Answer:
a) The demand function is
[tex]q(p) = -4 p + 107[/tex]
b) The nightly revenue is
[tex] R(p) = -4 p^2 + 107 p [/tex]
c) The profit function is
[tex]P(p) = -4 p^2 + 133.75 p - 939 [/tex]
d) The entrance fees that allow Swing Haven to break even are between 10.03 and 23.41 dollars per guest.
Step-by-step explanation:
a) Lets find the slope s of the demand:
[tex] s = \frac{79-43}{7-16} = \frac{36}{-9} = -4 [/tex]
Since the demand takes the value 79 in 7, then
[tex]q(p) = -4 (p-7) + 79 = -4 p + 107[/tex]
b) The nightly revenue can be found by multiplying q by p
[tex]R(p) = p*q(p) = p*( -4 p + 107) = -4 p^2 + 107 p[/tex]
c) The profit function is obtained from substracting the const function C(p) from the revenue function R(p)
[tex]P(p) = R(p) - C(p) = p*q(p) = -4 p^2 + 107 p - (-26.75p + 939) = \\\\-4 p^2 + 133.75 p - 939[/tex]
d) Lets find out the zeros and positive interval of P. Since P is a quadratic function with negative main coefficient, then it should have a maximum at the vertex, and between the roots (if any), the function should be positive. Therefore, we just need to find the zeros of P
[tex]r_1, r_2 = \frac{-133.75 \,^+_-\, \sqrt{133.75^2-4*(-4)*(-939)} }{-8} = \frac{-133.75 \,^+_-\, 53.526}{-8} \\r_1 = 10.03\\r_2 = 23.41[/tex]
Therefore, the entrance fees that allow Swing Haven to break even are between 10.03 and 23.41 dollars per guest.
We found the linear demand equation as q(p) = -4p + 107. The nightly revenue R(p) is R(p) = -4p^2 + 107p, and the profit P(p) is P(p) = -4p^2 + 133.75p - 939. Setting the profit equal to zero, we found the club breaks even at entrance fees $5.32 and $44.31.
Explanation:In this question, we're asked to formulate linear demand, revenue, and profit equations, and find the entrance fees for break even. First, let's find the linear demand equation.
To obtain this demand equation, we can use the two given points ($7, 79) and ($16, 43) and find the slope (rate of change) equals (43-79) / (16-7) = -4. Hence the demand equation will be q(p) = -4p + b. To find b, substitute one of the points into the equation, for example ($7, 79), we get b=107, hence q(p) = -4p + 107.
Next, let's find the nightly revenue R (p), which is simply the product of the entrance fee and the number of guests, hence R(p) = p * q(p) = p (-4p + 107) = -4p^2 + 107p.
The profit P(p) is the difference between revenue and costs, hence P(p) = R(p) - C(p) = -4p^2 + 107p - (-26.75p + 939) = -4p^2 + 133.75p - 939.
Finally, for Swing Haven to break even, the profit must be zero. By setting P(p) = 0 and solving the equation -4p^2 + 133.75p - 939 = 0, we get the two solutions p = 5.3216 and p = 44.3031, or roughly $5.32 and $44.31.
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Which two-dimensional cross sections are squares?
Select all that apply.
a cross-section that is perpendicular to the base of a cube
a cross-section that is parallel to the base of a triangular pyramid
a cross-section that is parallel to the base of a cylinder
a cross section through the center of a sphere
a cross-section that is perpendicular to the base of a cylinder whose base diameter and height are the same
Answer:
A cross-section that is perpendicular to the base of a cube.
A cross-section that is perpendicular to the base of a cylinder whose base diameter and height are the same.
Step-by-step explanation:
We have to select from options that the two-dimensional cross section are squares.
The correct options are :
A cross-section that is perpendicular to the base of a cube.
A cross-section that is perpendicular to the base of a cylinder whose base diameter and height are the same.
In both the cases the length and the width of the section are equal. (Answer)
Among the given options, only the cross-section that is perpendicular to the base of a cube is guaranteed to be a square. The other options will generally result in different shapes, such as triangles or circles.
Explanation:The question asks which two-dimensional cross sections are squares. To find the answer, we must consider the shape of the object and the orientation of the cross section.
A cross-section that is perpendicular to the base of a cube. If we cut a cube with a plane perpendicular to one of its faces, the cross section is the same shape as the face, which is a square.A cross-section that is parallel to the base of a triangular pyramid would not be a square because the base itself is a triangle.A cross-section that is parallel to the base of a cylinder would be a circle, as it would be cut along the cylinder's circular base.A cross section through the center of a sphere would also result in a circle, assuming the cut goes through the sphere's diameter.A cross-section that is perpendicular to the base of a cylinder whose base diameter and height are the same, also known as a right circular cylinder, would only result in a square if the cylinder is cut along a plane that is at 45 degrees to the base, which is not the typical perpendicular cut, so typically it would not be a square.At first glance, only the cross-section perpendicular to the base of a cube is a square. However, depending on specific conditions not typically met by the listed shapes, other cross-sections can appear square-shaped. Therefore, generally, the answer is a cross-section that is perpendicular to the base of a cube will be square.
