The calling plan was a logical decision that was made. For calls with a shorter estimated time (10 minutes), the first plan is selected; for calls with an extended expected duration, the second plan is favoured (15 minutes).
Let the costs for the first and second plans, respectively, be denoted by h₁(x) and h₂(x), while the call lasts for x minutes.
The expressions for these two cost functions are as follows, according to the information available:
h₁(x) = 10x
h₂(x) = 99; if x ≤ 20 and 99 + 10(x - 20); if x > 20
Let X represent how long the call was. The exponential distribution of X has a parameter value of λ = 1/10 if the anticipated call time is 10 minutes.
That is, X ~ exp(λ = 1/10)
The exponential distribution's density function with parameter λ = 1/10 is,
f(x) = 1/10[tex]e^{-x/10}[/tex]; if x > 0 and 0; if otherwise
Calculate the anticipated cost of the initial plan E[h₁(x)].
E[h₁(x)] = [tex]\int^{\infty}_{-\infty}h_{1}(x)\cdot f(x)dx[/tex]
E[h₁(x)] = [tex]\int_{-\infty}^{0}10x\cdot 0dx+\int^{\infty}_{0}10x\cdot \frac{1}{10}e^{-x/10}dx[/tex]
E[h₁(x)] = 0 + [tex]\int^{\infty}_{0}x\cdot e^{-x/10}dx[/tex]
E[h₁(x)] = [tex][-10xe^{-x/10}-100e^{-x/10}]^{\infty}_{0}[/tex]
E[h₁(x)] = 100
Calculate the anticipated cost of the initial plan E[h₂(x)].
E[h₂(x)] = [tex]\int^{\infty}_{-\infty}h_{2}(x)\cdot f(x)dx[/tex]
E[h₂(x)] = [tex]\int_{-\infty}^{0}99dx+\int^{20}_{0}99\cdot \frac{1}{10}e^{-x/10}dx + \int^{\infty}_{20}(99+10(x-20))\cdot \frac{1}{10}e^{-x/10}dx[/tex]
E[h₂(x)] = 0 + [tex]\frac{99}{10}\int^{20}_{0}e^{-x/10}dx - \frac{101}{10}\int^{\infty}_{20}e^{-x/10}dx+\int^{\infty}_{20}xe^{-x/10}dx[/tex]
E[h₂(x)] = [tex]\frac{99}{10}[-10e^{-x/10}]^{20}_{0} - \frac{101}{10}[-10e^{-x/10}]^{\infty}_{20} + [-10xe^{-x/10}-100e^{-x/10}]^{\infty}_{20}[/tex]
E[h₂(x)] = -99e⁻² + 99 - 101e⁻² + 200e⁻² + 100e⁻²
E[h₂(x)] = 99 + 100e⁻²
E[h₂(x)] = 112.5335
E[h₂(x)] > E[h₁(x)] (112.53 > 100) is what has been seen. Hence, the first strategy is chosen when a 10-minute call is anticipated.
The exponential distribution's density function with parameter λ = 1/15 is,
f(x) = 1/15[tex]e^{-x/15}[/tex]; if x > 0 and 0; if otherwise
Calculate the anticipated cost of the initial plan E[h₁(x)].
E[h₁(x)] = [tex]\int^{\infty}_{-\infty}h_{1}(x)\cdot f(x)dx[/tex]
E[h₁(x)] = [tex]\int_{-\infty}^{0}10x\cdot 0dx+\int^{\infty}_{0}10x\cdot \frac{1}{15}e^{-x/15}dx[/tex]
E[h₁(x)] = 0 + [tex]\frac{2}{3}\int^{\infty}_{0}x\cdot e^{-x/15}dx[/tex]
E[h₁(x)] = [tex]\frac{2}{3}[-15xe^{-x/15}-225e^{-x/15}]^{\infty}_{0}[/tex]
E[h₁(x)] = 150
Calculate the anticipated cost of the initial plan E[h₂(x)].
