, resulting in a sum of 716,144, Which is option D.
Explanation:
The sum of a geometric series is determined by the formula Sₙ = a(1 - rⁿ)/(1 - r), where Sₙ is the sum of the first N terms, a is the first term, r is the common ratio, and N is the number of terms. Since we have an 8-term geometric series with a first term of -11 and a common ratio of -5, we can calculate the last term (-11 x (-5)⁷) to ensure it is indeed 859,375, confirming the ratio and the number of terms.
The sum can then be calculated as follows: S₈ = -11 x (1 - (-5)⁸) / (1 - (-5)) = -11 x (1 - 390625) / (1 + 5) = -11 x (-390624) / 6 = -11 x -65104 = 716,144, which corresponds to option D.
15 points!!! please help me figure this out I am so confused
Answer:
10a. 439
10b. 1253
11a. linear
11b. $37.23
Step-by-step explanation:
10. Put the numbers in the equation and do the arithmetic. For logarithms, a scientific or graphing calculator will be required. The first attachment shows the result for 2 years = 24 months.
920log(3) ≈ 439 . . . after 4 months
920log(23) ≈ 1253 . . . after 2 years
___
11. Your experience with taxis tells you the fare is usually based on time and distance and some fixed charge. That is, it is roughly linearly related to distance. Plotting these data points will tell you the same thing: a linear model is suitable.
A graphing calculator or spreadsheet (or any of several web sites) can help you calculate the regression model. The second attachment shows my result:
fare ≈ $2.10 + 3.513×miles
So, for 10 miles, the expected fare is ...
$2.10 + 3.513×10 = $37.23
_____
Comment on these problems
It is useful to learn to use your calculator's various functions. That can save you a lot of effort and angst.
What are the slope and y-intercept of the linear function graphed to the left?
Answer:
y intercept equals 1
Step-by-step explanation:
y= -1/2x+1
the slope is -1/2
the y intercept is 1
What is the value of m < 3
Answer:
142°
Step-by-step explanation:
∠3 is an alternate exterior angle with ∠7, so is congruent to ∠7. ∠7 is supplementary to 38°, so has measure 180° -38° = 142°.
The measure of ∠3 is 142°.
According to a report, 51.6% of murders are committed with a firearm. (a) if 200 murders are randomly selected, how many would we expect to be committed with a firearm? (b) would it be unusual to observe 122 murders by firearm in a random sample of 200 murders? why?
Answer:
a) 103, b) No
Step-by-step explanation:
a) We need to multiply the probability by the amount of the sample to get:
200 × 51.6% = 103.2, rounded down to 103
b) As we have selected the people randomly, we have no control over the type of people we are given - this is theoretical and the estimate is not definite - all of the sample could have murdered by firearm or even none (even though it is highly unlikely).
In triangle ABC AD/DB = CE/EB. Complete the proof showing the segment DE is parallel to segment AC.
1.
a) (AD/DB) + 1 = (CE/EB) + 1
b) (AD/DB) + DE = (CE/EB) + DE
c) AD * EB = CE * DB
2.
a) Corresponding sides of congruent triangles are congruent.
b) Addition Property of Equality
c) cross multiplication
Edit: Answer is 1.A and 2.B (verified correct) thanks to
https://brainly.com/question/1428177
Answer:
1. [tex]\dfrac{AD}{DB}+1=\dfrac{CE}{EB}+1[/tex]
2. Addition property of equality
Step-by-step explanation:
In triangle ABC,
[tex]\dfrac{AD}{DB}=\dfrac{CE}{EB}.[/tex]
The addition property of equality states that if the same amount is added to both sides of an equation, then the equality is still true.
Use addition property of equality, add 1 to both sides of previouse equality:
[tex]\dfrac{AD}{DB}=\dfrac{CE}{EB}\\ \\\dfrac{AD}{DB}+1=\dfrac{CE}{EB}+1\\ \\\dfrac{AD+DB}{DB}=\dfrac{CE+EB}{EB}[/tex]
Answer:
(AD/DB) +1 = (CE/EB) +1 -----> Addition Property of Equality
Find the midpoint of the segment between the points (17,1) and (−2,8)
A. (19/2,−7/2)
B. (−15,−9)
C. (15/2,9/2)
D. (15,9)
Answer:
C. (15/2,9/2)
Step-by-step explanation:
To find the midpoint of two points
midpoint = (x1+x2)/2 , (y1+y2)/2
= (17+-2)/2, (1+8)/2
= 15/2, 9/2
Answer:
The correct option is C.