Frank started out in his car travelling 45 mph. When Frank was 1 3 miles away, Daniel started out from the same point at 50 mph to catch up with Frank. How long will it take Daniel to catch up with Frank?
Final answer:
It will take Daniel approximately 0.26 hours, or 15.6 minutes, to catch up with Frank.
Explanation:
To find how long it will take Daniel to catch up with Frank, we can use the formula time = distance / speed. Since Frank started out first, we can calculate his distance using the formula distance = speed * time. Let's assume it takes Daniel t hours to catch up with Frank. The time it takes Frank to travel 13 miles is 13 miles / 45 mph = 0.289 hours. Therefore, when Daniel starts, Frank has already traveled a distance of 0.289 hours * 45 mph = 13 miles. To catch up with Frank, Daniel needs to travel the same distance in t hours at a speed of 50 mph. So, 13 miles = 50 mph * t hours. Dividing both sides by 50 mph gives us t = 13 miles / 50 mph = 0.26 hours. Therefore, it will take Daniel approximately 0.26 hours, or 15.6 minutes, to catch up with Frank.
Significance tests A test of H0: p = 0.65 against Ha: p < 0.65 has test statistic z = −1.78. (a) What conclusion would you draw at the 5% significance level? At the 1% level? (b) If the alternative hypothesis were Ha: p ≠ 0.65, what conclusion would you draw at the 5% significance level? At the 1% level?
Answer:
(a) At 5% significance level, reject H0
At 1% significance level, reject H0
(b) At 5% significance level, fail to reject H0
At 1% significance level, fail to reject H0
Step-by-step explanation:
(a) The test is a one tailed test
At 5% significance level, the critical value is 1.645
Conclusion: Reject H0 because the test statistic -1.78 is less than the critical value 1.645
At 1% significance level, the critical value is 2.326
Conclusion: Reject H0 because the test statistic -1.78 is less than the critical value 2.326
(b) The test is a two tailed test
At 5% significance level, the critical value is 1.96. The region of no rejection of H0 lies between -1.96 and 1.96
Conclusion: Fail to reject H0 because the test statistic -1.78 falls within -1.96 and 1.96
At 1% significance level, the critical value is 2.576. The region of no rejection of H0 lies between -2.576 and 2.576
Conclusion: Fail to reject H0 because the test statistic falls within -2.576 and 2.576
The conclusion that can be made from an hypothesis test depends on
the significance level and p-value.
Response:
(a) The conclusion at 5% is there is statistical evidence to suggest that p < 0.65
At 1% level; fail to reject H₀: p = 0.65, there is statistical evidence to suggest that p = 0.65
(b) With Hₐ ≠ 0.65, the conclusion at the 5% significance level is that there is sufficient statistical evidence that p = 0.65
At the 1% level, fail to reject H₀: p = 0.65,
Which is the method to draw conclusion from an hypothesis test?The null hypothesis, H₀: p = 0.65
The alternative hypothesis, Hₐ: p < 0.65
The z-score is z = -1.78, which gives;
The p-value = 0.0375
(a) The significance level is 5%
Which gives, α = 0.05
Given that the p-value is less than the significant level, we have that
there is sufficient evidence against the null hypothesis, given that the
probability that the null hypothesis is correct is less than the significant
level of 5%.
Therefore, reject H₀, p = 0.65
There is sufficient statistical evidence to suggest that the the p is less than 0.65, (p < 0.65)However, at 1% significant level, α = 0.01, and the p-value, p = 0.0375 is
larger than the significance level.
Therefore, we fail to reject the null hypothesis and there is sufficient statistical evidence to suggest that p = 0.65(b) Hₐ: p ≠ 0.65
We have;
[tex]\alpha = \dfrac{5 \%}{2} = 2.5 \% = \mathbf{0.025}[/tex]
Which gives;
The p-value (0.0375) is larger than the significant level, therefore, we
fail to reject the null hypothesis.
There is sufficient statistical evidence to suggest that p = 0.65At the 1% level of significance, we have;
[tex]\alpha = \dfrac{1 \%}{2} = 0.5 \% = 0.005[/tex]
Which gives;
The p-value at z = -1.78 (p = 0.0375) is larger than the significant level
Therefore;
There is sufficient evidence to suggest that p = 0.65Learn more about hypothesis testing here:
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Zeke is racing his little brother niko they are running a total of 30 yards and zeke gives Niko a 12 yard head start zeke runs 2 yards every second but Niko only runs 1 yard every 2 seconds if x represents the number of seconds they have been racing and y represents the distance from the start line then
Answer:
Zeke will catch up with Niko at 16 yards from the start line, y = 16 yards.
Zeke will catch up Niko after 8 seconds, x = 8 seconds.