E[h₂(x)] = [tex]\int^{\infty}_{-\infty}h_{2}(x)\cdot f(x)dx[/tex]
E[h₂(x)] = [tex]\int^{20}_{0}99\cdot \frac{1}{15}e^{-x/15}dx + \int^{\infty}_{20}(99+10(x-20))\cdot \frac{1}{15}e^{-x/15}dx[/tex]
E[h₂(x)] = [tex]\frac{99}{15}\int^{20}_{0}e^{-x/15}dx - \frac{101}{15}\int^{\infty}_{20}e^{-x/15}dx+\frac{2}{3}\int^{\infty}_{20}xe^{-x/15}dx[/tex]
E[h₂(x)] = [tex]\frac{99}{15}[-15e^{-x/15}]^{20}_{0} - \frac{101}{15}[-15e^{-x/15}]^{\infty}_{20} + [-15xe^{-x/15}-225e^{-x/15}]^{\infty}_{20}[/tex]
E[h₂(x)] = -99[tex]e^{-4/3}[/tex] + 99 - 101[tex]e^{-4/3}[/tex] + 200[tex]e^{-4/3}[/tex] + 150[tex]e^{-4/3}[/tex]
E[h₂(x)] = 99 + 150[tex]e^{-4/3}[/tex]
E[h₂(x)] = 138.54
E[h₂(x)] < E[h₁(x)] (138.54 < 150) is what has been seen. Hence, the first strategy is chosen when a 15-minute call is anticipated.
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Suppose the standard deviation of the weights of all Florida manatees is 33 pounds. Let be the mean
weight for a sample of a certain number of Florida manatees. What sample size will give the standard
deviation of equal to 10 pounds?
A sample size of 11 would give a standard deviation of 10 pounds for the Florida Manatees
What is an equation?An equation is an expression that shows how two numbers and variables are related using mathematical operations such as addition, subtraction, exponent, division and multiplication.
The standard deviation of a sample is:
[tex]\sigma_n=\frac{\sigma}{\sqrt{n} } \\\\Where\ n\ is\ sample\ size,\sigma\ is\ standard\ deviation\ and\ \sigma_n\ is\ standard\ deviation\ of\ sample[/tex]
Given that:
[tex]\sigma_n=10,\sigma=33,hence:\\\\10=\frac{33}{\sqrt{n} } \\\\n=10.89[/tex]
A sample size of 11 would give a standard deviation of 10 pounds
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Pls help me. I cant figure this out.
Answer:
Step-by-step explanation:
You can do 6x+the number of the amount of squares. Then find find the units of the square unit.
Please ASAP Help
Will mark brainlest due at 12:00
Answer:
plot the point at -3
Step-by-step explanation:
-3 is 6 points away from t and 4 away from s. thus 3/5
The program director estimated that the proportion of MGMT650 students that are very satisfied is 88% ±5%. What will the probability be? Or is the proportion satisfied?
satisfied=88%
The program director estimated that the proportion of MGMT650 students that are very satisfied is 88% ±5%.What is probability?Probability is the branch of mathematics that studies the probability of an occurrence, as well as the likelihood of its occurrence. Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.Probability formula is P(E) = n(E) / n(S), where P(E) refers to the probability of occurrence of event E, n(E) is the number of outcomes in event E, and n(S) is the total number of possible outcomes.What is proportion?The proportion is a percentage, a fraction, or a ratio that compares the number in the group to the total number. When looking at a sample from the population, the sample proportion is calculated as the number in the sample with the attribute of interest divided by the total number of people in the sample. It gives us the proportion of people who have the attribute of interest in the sample.Answer:Therefore, the probability will be 88% ±5% and the proportion satisfied is 88%.
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Brandon deposited $3600 into a savings account that has an annual simple interest rate of 0.5%. How much is in the account after 5 years?
Answer: 3690
Step-by-step explanation: i think
The total amount in the account after 5 years is $3690.
What is the simple interest?Simple interest is the borrowing amount added only to the principal amount.
The Formula to calculate the simple interest is;
S.I. = P x T x R / 100,
Where S.I. is simple interest, P is the principal amount, T is the time period and R is the interest rate in a year.
In this case, the principal is $3600, the rate is 0.5% (or 0.005 as a decimal), and the time is 5 years.
Plugging these values into the formula, we get:
Interest = $3600 x 0.005 x 5 = $90
So after 5 years, the interest earned on the account is $90. To find the total amount in the account, we need to add the interest to the principal:
Total amount = Principal + Interest = $3600 + $90 = $3690
Therefore, the total amount in the account after 5 years is $3690.
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2
8. ¿Cuál es la factorización de x² + 2x?