Step-by-step explanation:
The given points are (17,1) and (−2,8).
We need to find the midpoint of given points.
Formula for midpoint :
[tex]Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
The midpoint of the segment between the points (17,1) and (−2,8) is
[tex]Midpoint=(\frac{17+(-2)}{2},\frac{1+8}{2})[/tex]
[tex]Midpoint=(\frac{15}{2},\frac{9}{2})[/tex]
The midpoint of the segment between the points (17,1) and (−2,8) is [tex](\frac{15}{2},\frac{9}{2})[/tex]
Therefore the correct option is C.
There are two newborns, Gary and Eric. The future lifetime of Gary is uniformly distributed between 0 to 60 years. The future lifetime of Eric is uniformly distributed between 0 to 40 years. Their future lifetimes are independent. Calculate the probability that Gary dies first.
Answer: 0.25
Step-by-step explanation:
Given : The future lifetime of Gary is uniformly distributed with interval [0 years , 60 years].
Then the probability density function for Gary's future lifetime will be:-
[tex]f(x)=\dfrac{1}{60-0}=\dfrac{1}{60}[/tex]
The future lifetime of Eric is uniformly distributed with interval [0 years , 40 years].
Then the probability density function for Erin's future lifetime will be:-
[tex]f(x)=\dfrac{1}{40-0}=\dfrac{1}{40}[/tex]
Now, the joint density function for Gary and Eric's future lifetime :-
[tex]f(x,y)=f(x)f(y)=\dfrac{1}{40\times60}=\dfrac{1}{2400}[/tex] [∵Their future lifetimes are independent. ]
Now, the probability that Gary dies first is given by :-
[tex]\int^{60}_{0}\int^{40}_{x}f(x,y)\ dy\ dx\\\\=\int^{60}_{0}\int^{40}_{x}\dfrac{1}{2400}\ dy\ dx\\\\=\int^{60}_{0}\dfrac{40-x}{2400}\ dx\\\\=\dfrac{1}{2400}[40x-\dfrac{x^2}{2}]^{60}_{0}\\\\=\dfrac{1}{2400}(2400-\dfrac{3600}{2})=0.25[/tex]
Hence, the probability that Gary dies first =0.25
Elly has 2 rectangular gardens. One measures 1809 cm by 2891 cm and the other measures 738 cm by 249 cm. Elly wants to put a fence around both, how much does she need to buy?
Answer:
She needs 11374 cm to buy
Step-by-step explanation:
* Lets explain how to solve the problem
- The dimensions of the first rectangle is 1809 cm and 2891 cm
- The dimensions of the first rectangle is 738 cm and 249 cm
- Elly wants to put a fence around both
- To find the length of the fence calculate the perimeters of the two
rectangles
- The perimeter of the rectangle = 2(b + h), where b , h are the
dimensions of the rectangle
# First rectangle
∵ The dimensions are 1809 cm and 2891 cm
∵ P = 2(b + h)
∴ P = 2(1809 + 2891) = 2(4700) = 9400 cm
# Second rectangle
∵ The dimensions are 738 cm and 249 cm
∵ P = 2(b + h)
∴ P = 2(738 + 249) = 2(987) = 1974 cm
∵ The length of the fence = the sum of the perimeters of the two
rectangles
∴ The length of the fence = 9400 + 1974 = 11374 cm
* She needs 11374 cm to buy
Answer:
She needs to purchase 11374
The difference i the length of her and her brother's fence is 8442
Step-by-step explanation:
First you need to find the perimeter by adding the lengths and widths all together.
1809+2891+738+249=5687
But you need to times it by 2 because it says Elly has 2 gardens.
5687 x 2=11374.
If you are confused on the second question the answer is down below ( The person who ask this question did have to ask the second question but on my math test this question has 2 parts).
