A function is denoted as y = f (x), where x is the argument or input of the function. This means that from f(6) follows that x= 6, and to get the answer we should replace x with 6.
f(6)=6^2÷ 3 + 6= 36÷ 3 + 6= 12+6= 18
f(6)=18
Answer:
The value of f(6) is, 18
Step-by-step explanation:
Given the function:
[tex]f(x) = x^2 \div 3+ x[/tex] .....[1]
We have to find the value of [tex]f(6)[/tex].
Put x = 6 in [1] we have;
[tex]f(6) = 6^2 \div 3+ 6[/tex]
⇒[tex]f(6) = 36 \div 3 +6[/tex]
⇒[tex]f(6) = \frac{36}{3}+6[/tex]
Simplify:
[tex]f(6) = 12 +6 = 18[/tex]
Therefore, the value of f(6) is, 18
Oscar Montez’s savings account has a principal of $7,201. It earns 6% interest compounded quarterly. What is the amount of interest he earned by the end of the second quarter?
Which of the following is a result of shifting a circle with equation (x + 3)² + (y - 2)² = 36 left 3 units?
Answer:
The answer is [The x-coordinate of the center of the circle decreases by 3.]
Step-by-step explanation:
21/80 in a simplified fraction
What times what equals 80.73
Find the missing length. The triangle in each pair are similar.
Answer:
39 UNIT
Step-by-step explanation:
According to similar triangle.
Let's call NG "X"
45/27 = 65/x
X=( 65*27)/45
X= 1755/45
X = 39
Solve for x. Enter your answer in interval notation using grouping symbols.
x^2+4x<45 ...?
If a satellite launch has a 97% chance of success, what is the probability of three consecutive successful
launches? ...?
Answer: The required probability of three consecutive successful launches is 91.27%.
Step-by-step explanation: Given that a satellite launch has a 97% chance of success.
We are to find the probability of three consecutive successful launches.
Let P(A) denotes the probability of the event of the success of the satellite launch.
Then, according to the given information, we have
[tex]P(A)=97\%=\dfrac{97}{100}=0.97.[/tex]
Therefore, the probability of three consecutive successful launches will be
[tex]p\\\\=P(A)\times P(A)\times P(A)\\\\=0.97\times0.97\times0.97\\\\=0.912673\\\\=0.912673\times100\%\\\\=91.2673\%\\\\=91.27\%.[/tex]
Thus, the required probability of three consecutive successful launches is 91.27%.
During World War I, the Germans had a gun
called Big Bertha that was used to shell Paris.
The shell had an initial speed of 2.41 km/s at
an initial inclination of 61.5 to the horizontal.
The acceleration of gravity is 9.8 m/s2 .
How far away did the shell hit?
Answer in units of km
How long was it in the air?
Answer in units of s
To find the distance the shell hit and the time it was in the air, we need to determine the total time it takes for the shell to hit the ground. The horizontal component of the shell's initial velocity remains constant, while the vertical component is affected by gravity. By solving for the time using the vertical component, we can then multiply it by the horizontal component to find the distance and convert it to kilometers.
Explanation:To find the distance that the shell hit, we need to determine the time it was in the air. We can do this by finding the total time it takes for the shell to hit the ground. The shell's initial velocity is given as 2.41 km/s at an angle of 61.5 degrees. We can break down the initial velocity into its horizontal and vertical components. The horizontal component remains constant, while the vertical component is affected by gravity. Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can solve for the time it takes for the shell to reach the ground.
Find the horizontal component of the initial velocity using the equation horz_vel = init_vel * cos(angle).Find the vertical component of the initial velocity using the equation vert_vel = init_vel * sin(angle).Using the vertical component, solve for the time it takes for the shell to reach the ground using the equation -vert_vel = 0 + 0 * t - 0.5 * acceleration * t^2.The time calculated in step 3 will give us the total time the shell was in the air.Multiply the total time by the horizontal component of the initial velocity to get the distance that the shell hit.Convert the distance from meters to kilometers by dividing by 1000.So, the shell hit a distance of [distance] km away and was in the air for [time] s.
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Which of the following is not a way to prove a quadrilateral is a parallelogram?
The way to not prove a quadrilateral is a parallelogram is; Show one set of opposite sides of the quadrilateral is congruent.
Parallelogram and CongruenceA parallelogram is a quadrilateral which has opposite sides to be congruent and parallel as the name implies and hence, opposite angles of the parallelogram are congruent.
However, showing one set of opposite sides of the quadrilateral is congruent is not a confirmatory test for a parallelogram, as it evades the parallel law of opposite sides of the Parallelogram.
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Simplify (8j3 + 5j2 – 3) – (5j3 + 7j2 – 12j + 7) ...?
Answer:
3j^3 - 2j^2 + 12j - 10
Step-by-step explanation:
I took the test and got a 100%
solve for X. y=1/4 (x)+3
A truck carried 3 1/3 ton of sand, but lost 1/4 ton of sand along the way. how many tons of sand were survived
Kurt johnson delivers packages for a delivery company. he receives $7.50 for every package delivered. what does kurt earn in a week if he delivers 48 packages? 360.00 405.00 555.00 640.00
Answer:
He earned $ 360.00.
Step-by-step explanation:
Given,
The amount he gets for a package of delivery = $ 7.50
The number of packages he delivered in a week = 48,
Hence, the amount he earned in the week = The amount he gets for a package of delivery × The number of packages he delivered
= 7.50 × 48
= $ 360.00
A furniture company misprinted a sales ad for a living room set but honors the advertised price. For each customer who purchases the living room set, the company suffers a loss of $125. Write a function to represent the company's total loss. What is the value of the function for an input of 50, and what does it represent? ...?