Step-by-step explanation:
i) distance to be run = 30 yards
ii) Niko has a head start of 12 yards.
iii) speed of Zeke = 2 yards / second
iv) speed of Niko = 1 yard every 2 seconds = 0.5 yard / second
v) x represents the number of seconds they have been racing.
vi) y represents the distance from the start line.
vii) the time at which Zeke catches up with Niko will be given by
[tex]x = \frac{y - 12}{0.5} = \frac{y}{2}[/tex]
Therefore 2y - 24 = 0.5y [tex]\Rightarrow[/tex] 1.5 y = 24 [tex]\therefore[/tex] y = 24 / 1.5 = 16 yards
Therefore x = 16 /2 = 8 seconds
The equations that represent Niko's and Zeke's distance from the start line are [tex]y = 12 + \frac 12 x[/tex] and [tex]y = 2 x[/tex], respectively.
The given parameters are:
[tex]Total = 30[/tex] --- the total distance
Niko is 12 yards ahead, and runs at 1 yard per 2 seconds. So, Niko's equation is
[tex]N i k o = 12 + \frac 12 x[/tex]
Zeke runs 2 yards per seconds. So, Zeke's equation is
[tex]Zeke = 2 x[/tex]
Hence, Niko's and Zeke's distance from the start line are [tex]y = 12 + \frac 12 x[/tex] and [tex]y = 2 x[/tex], respectively.
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Assume that the weight of two year old babies have distribution that is approximately normal with a mean of 29 pounds and a standard deviation of 3 pounds. what weight of two year old baby corresponds to 10th percentile?
Answer:
25.15 ponds is the weight of two year old baby corresponds to 10th percentile.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 29 pounds
Standard Deviation, σ = 3 pounds
We are given that the distribution of weight of two year old babies is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
We have to find the value of x such that the probability is 0.10
P(X < x)
[tex]P( X < x) = P( z < \displaystyle\frac{x - 29}{3})=0.10[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(z < -1.282) = 0.10[/tex]
[tex]\displaystyle\dfrac{x - 29}{3} = -1.282\\x = 25.154 \approx 25.15[/tex]
Thus, 25.15 ponds is the weight of two year old baby corresponds to 10th percentile.
Two different suppliers, A and B, provide a manufacturer with the same part. All supplies of this part are kept in a large bin. in the past, 5% of the parts supplied by A and 9% of the parts supplied by B have been defective. A supplies four times as many parts as B. Suppose you reach into the bin and select a part, and find it is nondetective. What is the probability that it was supplied by A
Answer:
The probability of selecting a non-defective part provided by supplier A is 0.807.
Step-by-step explanation:
Let A = a part is supplied by supplier A, B = a part is supplied by supplier B and D = a part is defective.
Given:
P (D|A) = 0.05, P(D|B) = 0.09
A supplies four times as many parts as B, i.e. n (A) = 4 and n (B) = 1.
Then the probability of event A and B is:
[tex]P(A)=\frac{n(A)}{n(A)+N(B)}= \frac{4}{4+1}=0.80\\P(B)\frac{n(B)}{n(A)+N(B)}= \frac{1}{4+1}=0.20[/tex]
Compute the probability of selecting a defective product:
[tex]P(D)=P(D|A)P(A)+P(D|B)P(B)\\=(0.05\times0.80)+(0.09\times0.20)\\=0.058[/tex]
The probability of selecting a non-defective part provided by supplier A is:
[tex]P(A|D')=\frac{P(D'|A)P(A)}{P(D')} = \frac{(1-P(D|A))P(A)}{1-P(D)}\\=\frac{(1-0.05)\times0.80}{(1-0.058)}\\ =0.80679\\\approx0.807[/tex]
Thus, the probability of selecting a non-defective part provided by supplier A is 0.807.
The required probability of selecting a non-defective part provided by supplier A is 0.807.
Let,
A part is supplied by supplier A,
B part is supplied by supplier B,
And D = a part is defective.
Given:
P ([tex]\frac{D}{A}[/tex]) =5% = 0.05,
P([tex]\frac{D}{B}[/tex]) = 9% = 0.09
A supplies four times as many parts as B, .
Then, n (A) = 4 and n (B) = 1.
The probability of event A and B is:
Probability of event P(A) = [tex]\frac{n (A)}{n (A) + n(B)}[/tex] = [tex]\frac{4}{4+1}[/tex]
P(A) = [tex]\frac{4}{5}[/tex]
And Probability of Event P(B) = [tex]\frac{n (B )}{n (A) + n(B)} = \frac{1}{4+1}[/tex]
P(B) = [tex]\frac{1}{5}[/tex]
Then , the probability of selecting a defective product:
P(D) = [tex]P(\frac{D}{A}) P(A) + P(\frac{D}{B}) P(B)[/tex]
P(D) = 0.50×0.80 + 0.09×0.20
P(D) = 0.058
The probability of selecting a non-defective part provided by supplier A is
[tex]P(\frac{A}{D'} )= \frac{P(D'(A)) . P(A)}{P(D')} \\\\[/tex]
= [tex]\frac{1- P(D(A)). P(A)}{1-P(A)} \\\\\frac{(1-0.05) . 0.80}{1- 0.05} \\\\[/tex]
= 0.807
Hence, the probability of selecting a non-defective part provided by supplier A is 0.807.