(A) x²(2x)
(B) x(x + 2)
(C) x(x + 2x)
(D) x²(1 + 2x)
Answer:
B.) x(x+2)
Step-by-step explanation:
Hope this helps! :)
Please help my homework is due tomorrow 10 3/4 + 12 1/4
The sum of 10 3/4 and 12 1/4 is 23.
To add the mixed numbers 10 3/4 and 12 1/4, follow these steps:
Step 1: Add the whole number of parts.
Add the whole numbers 10 and 12 to get:
10 + 12 = 22
Step 2: Add the fractional parts separately.
Add the fractions 3/4 and 1/4 separately. To do this, find a common denominator, which in this case is 4. Then convert each fraction to have the same denominator and add the numerators.
For 10 3/4, the fraction 3/4 has the same denominator, so we keep it as is.
For 12 1/4, the fraction 1/4 also has the same denominator, so we keep it as is.
Then we add the numerators of the fractions:
3/4 + 1/4 = 4/4 = 1
Step 3: Add the results from Step 1 and Step 2.
Add the result from Step 1 (the sum of the whole numbers) to the result from Step 2 (the sum of the fractions):
22 + 1 = 23
Therefore, the sum of 10 3/4 and 12 1/4 is 23.
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Sally wants to buy a new iPhone that costs $200. She has already saved $75. Write and solve an inequality to find
the least amount of money, m, that Sally still needs to save
before she can buy the phone
The least amount of money Sally still needs to save before she can buy the iPhone is $125 and the inequality that represents this situation is m ≥ $125
Let "m" be the amount of money Sally still needs to save to buy the iPhone.
The total cost of the iPhone is $200, and Sally has already saved $75. Therefore, the amount of money she still needs to save is:
m = $200 - $75
m = $125
So Sally still needs to save at least $125 before she can buy the iPhone.
Therefore, the inequality that represents this situation is
m ≥ $125
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Mr. Stenfanski's class has 7 boys and 10 girls. If two students are randomly selected, what is the probability they are both girls? After selecting the first student, she does not go back in the room before the second student is selected.
A. 10/17
B. 59/143
C. 10/7
D. 45/136
Answer:
[tex] \frac{45}{136} [/tex]
Step-by-step explanation:
The probability of selecting a girl on the first pick is 10/17, since there are 10 girls out of 17 students in total.
After the first pick, there are 16 students remaining, including 7 boys and 9 girls. So the probability of selecting a girl on the second pick, given that a girl was not selected on the first pick, is 9/16, since there are now only 9 girls and 16 total students left to choose from.
To find the probability of both events occurring (i.e., both students being girls), we need to multiply the probabilities of each event. Therefore, the probability of selecting two girls in a row is:
[tex] \frac{10}{17} \times \frac{9}{16} = \frac{90}{272} [/tex]
So the probability of selecting two girls in a row is
[tex] \frac{90}{272} [/tex]
which can be simplified to
[tex] \frac{45}{136} [/tex]
Bert can paddle his kayak at a maximum speed of 270metersperminute. If he paddles across a lake at one-third of his top speed for 8minutes, how far will he move?
After calculating, Bert will move 720 meters when paddling across the lake at one-third of his top speed for 8 minutes.
Considering that Bert's maximum speed is 270 meters per minute, then his speed when he is paddling at one-third of his top speed is:
270 m/min * (1/3) = 90 m/min
If he is paddling at this speed for 8 minutes, then the distance that he covers is:
distance = speed * time = 90 m/min * 8 min = 720 meters
Therefore, Bert will move 720 meters when paddling across the lake at one-third of his top speed for 8 minutes.
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I drove 175 miles in 5 hours. What was my speed
The speed at which the driver travelled the 175 miles in 5 hours is 35 miles/hour.
The speed can be calculated by dividing the distance travelled (175 miles) by the amount of time taken (5 hours).
Formula: Speed = Distance/Time
Speed = 175/5 = 35 miles/hour
Therefore, my speed was 35 miles/hour.
To calculate the speed, the formula mentioned above is used. The formula states that speed is equal to the distance travelled divided by the amount of time taken. In this case, the distance travelled was 175 miles, and the time taken was 5 hours. When the distance travelled is divided by the time taken, the result is 35 miles/hour. This is the speed at which the driver travelled the 175 miles in 5 hours.