The question is Elly's brother also wants to put up a fence around his garden that is 1034 centimeters by 432 centimeters. What is the difference in the length of fence that each will purchase?
First you have to find the perimeter of Elly's brother garden.
1034+432+1034+432=2932
Last we have to find out what is the difference in the length of fence that each will purchase.
To do that you will have to subtract Elly's perimeter and Elly's brothers perimeter.
11374-2932=8442
So Elly difference in the length of the fence is 8,442.
A right pyramid with a square base has a base edge length of 24 feet and slant height of 20 feet. The height of the pyramid is 'blank' feet.
Answer:16
Step-by-step explanation:
Answer:
The height of the pyramid is 16 feet.
Step-by-step explanation:
A right pyramid with a square base has a base edge length of 24 feet.
The slant height is 20 feet.
We take the half of base here that is 12.
Let the height be h, applying Pythagoras theorem.
[tex]h^{2} =20^{2} -12^{2}[/tex]
Solving for h;
[tex]h^{2} =400-144[/tex]
=> [tex]h^{2} =400-144[/tex]
=> [tex]h^{2} =256[/tex]
=> [tex]h=\sqrt{256}[/tex]
h = 16
Therefore, The height of the pyramid is 16 feet.
Please help me. these problems
Answer:
1st problem:
Converges to 6
2nd problem:
Converges to 504
Step-by-step explanation:
You are comparing to [tex]\sum_{k=1}^{\infty} a_1(r)^{k-1}[/tex]
You want the ratio r to be between -1 and 1.
Both of these problem are so that means they both have a sum and the series converges to that sum.
The formula for computing a geometric series in our form is [tex]\frac{a_1}{1-r}[/tex] where [tex]a_1[/tex] is the first term.
The first term of your first series is 3 so your answer will be given by:
[tex]\frac{a_1}{1-r}=\frac{3}{1-\frac{1}{2}}=\frac{3}{\frac{1}{2}=6[/tex]
The second series has r=1/6 and a_1=420 giving me:
[tex]\frac{420}{1-\frac{1}{6}}=\frac{420}{\frac{5}{6}}=420(\frac{6}{5})=504[/tex].
Given h(x) = x-1 and f(x) = x3-x2+x-1 is h(x) a factor of f(x)?
Answer:
Yes
Step-by-step explanation:
One way to tell is to look at the remainder from division by x-1, which is the value of f(1).
1³ -1² +1 -1 = 0
so (x -1) is a factor of f(x).
f(x) = (x -1)(x^2 +1) = h(x)(x^2 +1)
You have a secret that you tell to one person. Every hour, each of the people that know the secret tells one person. The number of people who know is N, and t is the number of hours since you told the first person. Is N a linear function of t?
Answer:
No, it is not a linear function. It is an exponential function.
Step-by-step explanation:
You have a secret that you tell to one person.
Every hour, each of the people that know the secret tells one person.
Let N be the people who know the secret.
Let t be the number of hours since you told the first person.
Now, when only you know the secret, means 1 person.
N(0) = 1
Next hour, there are now 2 people that know the secret.
N(1) = 2
After the next hour, these 2 people will tell 2 more people, so people doubled to 4.
N(2) = 4
One hour later it will be N(3) = 8
We can see the pattern as following.
[tex]N(t)=2^{t}[/tex]
Therefore, the function is exponential not linear.
Which number is graphed on the following number line?
Answer:
Step-by-step explanation:
looks like it's about 1/2
Looks approximately like x = 0.6 ish
are there MCQ choices?
Graph the ellipse with equation x squared divided by 36 plus y squared divided by 49 equals 1.
Check the picture below.
Step-by-step explanation:
We are asked to graph the equation of an ellipse given by [tex]\frac{x^2}{36}+\frac{y^2}{49}=1[/tex].
We know that standard from of an ellipse [tex]\frac{x^2}{a^2}+\frac{y^2}{b^1}=1[/tex], when [tex]a>b[/tex], then the ellipse will be horizontal and when [tex]a<b[/tex], then the ellipse will be vertical.