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Each chef at "Sushi Emperor" prepares 151515 regular rolls and 202020 vegetarian rolls daily. On Tuesday, each customer ate 222 regular rolls and 333 vegetarian rolls. By the end of the day, 444 regular rolls and 111 vegetarian roll remained uneaten.
Each chef at "sushi emperor" prepares 15 regular rolls and 20 vegetarian rolls daily. On tuesday, each customer ate 2 regular rolls & 3 vegetarian rolls. by the end of the day, 4 regular rolls & 1 vegetarian roll remained uneating. how many chefs were on tuesday ? and how many customers were they ?
Answer:There were 2 chefs and 13 customers on tuesday
Solution:Let x be the number of chefs at Sushi Emperor and y be the number of customers on Tuesday.
From given,
Each chef prepares 15 regular rolls and 20 vegetarian rolls daily
If each chef prepares 15 regular rolls, then x chefs prepare 15x regular rolls
If each customer ate 2 regular rolls, then y customers ate 2y regular rolls
By the end of the day, 4 regular roll remained un eating
Therefore,
15x - 2y = 4 --------- eqn 1
If each chef prepares 20 vegetarian rolls, then x chefs prepare 20x vegetarian rolls
If each customer ate 3 vegetarian rolls, then y customers ate 3y vegetarian rolls
By the end of the day, 1 vegetarian roll remained uneating
Therefore,
20x - 3y = 1 ---------- eqn 2
Let us solve eqn 1 and eqn 2
Multiply eqn 1 by 3
45x - 6y = 12 ------- eqn 3
Multiply eqn 2 by 2
40x - 6y = 2 ------- eqn 4
Subtract eqn 4 from eqn 3
45x - 6y = 12
40x - 6y = 2
( - ) --------------
5x = 10
x = 2
Substitute x = 2 in eqn 1
20(2) - 3y = 1
40 - 3y = 1
3y = 39
y = 13
Thus there were 2 chefs and 13 customers
Jacob bought 13 packs of gum to add to the 5 pieces he already had. He then shared all of his pieces of gum with six friends. If Jacob and his six friends each revived 27 pieces of gum, how many were in each pack
Answer:
14 gums.
Step-by-step explanation:
Given: Jacob bought 13 pack of gum
He already had 5 piece of gum.
He shared gum with six of his friends.
Each one of them received 27 pieces of gum.
Lets assume the number of gums in each pack be "x".
Total number of gum= [tex]number\ of\ gum\ in\ each\ pack\times number\ of\ pack + 5[/tex]
Also gum has been shared among jacob and his 6 friends, which is 7 person.
∴ Share of each person= [tex]\frac{Total\ number\ of\ gums}{number\ of\ person}[/tex]
Now, forming equation to find number of gums in each pack.
⇒ [tex]\frac{13\times x+5}{7} = 27[/tex]
Multiplying both side by 7
⇒ [tex]13x+5= 189[/tex]
Subtracting both side by 5
⇒ [tex]13x= 189-5[/tex]
⇒[tex]13x= 184[/tex]
Dividing both side by 13
⇒ [tex]x= \frac{184}{13}[/tex]
∴[tex]x= 14.15 \approx 14\ gum[/tex]
Hence, each pack have 14 gums.
The only contents of a container are 4 blue disks and 8 green disks. If 3 disks are selected one after the other, and at random and without replacement from the container, what is the probability that 1 of the disks selected is blue, and 2 of the disks selected are green?A. 21/55
B. 28/55
C. 34/55
D. 5/8
E. 139/220
Answer: B. [tex]\dfrac{28}{55}[/tex] .
Step-by-step explanation:
Given : Number of blue disks =4
Number of green disks = 8
Total disks = 12
Total number of combinations of drawing any 3 disks from 12 = [tex]^{12}C_3[/tex]
Number of combinations of drawing 1 blue and 2 green disks = [tex]^{4}C_1\times^{8}C_2[/tex]
Now , the probability that 1 of the disks selected is blue, and 2 of the disks selected are green will be :
[tex]\dfrac{^{4}C_1\times^{8}C_2}{^{12}C_3}\\\\=\dfrac{4\times\dfrac{8!}{2!6!}}{\dfrac{12!}{3!9!}}\\\\=\dfrac{4\times28}{220}\\\\=\dfrac{28}{55}[/tex]
Hence, the correct answer is B. [tex]\dfrac{28}{55}[/tex] .
Help asap, thank you! :) 2 questions, multiplying monomials.