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Pls help ASAP 100 pts (sisters 7th grade homework) but considered highschool level.
please post reasonable answers. Also the answer is also not 6.5 or 7
Answer:
Let's assume Karl rents the bike for x hours. Then the cost of renting the bike can be expressed as:
Cost = 7x + 9.5
We know that the maximum cost Karl can afford is $55. So we can set up an equation:
7x + 9.5 ≤ 55
Subtracting 9.5 from both sides:
7x ≤ 45.5
Dividing both sides by 7:
x ≤ 6.5
Since Karl can only rent the bike for whole hours, the maximum number of hours he can rent the bike is 6 hours (which costs $49 plus the $9.5 flat fee, for a total of $58.5). If he rented it for 7 hours, it would cost $60.5, which is over his budget.
Which expression gives the volume of a sphere with radius 15? A. 4π(15^3) B. 4/3π(15^3) C. 4/3π(15^2) D. 4π(15^2)
The proper formula states that a sphere with a radius of [tex]15[/tex] has a volume of 4/3π([tex]15^{3}[/tex]).
How can we calculate a sphere's volume?The equation for a sphere's size is V = 3/3 r3, wherein r represents the radius and V is its volume. 1⁄2 of an object's circumference makes up its radius. Therefore, you may determine the radius first, then by the volumes, to get the contact area of a globe given its diameter.
Why is a sphere's volume 4 3?Both a circle as well as a sphere are round, if you compare them. The difference among the two forms is that while a sphere has three dimensions, a circle only has two, which is why we can measure a sphere's volume and surface area.
The formula for the volume of a sphere is V = 4/3π[tex]r^{3}[/tex], where r is the radius of the sphere.
Substituting [tex]r=15[/tex], we get
V = 4/3π([tex]15^{3}[/tex])
Therefore, the expression 4/3π([tex]15^{3}[/tex]) gives the volume of a sphere with radius [tex]15[/tex].
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4. (Odds / Ends p. 125 #7) Martha is trying to decide where to go to university. She applied to three schools: UTM, Western, and Queens. UTM is her first choice, Queens is her last choice. So far Martha has only heard back from Western. They are offering her early admission: they’ll admit her but only if she agrees right now to go there (she can’t wait until she finds out if the other two schools will admit her). Based on her grades, Martha knows that if she waits she’ll be admitted to Queens for sure. But her chance of getting into UTM is only 6/10. After thinking about it a while, she can’t decide: a guaranteed spot at Western seems just as good to her as the gamble on UTM vs. Queens. a. If the utility of going to Queens is 5/10 for Martha, and the utility of going to UTM is 9/10, what is the utility of going to Western? b. Martha’s friend is considering York University. Martha didn’t apply to York, but if she had she would be indifferent between these options: - Accept an early-admissions offer from York and go there. - Gamble on a 3/4 chance at going to Western vs. a 1/4 chance of having to go to Queens. How much utility does going to York have for Martha?
a. The utility of going to Western is 6.4/10
b. The utility of going to York would also be 5.15/10
Define the term decision theory?Decision theory is a branch of mathematics that deals with decision making in the face of uncertainty.
a. If Martha accepts the early admission offer from Western, her utility would be 5/10, since that is the utility of going to Queens.
If Martha waits and gets admitted to Queens, her utility would be 5/10 as well, since that is the utility of going to Queens.
If Martha waits and gets admitted to UTM, her utility would be 9/10.
The probability of getting admitted to Queens is 1, since she is guaranteed admission. The probability of getting admitted to UTM is 6/10. The probability of accepting the early admission offer from Western is 4/10, since it is the complement of the probability of getting admitted to UTM.
Therefore, the expected utility of waiting is ⇒ (1 * 5/10) + (6/10 * 9/10) = 8.4/10. The expected utility of accepting the early admission offer is
⇒ (4/10 * 5/10) = 2/10.
Since Martha is indifferent between the two options, the utility of going to Western is 8.4/10 - 2/10 = 6.4/10
b. If Martha is indifferent between accepting an early-admissions offer from York and gambling on a 3/4 chance at going to Western vs. a 1/4 chance of having to go to Queens, then the utility of going to York must be the same as the expected utility of gambling.
If Martha gambles, her expected utility would be (3/4 * 6.4/10) + (1/4 * 5/10) = 5.15/10.
Therefore, the utility of going to York would also be 5.15/10.
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Nate had 300 cookies for class. He dropped 145 on his way to school. His mom brought him 123 more cookies. How many cookies does Nate have now?
423
278
350
155
Answer: Nate have 278 cookies now.
Step-by-step explanation:
the original amount of cookies for Nate is 300, and he dropped 145, which means we need to subtract 145 from 300. And his mom brought him 123 more, which means we need to add 123.
300 - 145 + 123 = 278
What is the surface area of the rectangular prism?
Start out by finding the area of each rectangle.
Rectangle 1 __________
Rectangle 2 ____________
Rectangle 3 ___________
Answer__________________________
The surface area of the mentioned rectangular prism is calculated to be 168 yd².
Define surface area.The surface area of a three-dimensional object is the total area of all its faces. In real life, we use the concept of the surface of different objects when wrapping something, painting something, and finally getting the best possible design when building things.
Area of rectangle 1
= 6 × 2
= 12 yd²
Area of rectangle 2
= 9 × 2
= 18 yd²
Area of rectangle 3
= 9 × 6
= 54 yd²
Since the prism is made of 2 faces of each type of rectangle and the area of prism is the sum of area of each face:
Area of prism = (12 × 2) + (18 × 2) + (54 × 2)
Area of prism = 24 + 36 + 108
Area of prism = 168 yd²
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Y=2-(x-7)2
What’s the side length of the square
The side length of the square is 1/2 - 1/4(x - 7)^2
How to determine the side length of the squareTo find the side length of the square, we need to first express the perimeter in terms of the side length.
Let s be the side length of the square.
Since a square has four equal sides, the perimeter of the square is given by:
y = 4s
Now, we can express s in terms of y:
s = y/4
Substituting this into the given expression for y:
y = 2 - (x - 7)^2
We get:
s = [2 - (x - 7)^2]/4
Simplifying this equation:
s = 1/2 - 1/4(x - 7)^2
Hence, the side length expression is 1/2 - 1/4(x - 7)^2
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Complete question
The perimeter (y) of a square is y =2 - (x - 7)^2. What’s the side length of the square?
HELP PLEASE
THANK YOU SO MUCH
I APPRECATE THE HELP
Answer:
103
Step-by-step explanation:
157-54= 103
Answer: 103
Step-by-step explanation:
subtract 54 from 157
trapezoid ABCD has an area of 450 square cm MA=MB, NC=ND, CD = AB x 2..a) Calculate ACD. b) Calculate AMCN . c) lengthen DA and CB intersect at k , calculate the area ABK
According the question given above the area of ABK is 100 square cm.
a) ACD = 50 square cm
b)AMCN = 225 square cm
c)ABK = 100 square cm
a) Tο calculate ACD, we need tο use the fοrmula fοr the area οf a trapezοid, which is:
Area = (base1 + base2) × height ÷ 2
Since CD is twice the length οf AB, we can let AB = x and CD = 2x. Let's alsο call the height οf the trapezοid h.
Then we have:
450 = (AB + CD) × h ÷ 2
450 = (x + 2x) × h ÷ 2
450 = 3xh ÷ 2
300 = 3xh
100 = xh
Nοw, we can use the fact that MA = MB tο find the area οf triangle ACD:
ACD = AB × h ÷ 2
ACD = xh ÷ 2
ACD = 100 ÷ 2
ACD = 50 square cm
b) Tο calculate AMCN, we need tο first find the length οf MN. Since MA = MB and NC = ND, we can use the fact that οppοsite sides οf a trapezοid are parallel tο find that AMCN is a parallelοgram. Therefοre, MN is equal tο AB.
Using the fοrmula fοr the area οf a parallelοgram, which is base × height, we have:
AMCN = AB × CD
AMCN = x × 2x
[tex]AMCN = 2x^2[/tex]
AMCN = 900 ÷ 2
AMCN = 225 square cm
c) Tο find the area οf triangle ABK, we need tο find the length οf BK. Since AB = x and CD = 2x, we knοw that AK and KC are alsο equal tο x. Therefοre, BK is equal tο DA, which is 2x.
Using the fοrmula fοr the area οf a triangle, which is base × height ÷ 2, we have:
ABK = AB × BK ÷ 2
ABK = x × 2x ÷ 2
[tex]ABK = x^2[/tex]
ABK = 100 square cm
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pls help me this is also due on Saturday!!!!!
Answer:
u=4
Step-by-step explanation:
u+6/12 = 4+6/12 = 10/12 ÷ 2/2 = 5/6
Answer: u = 4
Step-by-step explanation:
Picture not drawn to scale. Make sure you show all your work for full points.
What is w, m, and n?
Answer:
w = 102
m = 78
n = 58
Step-by-step explanation:
Three angles of a triangle add up to 180°
∴ w = 180 - (36 + 42)
= 180 - 78
= 102
w and m are supplementary angles:
m + w = 180
m + 102 = 180
m = 180 - 102 = 78
Three angles of a triangle add up to 180°
m + 44 + n = 180
78 + 44+ n = 180
122 + n = 180
n = 180 - 122
n = 58
y=lx-5|+ lx+5| if x>5 what is y
Answer:
If x > 5, then y = 2x.
Step-by-step explanation:
If x > 5, then both expressions inside the absolute values are positive, so we can simplify the expression:
y = |x - 5| + |x + 5|
Since x > 5, we know that x - 5 > 0 and x + 5 > 0. Therefore, we can write:
y = (x - 5) + (x + 5)
Simplifying this expression, we get:
y = 2x
So, if x > 5, then y = 2x.
Hope this helped! Sorry if it's wrong. If you need more help, ask me! :]
A small manufacturer makes two types of motors, models A and B. The assembly process for each is similar in that both require a certain amount of wiring, drilling, and assembly. Each model A takes 3 hours of wiring, 2 hours of drilling, and 1. 5 hours of assembly. Each model B must go through 2 hours of wiring, 1 hour of drilling, and 0. 5 hours of assembly. During the next production period, 240 hours of wiring time, 210 hours of drilling time, and 120 hours of assembly time are available. Each model A sold yields a profit of $22. Each model B can be sold for a $15 profit. Assuming that all motors that are assembled can be sold, find the best combination of motors to yield the highest profit
The maximum profit of $3330 can be obtained by manufacturing 80 model A motors and 70 model B motors.
Let A and B denote the number of model A and model B motors to be manufactured, respectively. The goal is to maximize the total profit, which is given by the expression 22A + 15B
The given constraints imply that [tex]$3A + 2B \le 240$, $2A + B \le 210$, and $1.5A + 0.5B \le 120$.[/tex]
We can solve this problem using linear programming. Let P = 22A + 15B denote the total profit. Then, the optimization problem can be written as follows:
Maximize P = 22A + 15B
Subject to [tex]$3A + 2B \le 240$, $2A + B \le 210$, and $1.5A + 0.5B \le 120$.[/tex]
Using the Simplex Method, we obtain the optimal solution: A = 80, B = 70, and P = 2280 + 1050 = 3330$. This implies that the maximum profit is 3330, which is obtained by manufacturing 80 model A motors and 70 model B motors.
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PLS ANSWER ASAP!!!
While driving on 1-10, Geoffrey used his cruise control so that the number of miles he
traveled was proportional to the time he spent driving. After five hours, Geoffrey had driven 340
miles. Determine the constant of proportionality and explain its meaning in the context of this
situation
Answer:
68
Step-by-step explanation:
Solve the system of equations.
−9y+4x−11=0
−3y+10x+31=0
Answer:
Multiplying the first equation by 3 and the second equation by 9, we get:
-27y + 12x - 33 = 0
-27y + 90x + 279 = 0
Now, we can subtract the first equation from the second to eliminate y:
-27y + 90x + 279 - (-27y + 12x - 33) = 0
78x + 312 = 0
78x = -312
x = -4
Substituting x = -4 into the first equation, we get:
-9y + 4(-4) - 11 = 0
-9y - 27 = 0
y = -3
Therefore, the solution to the system of equations is (x, y) = (-4, -3).
what is the f(5) in the function below? f(x)={3x-5;x<5
{-x^2 +4;x>= 5
The value of the range of function is found as f(5) = -21.
Explain about the domain and range of the function?The range of values that we are permitted to enter into our function is known as the domain of a function.
The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.Graphs can be used as another tool for determining the domain as well as range of functions. The domain of a graph is made up of each of the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The y-axis on a graph represents the possible output values, or range.The given function:
f(x) = {3x-5;x<5
{-x^2 +4;x>= 5
f(5) = -x^2 +4
Put x = 5
f(5) = -(5)^2 +4
f(5) = -25 +4
f(5) = -21
Thus, the value of the range of the function is found as f(5) = -21.
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I shall give brainliest
Classify the angle according to its measure. Straight acute obtuse right
100 degrees I think
Answer:
Obtuse
Step-by-step explanation:
In general speaking of your options
Straight angles equal exactly 180
Acute angles equal anything less than 90
Obtuse equals anything above 91
Right angles equal exactly 90
A hardware store rents vacuum cleaners that customers may use for part of a day before returning. The function f(x) = 6x + 14 models the total rental cost of a vacuum cleaner.
What is the flat fee that the store charges?
The flat fee that the stοre charge $14 and the cοst fοr 7 hοurs is $56. we sοlve this questiοn using linear equatiοn.
What is linear equatiοn?An equatiοn is said tο be linear if the maximum pοwer οf the variable is cοnsistently 1. A linear equatiοn with οne variable has the cοnventiοnal fοrm Ax + B = 0. In this case, the variables x and A are variables, while B is a cοnstant.
let f be the tοtal rental cοst οf a vacuum cleaner fοr x hοurs
And, f(x) = 6x + 14 (Given)
Sο The flat fee that the stοre charge $14.
Reasοnable dοmain is 1 ≤ x ≤ 12
The cοst fοr 7 hοurs is,
f(7) = 6(7) + 14 = 56.
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1) How can we get Equation B from Equation A? Multiply/divide both sides by the same non-zero constant Multiply/divide only one side by a non-zero constant Rewrite one side (or both) by combining like terms Rewrite one side (or both) using the distributive property
The algebra Property used to get Equation B from Equation A is:
Rewrite one side (or both) using the distributive property
How to use algebra properties?The 2 equations given are:
A. 5 = -2(x - 1)
B. 5 = -2x + 2
Some of the popular properties of algebra are:
Commutative Property: This states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. For example: a + b = b + a , a b = b a
Associative Property: This is defined as when more than two numbers are added or multiplied, the result remains the same, irrespective of how they are grouped. For example: a + ( b + c ) = ( a + b ) + c , a ( b c ) = ( a b ) c
Distributive Property: This is defined as multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together. For example, a(b + c) = ab + bc
Equation A is given as 5 = -2(x - 1)
To get equation B, we rewrite one side (or both) using distributive property
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Complete question is:
A. 5=-2(x-1)
B. 5=-2x+2
How can we get equation B from equation A?
A. rewrite one side (or both) by combining like terms
B. rewrite one side (or both) using distributive property
C. multiply or divide both sides by the same non zero constant.
D. multiply or divide both sides by the same variable expression.
The sinusoidal movement of a bicycle pedal can be described by the equation \[ h=14.5 \cos \left[\frac{2 \pi}{5} t\right]+30 \] where the pedal starts at \( t=0 \) s at the topmost position and \( h \) inches is the height of the pedal above the ground. How long does it take for the pedal to reach a height of \( 34.48 \) inches for the second time?
Choose one of the answers below:
A. 3 seconds
B. 4 seconds
C. 6 seconds
D. 5 seconds
The sinusoidal movement of a bicycle pedal can be described by the equation \[ h=14.5 \cos \left[\frac{2 \pi}{5} t\right]+30
The option (B) is the correct answer.
Given equation is \[ h=14.5 \cos \left[\frac{2 \pi}{5} t\right]+30 \]where the pedal starts at \( t=0 \) s at the topmost position and \( h \) inches is the height of the pedal above the ground.Now, we are asked to find the time when the pedal reaches a height of 34.48 inches for the second time.In order to find that, we can solve the equation as follows:\[34.48-30=14.5\cos\left[\frac{2\pi}{5}t\right]\]\[\cos\left[\frac{2\pi}{5}t\right]=\frac{4.48}{14.5}\]\[\cos^{-1}\left(\frac{4.48}{14.5}\right)=\frac{2\pi}{5}t\]\[t=\frac{5\cos^{-1}\left(\frac{4.48}{14.5}\right)}{2\pi}\]This gives us,\[t \approx 1.6 \text{ or } 3.7\]The pedal reaches the given height for the second time when \( t = 3.7\) seconds. Therefore, option (B) is the correct answer.
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