We can rewrite our given ellipse as: [tex]\frac{x^2}{6^2}+\frac{y^2}{7^2}=1[/tex].
Upon looking at our given ellipse we can see that the horizontal radius is less than vertical radius, so our ellipse will be a vertical ellipse. The center of our ellipse is at origin (0,0).
Upon graphing our ellipse, we will our required graph as:
A 60 room hotel is filled to capacity every night at a rate of $40 per room. The management wants to determine if a rate increase would increase their profit. They are not interested in a rate decrease. Suppose management determines that for each $2 increase in the nightly rate, five fewer rooms will be rented. If each rented room costs $8 a day to service, how much should the management charge per room to maximize profit?
Final answer:
To maximize profit, the hotel management should determine the rate at which the difference in revenue gained from increasing the rate and the cost to service fewer rooms is maximized. By analyzing different rate increases and subtracting the cost of servicing fewer rooms, the management can identify the rate that will generate the highest profit. For example, by increasing the rate to $42 per room, the hotel could maximize profit at $1940.
Explanation:
To determine the price at which the hotel management should charge per room to maximize profit, the management needs to consider the relationship between the price, the number of rented rooms, and the cost to service each room.
First, let's establish the initial conditions:
60 rooms are rented at a rate of $40 per room.
Each rented room costs $8 per day to service.
Next, management determines that for each $2 increase in the nightly rate, five fewer rooms will be rented. To maximize profit, the management should find the rate at which the difference in revenue gained from increasing the rate and the cost to service fewer rooms is maximized.
Here is the step-by-step calculation:
Calculate the initial revenue: $40/room * 60 rooms = $2400
Calculate the initial cost: $8/room * 60 rooms = $480
Calculate the initial profit: $2400 - $480 = $1920
Calculate the new revenue: ($40 + $2)/room * (60 - 5) rooms = $2280
Calculate the new cost: $8/room * (60 - 5) rooms = $440
Calculate the new profit: $2280 - $440 = $1840
Repeat steps 4-6 for different rate increases until the profit is maximized.
Based on this analysis, the management should charge a rate that allows them to profit the most, such as $42/room, which would result in a profit of $1940.
Management should charge $44 per room to maximize profit.
To determine the optimal room rate to maximize profit, we'll utilize concepts from algebra and profit modeling. Let's define the variables:
x: the number of $2 increases in the room rateCurrent room rate: $40New room rate: $40 + 2xNumber of rooms rented: 60 - 5xCost to service each room: $8The revenue, R, can be calculated as:
R = (40 + 2x)(60 - 5x)
The cost, C, of servicing the rooms can be calculated as:
C = 8(60 - 5x)
The profit, P, is given by:
P = R - C
Substituting the revenue and cost formulas:
P = (40 + 2x)(60 - 5x) - 8(60 - 5x)
Let's expand and simplify this equation:
P = (40 + 2x)(60 - 5x) - 8(60 - 5x)
[tex]P = 2400 - 200x + 120x - 10x^2 - 480 + 40x[/tex]
[tex]P = -10x^2 - 40x + 1920[/tex]
To find the value of x that maximizes the profit, we need to find the vertex of the quadratic function. The vertex form of a parabola given by [tex]ax^2 + bx + c[/tex] is at:
[tex]x = \frac{-b}{2a}[/tex]
Substituting a = -10 and b = -40:
[tex]x = -\frac{-40}{2 \times -10} = 40/20 = 2[/tex]
Thus, the management should increase the rate by 2 increments of $2, or $4. Therefore, the optimal room charge is:
$40 + $4 = $44
The equation of a line is -6x - 2y = -18. What is the x-intercept & y-intercept of the line?
a. x-intercept = 3 y-intercept = 9
b. x-intercept = 9 y-intercept = 3
c. x-intercept = -3 y-intercept = -9
d. x-intercept = -9 y-intercept = -3
Answer:
a. x-intercept = 3 , y-intercept = 9.
Step-by-step explanation:
-6x - 2y = -18
Convert to slope-intercept form:
-2y = 6x - 18
y = -3x + 9
So the y-intercept (when x = 0) is when y = 9..
Solving for x to find the x-intercept:
0 = -3x + 9
3x = 9
x = 3.