Answer:
Correct answer choices are [tex]27x^{2}[/tex] and [tex]657 cm^{2}[/tex]
Step-by-step explanation:
We are able to arrive at these answers through basic equation used to calculate area of an triangle and monomial laws
In 1995, Orlando, Florida was about 175,000. At that same time , the population was growing at a rate of about 2000 per years, write an equation in slope - intercept form to find orlando's population for any year
Answer:
Y=2000x+175,000
Step-by-step explanation:
y=mx+b so your M will be your 2000 and your x is gonna be years, and your b is gonna be 175,000
Two cars entered an interstate highway at the same time at different locations and traveled in the same direction. The initial distance between the cars was 30 miles. The first car was going 70 miles per hour and the second was going 60 miles per hour. How long will it take for the first car to catch the second one?
Answer: it will take 0.23 hours for the first car to catch the second one.
Step-by-step explanation:
Let t represent the time it will take for the first car to catch the second one.
The initial distance between the cars was 30 miles. This means that by the time both cars meet, they would have covered a total distance of 30 miles.
Distance = speed × time
The first car was going 70 miles per hour.
Distance covered by the first car after t hours is
70 × t = 70t
The second was going 60 miles per hour. Distance covered by the second car after t hours is
60 × t = 60t
Since the total distance covered is 30 miles, then
70t + 60t = 30
130t = 30
t = 30/130 = 0.23 hours
Identify the zeros of the function f(x) =2x^2 − 2x + 13 using the Quadratic Formula. SHOW WORK PLEASE!! I NEED HELP!!
Answer:
[tex]x=\frac{1+5i} {2}[/tex] and [tex]x=\frac{1-5i} {2}[/tex]
Step-by-step explanation:
we know that
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]f(x)=2x^{2} -2x+13[/tex]
Equate the function to zero
[tex]2x^{2} -2x+13=0[/tex]
so
[tex]a=2\\b=-2\\c=13[/tex]
substitute in the formula
[tex]x=\frac{-(-2)\pm\sqrt{-2^{2}-4(2)(13)}} {2(2)}[/tex]
[tex]x=\frac{2\pm\sqrt{-100}} {4}[/tex]
Remember that
[tex]i=\sqrt{-1}[/tex]
so
[tex]x=\frac{2\pm10i} {4}[/tex]
Simplify
[tex]x=\frac{1\pm5i} {2}[/tex]
therefore
[tex]x=\frac{1+5i} {2}[/tex] and [tex]x=\frac{1-5i} {2}[/tex]
Sixty-seven biscuits are to be fed to 10 pets; each pet is either a cat or a dog. Each dog is to get seven biscuits, and each cat is to get six. How many dogs are there?
Answer:
There are 7 dogs.
Step-by-step explanation:
7 (dogs) x 7 (biscuits) = 49
3 (cats) x 6 (biscuits) = 18
49 + 18 = 67
A tower that is 106 feet tall casts a shadow 141 feet long. Find the angle of elevation of the sun to the nearest degree.
Final answer:
To determine the angle of elevation of the sun, calculate the inverse tangent (arctan) of the height of the tower (106 feet) divided by the length of its shadow (141 feet). The angle of elevation is approximately 37 degrees to the nearest degree.
Explanation:
To find the angle of elevation of the sun given that a 106 feet tall tower casts a shadow of 141 feet long, we can use trigonometry. Specifically, the tangent of the angle, which is the ratio of the opposite side (the height of the tower) to the adjacent side (the length of the shadow).
We use the formula:
tangent of angle = opposite / adjacent
Tan(angle) = 106 / 141
Now we need to calculate the inverse tangent (arctan) of this ratio to find the angle in degrees:
Angle = arctan(106/141)
After performing this calculation with a calculator or using a trigonometric table, we find that the angle to the nearest degree is approximately 37 degrees.
Which is the graph of f (x) = 4 (1/2) Superscript x?
Answer:
Option (2) is correct graph.
Step-by-step explanation:
Given:
The function to graph is given as:
[tex]f(x)=4(\frac{1}{2})^x[/tex]
Now, the above function is an exponential function of the form [tex]f(x)=ka^x[/tex]
Where, 'k' and 'a' are constants.
The range of an exponential function is always greater than 0.
The domain is all real numbers.
Now, for graphing it, we need to find some points on it and its end behaviour.
Now, for x = 0, the function value is given as:
[tex]f(0)=4(\frac{1}{2})^0=4[/tex]
So, (0, 4) is a point on the graph.
Now, for x = 1, the function value is given as:
[tex]f(1)=4(\frac{1}{2})^1=4\times\frac{1}{2}=2[/tex]
So, (1, 2) is another point on the graph.
Now, for x = 2, the function value is given as:
[tex]f(2)=4(\frac{1}{2})^2=4\times\frac{1}{4}=1[/tex]
So, (2, 1) is another point on the graph.
Now, as 'x' tends to ∞, the function value tends to:
[tex]f(x\to\infty)=4\cdot\frac{1}{2}^{\infty}=\frac{4}{\infty}=0[/tex]
So, as
[tex]x\to\infty,f(x)\to0\\\\x\to-\infty,f(x)\to\infty[/tex]
Now, from among all the options, only option (2) fulfills all the conditions given above.