What is the best approximation of the sine of 50°?
A. 0.2624
B. 0.6428
C. 0.7660
D. 1.1918
Mr. Shaw graphs the function f(x) = –5x + 2 for his class. The line contains the point (-2, 12). What is the point-slope form of the equation of the line he graphed?
a.) y – 12 = –5(x + 2)
b.) y – 12 = 2(x + 2)
c.) y + 12 = 2(x – 2)
d.) y + 12 = –5(x – 2)
Miss fernandez built two rectangular gardens the length of garden a is 2 feet longer than twice its width the list of garden b is 1 foot less than the width of garden a the length of garden b is 2.5 times its width the two gardens have the same perimeter what are the dimensions of the gardens
Which of the following statements is true?
A.A radius is always a chord.
B.A tangent is always a secant.
C.A diameter is always a chord.
D.A chord is always a diameter.
Please help
A vehicle travels on a highway at a rate of 65 mi/h how long does it take the vehical to travel 25 mi?
Answer:
Step-by-step explanation:
A vehicle travels at a rate of 65 m/h, How long does it take the vehicle to travel at 25 miles?
Apply the "distance formula":
d = rt
25 = 65t
25/65 = t
5/13 hour = t
or
0.385 hour = t
or
23.08 minutes = t
Wendy wants $15,000 saved in 6 years to make a down payment on a house. How much money should she invest now at 4.65% compounded annually in order to meet her goal?
PLEASE HELP!!
Oscar entered y=−0.4^x+3y=−0.4^x+3 into an online graphing tool.
What function did he graph?
y=(−0.4)x+3y=(−0.4)x+3
y=(−0.4)x+3y=(−0.4)x+3
y=−(0.4)x+3y=−(0.4)x+3
y=−(0.4)x+3
A surveyor, standing 100 ft. from the base of a building, measures the angle of elevation to the top of the building to be 75 degrees. How accurately must the angle be measured for the percentage error in estimating the height of the building to be less than 4%?
Wally bakes muffins. in each batch of 12 muffins, he bakes 8 bluberry muffins write in simplest form the fraction of muffins that are not blue berry
Answer:
probably 4/12 = 1/3 muffins are not blueberry
Step-by-step explanation:
An Antique vase is projected to be worth $1000 in 2 years and $1,300 after 5 years. If the value continues to appreciate at the same rate, what will it be worth in 8 years?
The value of the antique vase after 8 years with a consistent appreciation rate, it would amount to $1,600.
An antique vase:
Value after 2 years: $1,000
Value after 5 years: $1,300
To find the value after 8 years, we can assume a constant rate of appreciation:
In 8 years, the value will be: $1,000 + ($1,300 - $1,000) = $1,300 + ($1,300 - $1,000) = $1,600
What is the solution to the equation?
5(8 + 7) = 5 • x + 5 • 7
A.
x = 1
B.
x = 5
C.
x = 7
D.
x = 8
In the image, two circles are centered at A. The circle containing B was dilated to produce the circle containing B′. What is the scale factor of the dilation?
1
2
0.5
-0.5
Answer:
The diameter of B is from -2 to 2, which = 4 units.
The diameter of B' is from -1 to 1, which equals 2 units.
2/4 = 1/2 = 0.5 scale factor.
The answer is C. 0.5
Step-by-step explanation:
What is d if p equals 15 in d=-3p^2+168p-315
is 87 a prime or composite
Answer:
Prime
Step-by-step explanation:
77 is composite
It has other factors besides 1 and itself
68 -composite
52-composite (it is even)
31 -prime
59-prime
The mean number of hours that Raphael worked over the past four weeks is 37.75. If he works 40 hours this week, what will the mean number of hours be that he will have worked over the five-week period?
What is the five-week mean?
A candy manufacturer makes two types of special candy, say A and B. Candy A consists of equal parts of dark chocolate and caramel and Candy B consists of two parts of dark chocolate and one part of walnut. The company has in stock 430 kilograms of caramel, 360 kilograms of dark chocolate, and 210 kilograms of walnuts. The company sells Candy A for P285 and Candy B for P260 per kilograms. How much of each candy should the manufacturer produce to maximize profit?
To maximize profit, the candy manufacturer should use mathematical linear programming. The decision variables are the amounts of Candy A (x) and Candy B (y). The profit function P = 285x + 260y is to be maximized subject to constraints arising from available stock of dark chocolate, caramel, and walnuts, leading to a typical linear programming problem.
Explanation:To solve this problem, we need to use Linear Programming, a mathematical model that helps in making optimal decisions. The candies are what we call decision variables. Our decision variables here are Candy A and Candy B.
Candy A: x kilograms (dark chocolate and caramel in equal parts).
Candy B: y kilograms (two parts of dark chocolate and one part of walnut).
We want to maximize the profit function P = 285x + 260y subject to constraints arising from the available stock of dark chocolate (DC), caramel (C), and walnuts (W).
DC constraint: A uses DC in equal parts, and B uses two parts DC. Therefore, x + 2y ≤ 360.C constraint: A uses equal parts C, x ≤ 430 (as B doesn't use C).W constraint: B uses one part W, y ≤ 210 (as A doesn't use W).
The next step is to solve these inequalities graphically or using mathematical methods to get values of x and y that maximize P while respecting constraints. This case, where we want to optimize a certain function with respect to constraints, is a typical linear programming problem in mathematics.
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