You buy a rental property for $180,000. Assuming that you could sell the property for $250,000 at the end of 6 years, what is your return based on the following cash flows? Year 0 (now) = – 180,000 End of Year 1 = + 24,000 End of Year 2 = + 24,000 End of Year 3 = – 3,000 and +12,000 End of Year 4 = + 18,000 End of Year 5 = + 30,000 End of Year 6 = + 32,000
Answer:
15.542%
Step-by-step explanation:
For uneven cash flows such as those in this problem, there is no formula for "internal rate of return" (IRR). It must be computed graphically or iteratively. Spreadsheets and financial calculators are equipped to do this calculation. Attached is the result of the calculation done by a graphing calculator.
The sum of "present value" of each of the cash flows is zero when the discount rate is the IRR.
A bag contains 9 marbles: 3 are green, 4 are red, and 2 are blue. Lashonda chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that both marbles she chooses are blue? Write your answer as a fraction in simplest form.
Answer:
2/9
Step-by-step explanation:
Because there's 2 blue marbles and 9 in total
The time spent waiting in the line is approximately normally distributed. The mean waiting time is 6 minutes and the standard deviation of the waiting time is 2 minutes. Find the probability that a person will wait for more than 4 minutes.
Answer:
0.034
Step-by-step explanation:
Data:
Let the standard deviation be : [tex]\sigma = 2[/tex]
The mean be: [tex]\mu = 6[/tex]
Therefore, P (x>4) which is the probability that a person will wait for more than 4 minutes is given by:
[tex]z = \frac{X- \mu }{\sigma }[/tex]
= [tex]\frac{4-6}{2} \\= -1[/tex]
Therefore,
P(x > 4) = P (z > -1)
= P (z < -1)
From the z-tables, we find 0.034
To find the probability that a person will wait for more than 4 minutes, calculate the z-score and use a standard normal distribution table or calculator. The probability is approximately 0.8413 or 84.13%.
Explanation:To find the probability that a person will wait for more than 4 minutes, we need to calculate the z-score for the value 4 using the given mean and standard deviation. The z-score formula is z = (x - mean) / standard deviation. Plugging in the values, we get z = (4 - 6) / 2 = -1. Now, we can use a standard normal distribution table or a calculator to find the probability associated with this z-score.
Using a standard normal distribution table, the probability of a z-score less than -1 is approximately 0.1587.
Therefore, the probability of a person waiting for more than 4 minutes is approximately
1 - 0.1587 = 0.8413 or 84.13%.
Learn more about Probability here:https://brainly.com/question/32117953
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These are the means and standard deviations for examples of heights from two kinds of trees.
Table:
Tree A - (Mean: 25ft) (Standard deviation: 5ft)
Tree B - (Mean: 60 ft) (Standard deviation: 12 ft)
Select the TWO true statement.
A. Tree A's heights are more spread out than tree B's heights.
B. Tree A's heights are less spread out than tree B's heights.
C. Tree A has a greater average height than tree B.
D. Tree A has a lower average height than tree B.
Step-by-step explanation:
Tree A's heights are less spread out than tree B's heights. Tree A has a lower average height than tree Bs
1.2, 3, 7.5, 18.75, ... Which formula can be used to describe the sequence? a.F(x) = 1.2(2.5)^x – 1 b.F(x) = 2.5(1.2)^x – 1 c.F(x) = 1.2(2.5)^x d.F(x) = 1.2(2.5)^x
Answer:
a. F(x) = 1.2(2.5)^(x – 1)
Step-by-step explanation:
The sequence is geometric with first term 1.2 and common ratio 3/1.2 = 2.5. The explicit formula for such a sequence is ...
a[n] = a[1]·r^(n-1)
For a[1] = 1.2 and r = 2.5, and using x as the term number, the formula is ...
F(x) = 1.2·2.5^(x-1) . . . . . matches selection A
The formula that could be used for showing the sequence is option A.[tex]F(x) = 1.2(2.5)^{(x - 1)}[/tex]
Calculation of formula used:The sequence should be geometric which means the first term 1.2 and the common ratio is [tex]3\div 1.2[/tex] = 2.5.