So, option (2) is correct graph.
Answer:
option 2
Step-by-step explanation:
Does the graph represent a function? Why or Why Not
Answer:
not a function - it does not pass the vertical line test.
Step-by-step explanation:
Calculate the average rate of change of the given function f over the intervals [a, a + h] where h = 1, 0.1, 0.01, 0.001, and 0.0001. (Technology is recommended for the cases h = 0.01, 0.001, and 0.0001.) HINT [See Example 4.] (Round your answers to five decimal places.) f(x) = 3 x ; a = 7
Step-by-step explanation:
average rate of change of function is given by :
[tex]f= (f(a+h)-f(a))/h[/tex]
where
[tex]f(x)=3x[/tex]
and a= 7
so inserting values is formula for h=1
[tex]f=(f(7+1)-f(7))/1[/tex]
[tex]f= f(8)-f(7)= 3(8)-3(7)=24-21=3[/tex]
now for h= 0.1
[tex]f=(f(7+0.1)-f(7))/0.1=(f(7.1)-f(7))/0.1=(3(7.1)-3(7))/0.1[/tex]
[tex]f=3[/tex]
similarly average rate of change of given function is same for all given step sizes.
Final answer:
The question involved calculating the average rate of change of the function f(x) = 3x over various intervals, showing that the rate of change is constant and equals 3 for all given values of h.
Explanation:
The question asks to calculate the average rate of change of the function f(x) = 3x over the intervals [a, a + h] for values of h = 1, 0.1, 0.01, 0.001, and 0.0001, where a = 7.
The average rate of change is calculated using the formula [tex]\frac{f(a+h) - f(a)}{h}[/tex]
For each value of h, we substitute a and h into the function and use the formula to find the average rate of change.
For h = 1, the average rate of change is 3.
For h = 0.1, the average rate of change is also 3.
For h = 0.01, the average rate of change remains 3.
For h = 0.001, the average rate is again 3.
Similarly, for h = 0.0001, the average rate of change is 3.
Using technology for values of h smaller than 0.1 is recommended due to the precision required in calculations. However, for this particular function, the rate of change is constant across these intervals, simplifying the process.
The math club has $1256 to send on food for a party. Beef = $11, chicken = $9 and vegetarian = $7. * Vegetarian dishes are purchased. Write an inequality
Answer:
[tex]11b+9c+7v\leq 1256[/tex]
Step-by-step explanation:
Let 'b' plates of beef, 'c' plates of chicken, and 'v' plates of vegetarian dishes are purchased for the party.
Given:
Cost of 1 plate of beef dish = $11
Cost of 1 plate of chicken dish = $9
Cost of 1 plate of vegetarian dish = $7
Total money available to spend = $1256
So, as per question:
Total money spent on purchasing the dishes must be less than or equal to the total money available by the Math club.
Total cost of all the dishes is equal to the sum of the costs of 'b' plates of beef, 'c' plates of chicken, and 'v' plates of vegetarian dishes.
Therefore, total cost of all the dishes is given as:
Total cost = [tex]11b+9c+7v[/tex]
Now, the inequality for the given situation is:
Total cost on dishes ≤ Total money available to spend
⇒ [tex]11b+9c+7v\leq 1256[/tex]
Hence, the inequality is [tex]11b+9c+7v\leq 1256[/tex]
hello loves!! I've been stuck on this question for like 2 hours lol! i need some help, ill give 100 points :)
Answer:
61.12 units²
Step-by-step explanation:
(½ × pi × r²) + (½ × b × h)
½ [(3.14 × 4²) + (8 ×9)]
½(122.24)
61.12 units²
Answer:
61.13 units squared
Step-by-step explanation:
This figure is composed of a semicircle and a triangle. Let's find these areas separately:
1) SEMICIRCLE:
The area of a semicircle is: [tex]A=\frac{\pi r^2}{2}[/tex] , where r is the radius (which is the distance from the center to a point on the circle). In this case, the radius of the circle is 4. So, we have:
[tex]A=\frac{\pi *4^2}{2} =\frac{16\pi }{2} =8\pi[/tex] ≈ 25.13 units squared
2) TRIANGLE:
The area of a triangle is: [tex]A=\frac{bh}{2}[/tex] , where b is the base and h is the height. Here, the base is 8 (b = 8) and the height is 9 (h = 9). So, we have:
[tex]A=\frac{8*9}{2} =\frac{72}{2} =36[/tex] units squared
Finally, we add these two areas together:
25.13 + 36 = 61.13 units squared.
Hope this helps!
Home Away, a nongovernmental not-for-profit organization, provides food and shelter to victims of natural disasters. Home Away received a $15,000 gift with the stipulation that the funds be used to buy beds. In which net asset class should Home Away report the contribution?
Answer:
Home away should record the contribution to a Net assets with donor restriction
Step-by-step explanation
A Net asset with donor restriction is the part of net assets of a not- for - profit making organisation that is subject to donor-imposed restrictions.
The stipulation that the fund of $15,000 should be used to buy beds automatically makes it to be classified as a Net assets with donor restriction item.
I have some geometric sequence questions, will give 5 points for every answer and will give Brainliest!
1. List the first four terms of a geometric sequence with t5 = 24 and t6 = 3
2. List the first four terms of a geometric sequence with t1 = 4 and tn = -3tn-1
3. Find the three geometric means between 1/2 and 8
Thank you so much!!
Answer:
Step-by-step explanation:
1) since the sixth term is 3 and the fifth term 24, the common ratio would be 3/24 = 1/8
The formula for finding the nth term of a geometric sequence is
Tn = ar^(n - 1)
If t6 = 3,r = 1/8, then
3 = a × 1/8^(6 - 1) = a × (1/8)^5
a = 3/(0.125)^5 = 98304
The first term is 98304.
Second term is 98304 × 1/8 = 12288
Third term is 12288 × 1/8 = 1536
Third term is 1536 × 1/8 = 192
2) t1 = 4
t2 = - 3t(2- 1) = - 3t1 = - 3 × 4 = - 12
t3 = - 3t(3- 1) = - 3t2 = - 3 × - 12 = 36
t4 = - 3t(4- 1) = - 3t3 = - 3 × 36 = - 108
3) let the numbers be t2,t3 and t4
The sequence becomes
1/2, t2,t3, t4,8
The formula for finding the nth term of a geometric sequence is
Tn = ar^(n - 1)
8 = 1/2 × r^(5 - 1)
8 = 1/2 × r^4
16 = r^4
2^4 = r^4
r = 2
t2 = 1/2 × 2 = 1
t3 = 1 × 2 = 2
t4 = 2 × 2 = 4
The rate of transmission in a telegraph cable is observed to be proportional to x2ln(1/x) where x is the ratio of the radius of the core to the thickness of the insulation (0
Answer:
The value of x that gives the maximum transmission is 1/√e ≅0.607
Step-by-step explanation:
Lets call f the rate function f. Note that f(x) = k * x^2ln(1/x), where k is a positive constant (this is because f is proportional to the other expression). In order to compute the maximum of f in (0,1), we derivate f, using the product rule.
[tex]f'(x) = k*((x^2)'*ln(1/x) + x^2*(ln(1/x)')) = k*(2x\,ln(1/x)+x^2*(\frac{1}{1/x}*(-\frac{1}{x^2})))\\= k * (2x \, ln(1/x)-x)[/tex]
We need to equalize f' to 0
k*(2x ln(1/x) - x) = 0 -------- We send k dividing to the other side2x ln(1/x) - x = 0 -------- Now we take the x and move it to the other side2x ln(1/x) = x -- Now, we send 2x dividing (note that x>0, so we can divide)ln(1/x) = x/2x = 1/2 ------- we send the natural logarithm as exp1/x = e^(1/2)x = 1/e^(1/2) = 1/√e ≅ 0.607Thus, the value of x that gives the maximum transmission is 1/√e.
The rate of transmission in a telegraph cable is given by the equation: rate of transmission = x^2 ln(1/x), where x is the ratio of the radius of the core to the thickness of the insulation.
Explanation:The rate of transmission in a telegraph cable is given by the equation: rate of transmission = x2 ln(1/x), where x is the ratio of the radius of the core to the thickness of the insulation.
This equation shows that the rate of transmission is directly proportional to the square of x and logarithmically inversely proportional to x.
For example, if x is 0.5, the rate of transmission is (0.5)2 ln(1/0.5) = 0.25 ln(2).
Learn more about Rate of transmission here:https://brainly.com/question/3311292
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Julia earns $6 an hour babysitting and earns $5 an hour walking dogs. She earned $43 after working a total of 8 hours at her two jobs. Complete the system of equations below to represent the situation. Let b= the number of hours that Julia babysits and d= the number of hours she walks dogs. _+_=8 _+_=43
Answer: the equations are
b + d = 8
6x + 5y = 43
Step-by-step explanation:
Let b represent the number of hours that Julia babysits.
Let d represent the number of hours she walks dogs.
Julia worked for a total of 8 hours babysitting and walking the dogs.. This means that
b + d = 8
Julia earns $6 an hour babysitting and earns $5 an hour walking dogs. She earned a total of $43 after working a total of 8 hours at her two jobs. This means that
6x + 5y = 43
A broker/dealer bought ABC stock at 8 for its inventory position. A month later when the inter-dealer market for ABC was 10.50 -- 11.25, the broker/dealer sold the stock to a customer. The basis for the dealer's markup will be:[A] 8.00[B] 8.75[C] 10.50[D] 11.25
Answer:
[D] 11.25
Step-by-step explanation:
Broker/dealers must trade with customers based on the current bid and ask.
10.50 Bid for customers selling
11.25 Ask for customers buying
A furniture salesperson earns 4.5% commission on every piece of furniture sold. The salesperson sells a sofa for $1000 and a chair for $200. What commission does the salesperson earn?
Answer: the salesperson earns $54 as commission.
Step-by-step explanation:
A furniture salesperson earns 4.5% commission on every piece of furniture sold. The salesperson sells a sofa for $1000. This means that the commission that he earned from the sale of the sofa is
4.5/100 × 1000 = 0.045 × 1000 = $45
The salesperson also sold a chair for $200. This means that the commission that he earned from the sale of the chair is
4.5/100 × 200 = 0.045 × 200 = $9
The total commission that the salesperson earns is
45 + 9 = $54
(6-2i)^2 which is the coefficient of i ?
A.−24
B.−12
C.16
D.24
Option A: -24 is the coefficient of i
Explanation:
The expression is [tex](6-2 i)^{2}[/tex]
To determine the coefficient of i, first we shall find the square of the binomial for the expression [tex](6-2 i)^{2}[/tex]
The formula to find the square of the binomial for this expression is given by
[tex](a-b)^{2}=a^{2}-2 a b+b^{2}[/tex]
where [tex]a=6[/tex] and [tex]b=2i[/tex]
Substituting this value and expanding, we get,
[tex](6-2 i)^{2}=6^{2} -2(6)(2i)+(2i)^{2}[/tex]
Simplifying the terms, we have,
[tex](6-2 i)^{2}=36-24i-4[/tex]
Thus, from the above expression the coefficient of i is determined as -24.
Hence, Option A is the correct answer.
please help with a, b, and c. thank you!:)
Answer:
The answer to your question is below
Step-by-step explanation:
a) The intervals in which the graph is decreasing are the right section of the first parabola, the left section of the second parabola and also the right section of the third parabola.
(9, 11) U (14.5, 17) U (21, 27)
b) There are only two intervals in which the graph is increasing
(1, 9) U (17, 21)
c) During the time the graph is increasing, Andre is getting away from his origin.
4 Erin and Devon are playing a game. Erin has 42 points. If Devon had 14 more points, he'd have double the points Erin has. How many points does Devon have?
Final answer:
The question is a mathematical problem where we find that Devon has 70 points after setting up and solving an algebraic equation based on the conditions given.
Explanation:
The student's question revolves around a Mathematical problem concerning the points scored by two players, Erin and Devon, in a game. Erin has 42 points, and the question provides a condition that if Devon had 14 more points, he would have double the points Erin has. This scenario can be translated into an algebraic equation to solve for the number of points Devon currently has.
Let's denote the current number of points Devon has as D. According to the problem, if Devon had 14 more points, his total would be D + 14. We are also told that this hypothetical total would be double the points Erin has, which is 42. Therefore, we can write the equation as:
D + 14 = 2 × 42
By solving this equation, we can find out how many points Devon has:
D + 14 = 84 (since 2 × 42 equals 84)D = 84 - 14D = 70Devon currently has 70 points.
Erin has 42 points. Devon has 70 points. If he had 14 more, he'd have double Erin's points.
let's break it down step by step:
Given:
- Erin has 42 points.
- If Devon had 14 more points, he'd have double the points Erin has.
Let's denote Devon's points as [tex]\( D \).[/tex]
According to the given information, if Devon had 14 more points, he'd have double the points Erin has. So, mathematically, we can represent Devon's points as [tex]\( 2 \times 42 \)[/tex] when we add those 14 points.
So, we can write the equation:
[tex]\[ D + 14 = 2 \times 42 \][/tex]
Now, let's solve for [tex]\( D \):[/tex]
[tex]\[ D + 14 = 84 \][/tex]
Subtract 14 from both sides of the equation:
[tex]\[ D = 84 - 14 \]\[ D = 70 \][/tex]
So, Devon currently has 70 points.
At a college, the cost of tuition increased by 10%. Let b represent the former cost of tuition. Use the expression b+0.10b for the new cost of tuition.
Question is Incomplete,Complete question is given below;
At a college, the cost of tuition increased by 10%. Let b be the former cost of tuition. Use the expression b + 0.10b for the new cost of tuition.
a) Write an equivalent expression by combining like terms.
b) What does your equivalent expression tell you about how to find the new cost of tuition?
Answer:
a. The equivalent expression is [tex]1.1b[/tex].
b. The new cost of tuition is 1.1 times the former cost of tuition.
Step-by-step explanation:
Given:
Former cost of tuition = [tex]b[/tex]
the cost of tuition increased by 10%.
New cost of tuition = [tex]b+0.10b[/tex]
Solving for part a.
we need to find the equivalent expression by combining the like terms we get;
Now Combining the like terms we get;
new cost of tuition = [tex]b(1+0.1) = 1.1b[/tex]
Hence The equivalent expression is [tex]1.1b[/tex].
Solving for part b.
we need to to say about equivalent expression about how to find the new cost of tuition.
Solution:
new cost of tuition = [tex]1.1b[/tex]
So we can say that.
The new cost of tuition is 1.1 times the former cost of tuition.