Now The explicit formula should be
[tex]a[n] = a[1].r^{(n-1)}[/tex]
Now
Here a[1] = 1.2
and r = 2.5,
So, the formula is
[tex]F(x) = 1.2\times 2.5^{(x-1)[/tex]
Learn more about the sequence here: https://brainly.com/question/21258074
Select the correct answer from each drop-down menu.
Monica built a remote-controlled, toy airplane for a science project. To test the plane, she launched it from the top of a building. The plane traveled a horizontal distance of
50 feet before landing on the ground. A quadratic function which models the height of the plane, in feet, relative to the ground, at a horizontal distance of x feet from the building
is shown
200+
-8060-40
20
-50+
20 40 GO 80
*
100
Since the domain represents
interval [
the airplane while it was in the air, the values of the domain should be restricted to the
Resot
Answer:
a horizontal distance of x feet from the building[0, 50]Step-by-step explanation:
The problem statement tells you that x represents the horizontal distance in feet that the airplane is from the building. The domain is the set of useful values of x, which will be from 0 to 50 feet. Values of x less than 0 or more than 50 make no sense in this scenario.
what are the multiples of -42?
Need help asap if you don't mind. Thanks
Answer:
1, 2, 3, 6, 7, 14, 21, 42 [start from the outer ends, then come inner, placing negative symbols on either or]
Step-by-step explanation:
Just like what "dashabo123" said, you can hand each number a negative one at a time before moving to the next set of factors.
I am joyous to assist you anytime.
HELP! ONLY IF YOU KNOW THE ANSWER
also this goes with the other question I asked
Write the standard equation of the conic section you chose with its center or vertex at the origin. Describe the graph.
Answer:
Attached
Step-by-step explanation:
The conic section you can chose is a parabola
A parabola is a curve where any point on the curve is equidistant from the focus and from a directrix
When you have the vertex and focus points, you can write the equation of the parabola then graph it on a graph tool to visualize the curve.
Assume the vertex is at (3,1) and focus is at (3,5), then you notice here the x-coordinate for vertex and focus is the same , to mean one is top of the other.
This is a regular vertical parabola the x part is squared.
Vertex and focus are 4 units apart. This is by checking the difference in values of y-axis of vertex and focus.This is your p
The equation of the parabola will be
(x-h)²=4p(y-k)
but p=4
(x-3)²=4(4)(y-1)
(x-3)²=16(y-1)
x²-6x+9=16y-16
x²-6x-16y+25=0-----------------equation of the parabola
It is a right-side up parabola
Answer:
I only know question number one; the answer is
A parabola is a curve where any point on the curve is equidistant from the focus and from a directrix.
Step-by-step explanation:
*THIS IS AN EASY ONE PLEASE HELP**Convert to Rectangular: r*tanΘ/secΘ=2
y=2
y=½
x=2
x=½
Answer:
y = 2
Step-by-step explanation:
r tan θ / sec θ = 2
First, simplify tan θ / sec θ:
r (sin θ / cos θ) / (1 / cos θ) = 2
r sin θ = 2
Remember that r cos θ = x and r sin θ = y:
y = 2
Answer:
Answer is A hope that helped
Step-by-step explanation:
Choose a number between and that is a multiple 45 of and 95 . Write all the numbers that she could choose. If there is more than one number, separate them with commas.
Answer with explanation:
To find the common multiple of 45 and 95,we will find HCF of 45 and 95.
45=3 × 3× 5
95=5 × 19
⇒H CF(45,95)
=3 × 3×5×19
=855
→Common multiple of 45 and 95 =855
→There are infinite number of multiple of 855 which are 855, 1710, 2565,.....
You have not written between which two numbers.So, you should write multiple of 855 such that it is smaller than the greater number.
If 10 were added to each of the values in a data set that originally had a standard deviation of 6, the standard deviation of the resulting data would be 6 true false
Answer:
TRUE
Step-by-step explanation:
Changing the mean by adding the same number to every data value does not change the differences those values have from the new mean. Hence the standard deviation remains unchanged. If it was 6, it will be 6.
Answer:
True because standard divination stays the same
Step-by-step explanation: