The total sales of a company (in millions of dollars) t months from now are given by S(t)=0.05t +0,51+6t+7 (A) Find S'(t). (B) Find S(5) and S (5) (to two decimal places) (C) Interpret S(8)=112.60 and S'(8) = 23.60. The price p (in dollars) and the demand x for a particular clock radio are related by the equation x = 2000 - 40p (A) Express the price p in terms of the demand x, and find the domain of this function. (B) Find the revenue R(x) from the sale of x clock radios. What is the domain of R? (C) Find the marginal revenue at a production level of 1500 clock radios. (D) Interpret R' (1900) = - 45.00.
Answers
To interpret \(\(R'(1900)\) = -45.00, it means that at a production level of 1900 clock radios, the marginal revenue is decreasing at a rate of $45.00 per unit.
To find \(\(S'(t)\)\), we take the derivative of the function \(\(S'(t)\)\):
\(\[S(t) = 0.05t + 0.51 + 6t + 7\]\[S'(t) = \frac{d}{dt}(0.05t + 0.51 + 6t + 7)\]\[S'(t) = 0.05 + 6\]\)
Therefore, \(\(S'(t) = 6.05\).\)
To find S(5) and \(\(S'(5)\),\) we substitute t = 5 into the function s(t) and \(\(S'(t)\):\)
\(\[S(5) = 0.05(5) + 0.51 + 6(5) + 7\] \[S(5) = 0.25 + 0.51 + 30 + 7\] \[S(5) = 37.76\]\)
Therefore, S(5) = 37.76 (rounded to two decimal places).
\(\(S'(5) = 6.05\)\)
To interpret S(8) = 112.60 and \(\(S'(8)\) = 23.60
(S(8) = 112.60) means that after 8 months, the total sales of the company are $112.60 million.
\(\(S'(8)\) = 23.60\) means that at the 8th month, the rate of change of the total sales is $23.60 million per month.
The equation relating the price (p) (in dollars) and the demand (x) for a particular clock radio is x = 2000 - 40P
To express the price (p) in terms of the demand (x), we rearrange the equation:
\(\[x = 2000 - 40p\] \[40p = 2000 - x\] \[p = \frac{2000 - x}{40}\]\)
The domain of this function is all values of \(x\) such that \(\(x \leq 2000\) and \(x \neq 2000\).\)
The revenue R(x) from the sale of (x) clock radios is given by:
\(\[R(x) = x \cdot p\]\[R(x) = x \cdot \left(\frac{2000 - x}{40}\right)\]\)
The domain of R(x) is the same as the domain of (p), which is all values of (x) such that \(\(x \leq 2000\) and \(x \neq 2000\).\)
To find the marginal revenue at a production level of 1500 clock radios, we take the derivative of the revenue function R(x) with respect to (x):
\(\[R(x) = x \cdot \left(\frac{2000 - x}{40}\right)\]\[R'(x) = \frac{d}{dx}\left(x \cdot \left(\frac{2000 - x}{40}\right)\right)\]\)
Simplifying and applying the product rule, we find:
\(\[R'(x) = \frac{-x}{20} + \frac{2000 - x}{40}\]\)
Therefore, the marginal revenue at a production level of 1500 clock radios is given by \(\(R'(1500)\).\)
To interpret \(\(R'(1900)\) = -45.00, it means that at a production level of 1900 clock radios, the marginal revenue is decreasing at a rate of $45.00 per unit.
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Related Questions
Write -a^3b^6 and -27x^6b^9 as cubes of a monomial.
-a^3b^6=( )
^3 -27x^6b^9=( )^3
Answers
Answer:
I'm sorry I don't know the first one but the second one is (-3x^2b^3)^3
Step-by-step explanation:
what is the first term, common difference, and 16th term
Answers
Answer:
The 1st term is -67
Step-by-step explanation:
I. When Sn = \(\frac{n}{2}\)(\(a_{1} + a_{n}\))
If Sn = 124, n = 8 and \(a_{n}\) = 98
124 = 8/2(a + 98)
124 = 4(a + 98)
124 = 4a + 392
124 - 392 = 4a
-268/4 = a
-67 = \(a_{1}\)
Hope that help :D
Let the variable X follow Normal distribution with mean μ and standard deviation σ. Determine whether following statement is True or False.
(a) The density curve of X is symmetric about 0.
(b) If we define a variable Z as (X − μ)/σ, then Z has the standard normal distribution.
(c) The standard deviation of Z = (X − μ)/σ is 0.
(d) P(X ≥ μ) = 0.5.
Answers
a. the density curve of X is symmetric about 0 based on the given statement alone. b. This is a result of standardizing X by subtracting the mean μ and dividing by the standard deviation σ. c. The expression (X - μ)/σ scales and shifts the distribution of X to have mean 0 and standard deviation 1, resulting in Z. d. The value of this probability depends on the distribution's parameters and the characteristics of the normal distribution.
(a) The statement is False. The density curve of X being symmetric about 0 implies that the mean of X is 0. However, the statement does not provide any information about the mean μ of X, so we cannot conclude that the density curve of X is symmetric about 0 based on the given statement alone.
(b) The statement is True. If we define a variable Z as (X - μ)/σ, where X follows a normal distribution with mean μ and standard deviation σ, then Z follows the standard normal distribution (a normal distribution with mean 0 and standard deviation 1). This is a result of standardizing X by subtracting the mean μ and dividing by the standard deviation σ.
(c) The statement is False. The standard deviation of Z = (X - μ)/σ is not 0. The standard deviation of Z is always 1, as it follows the standard normal distribution. The expression (X - μ)/σ scales and shifts the distribution of X to have mean 0 and standard deviation 1, resulting in Z.
(d) The statement is False. The probability that X is greater than or equal to μ depends on the specific parameters of the normal distribution, such as the mean μ and the standard deviation σ. Without additional information about these parameters, we cannot conclude that P(X ≥ μ) is equal to 0.5. The value of this probability depends on the distribution's parameters and the characteristics of the normal distribution.
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calculate the cost of manufacturing a standard cereal box if cardboard costs 0.05 per square inch312 volume286 surface area
Answers
Given:
The cardboard costs 0.05 per square inch
And the surface area = 286
So, the total cost is the product of the surface area and the cost per square in.
Total cost =
\(286*0.05=14.3\)So, the answer will be Total cost = $14.30
Please Help! I have no idea what this is! Also, do NOT put the answer in a link, as I cannot access it. Just give me the plain answer.
Answers
Answer:
\(1.962*10^{8}\)
Step-by-step explanation:
When given the area and one side length, we can find the other side length by dividing.
So, \(\frac{5.612*10^{14}}{9.2*10^{7}}\)= \(6.1*10^{6}\)
The perimeter would be \(6.1*10^{6}\)+\(6.1*10^{6}\)+\({9.2*10^{7}}\)+\({9.2*10^{7}}\) = \(1.962*10^{8}\)
Hope this is correct and helps!
Find the domains of definition and derivatives of the following analytic functions. (a) (2 pts) + sin(22 – 9). e 22 (b) (2 pts) log(-22). (c) (2 pts) 23-2i (d) (3 pts) (3 – 2i). (e) (3 pts) tan(2iz – 1).
Answers
Applying the chain rule, the derivative of f(z) is:
f'(z) = sec^2(2iz - 1) * 2i
(a) The domain of definition of the function f(x) = (2 + sin(22 - 9)) * e^22 is all real numbers since both sine and exponential functions are defined for any real value of their arguments. Therefore, the domain of definition for this function is (-∞, +∞).
To find the derivative of this function, we can use the chain rule. Let's denote the inner function as g(x) = 22 - 9. The derivative of the outer function is e^22. The derivative of the inner function is dg/dx = 0 since it is a constant. Therefore, applying the chain rule, the derivative of f(x) is:
f'(x) = (2 + sin(22 - 9)) * e^22 * 0 + cos(22 - 9) * e^22 * (-1)
Simplifying this expression, we get:
f'(x) = -cos(22 - 9) * e^22
(b) The logarithm function, log(-22), is undefined for negative numbers and zero. Therefore, the domain of definition for this function is (-∞, 0) U (0, +∞). Since the function is not defined for negative numbers, its derivative is also undefined.
(c) The function f(z) = 23 - 2i is defined for all complex numbers z. Therefore, the domain of definition for this function is the set of all complex numbers.
To find the derivative of this function, we treat z as a complex variable. Since the function is constant, the derivative of f(z) is 0.
(d) The function f(z) = 3 - 2i is defined for all complex numbers z. Therefore, the domain of definition for this function is the set of all complex numbers.
To find the derivative of this function, we treat z as a complex variable. Since the function is constant, the derivative of f(z) is 0.
(e) The function f(z) = tan(2iz - 1) is defined for complex numbers z except for the values of z where the tangent function is undefined. The tangent function is undefined at odd multiples of π/2. Therefore, the domain of definition for this function is the set of complex numbers excluding values where 2iz - 1 = (2n + 1)(π/2) for n ∈ Z.
To find the derivative of this function, we can use the chain rule. Let's denote the inner function as g(z) = 2iz - 1. The derivative of the outer function is sec^2(2iz - 1). The derivative of the inner function is dg/dz = 2i. Therefore, applying the chain rule, the derivative of f(z) is:
f'(z) = sec^2(2iz - 1) * 2i
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pls help i am speedrunning overdues rn
Answers
The amount of soil needed to fill the garden box is given as follows:
1728 ft³.
How to obtain the volume of a rectangular prism?The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:
Volume = length x width x height.
The figure in this problem is composed by two prisms, with dimensions given as follows:
19 ft, 12 ft and 6 ft.10 ft, 3 ft and 12 ft.Hence the volume is given as follows:
V = 19 x 12 x 6 + 10 x 3 x 12
V = 1728 ft³.
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a car uses 20l of a jorney of 180km.how many litres will it use for a journey of 108km
Answers
Allan can make 8 pizzas in 15 minutes at the pizza restaurant where he works. If the number of pizzas varies directly with minutes, how many pizzas can Allan make in 3 hours? Please Help
Answers
Answer:
96 pizzas
Step-by-step explanation:
Allan can make 8 pizzas in 15 minutes at the pizza restaurant where he works.
We are told that;
If the number of pizzas varies directly with minutes,
P ∝ M
P = kM
Hence:
8 = 15k
k = 8/15
How many pizzas can Allan make in 3 hours?
Convert 3 hours to minutes
1 hour = 60 minutes
3 hours = x
x = 3 × 60
x = 180 minutes
Hence,
M = 180 minutes
k = 8/15
P = kM
P = 8/15 × 180
P = 96 pizzas
Therefore, Allan can make 96 pizzas in 3 hours
Given the following demand data, Period Demand 1 44 2 42 3 44 4 42 5 47 a. Compute a weighted average forecast using a weight of 0.4 for the most recent period, 0.3 for the next most recent, 0.2 for t
Answers
To compute a weighted average forecast for the given demand data, we assign weights to each period based on their relative importance. The most recent period has a weight of 0.4, the next most recent period has a weight of 0.3, and the remaining periods have weights of 0.2 each. By multiplying each demand value with its corresponding weight and summing the results, we can calculate the weighted average forecast.
To compute the weighted average forecast, we multiply each demand value by its corresponding weight and sum the results. Given the demand data:
Period 1: Demand = 44
Period 2: Demand = 42
Period 3: Demand = 44
Period 4: Demand = 42
Period 5: Demand = 47
Using the provided weights, we assign the following weights to each period:
Period 1: Weight = 0.4
Period 2: Weight = 0.3
Period 3: Weight = 0.2
Period 4: Weight = 0.2
Period 5: Weight = 0.2
Now, we multiply each demand value by its corresponding weight:
Weighted Demand for Period 1: 44 * 0.4 = 17.6
Weighted Demand for Period 2: 42 * 0.3 = 12.6
Weighted Demand for Period 3: 44 * 0.2 = 8.8
Weighted Demand for Period 4: 42 * 0.2 = 8.4
Weighted Demand for Period 5: 47 * 0.2 = 9.4
Finally, we sum up the weighted demand values:
Weighted Average Forecast = 17.6 + 12.6 + 8.8 + 8.4 + 9.4 = 56.8
Therefore, the weighted average forecast for the given demand data is 56.8.
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What is the explicit formula for this sequence?
5, 2, -1, -4, ...
O A. an= -5+ (n - 1)(-3)
B. an = 5+ (n - 1)(3)
C. an= -3+ (n - 115
O D. a, = 5 + (n - 1)(-3)
Answers
Answer:
C. an= -3+ (n - 115)
Step-by-step explanation:
hope it help
Use decomposition to find the area of the figure. A drawing of a right-angled trapezoid with length of two parallel sides measuring 10 yards and 13 yards. The height of the trapezoid is 8 yards. The area is
square yards. Skip to navigation
Answers
In the given problem, we need to find the area of the trapezoid in which the height is 8 yards. The area of the given trapezoid is 92 square yards.
If the length of a trapezoid's parallel sides and the distance (height) between them are known, the area of the shape may be determined.
A = (a+b)h/2 is the formula for a trapezoid's surface area.
where "a" and "b" are the lengths of the base of the trapezoid and "h" represents the height of the figure.
We have been given the values,
The length of the bases is 10 and 13 yards and,
the height of the trapezoid is 8 yards.
So, according to the formula for determining the area,
Area of a trapezoid,
"A" = {(10 + 13)8} / 2
⇒ A = {184}/2
⇒ A = 92 square yards.
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Just 17 18 19 please
Answers
[17] 92°
The sum of two non-adjacent angles is equal to the exterior angle:
x + 45 = 2x - 2
47 = x
Then, 2x - 2 -> 2(47) -2 -> 92
[18] 114°
Pretty much the same process
24 + 2x + 18 = 3x + 6
42 + 2x = 3x + 6
36 = x
Then, 3x + 6 -> 3(36) + 6 = 114
[19] 158°
Annnd again, formatted differently though,
x + 90 + 3x + 2 = 180
4x + 92 = 180
4x = 88
x = 22
Then, 180 - 22 = 158
Have a nice day! - Sorry for the wait, I made it super complicated, still got the right answer, and then used the actual formula lol
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Answer:
17)
2x-2=92
18)
3(36)+6=114
19)
22+ex angle=180
ex angle=158
Step-by-step explanation:
17)
2x-2=x+45
x=47
2(47)-2= 92
18)
24+2x+18=3x+6
2x+42=3x+6
x=36
3(36)+6=114
19)
90+x+3x+2=180
92+4x=180
4x=88
x=22
x+ex angle=180
22+ex angle=180
ex angle=158
f(0) = g(0)
f(-2) = g(-2)
f(0) = g(-2)
f(-2) = g(0)
Answers
Answer:
f(-2) = g(-2)
What is the distance between(-6.4) and (-8.6)
Answers
Answer:
Ans is in attachment
hope it helps :)
plz mark as brainliest
A certain quantity decays exponentially over time. The initial quantity at t = 0 is 1,000. The quantity
decays at a rate of 2%. What is the quantity at t = 4?
A. 0.00016
B. 1.6000
C. 903.9208
D. 922.3682
Answers
Answer:
D: 922.3682
Step-by-step explanation:
First you take 1000 and subtract 20 from it.( 2% of 1000 = 1000x0.02x2=20).
You could do this on a calculator by entering 1000 and then subtracting 2% by clicking minus then, 2 then percent, then equals. you get 980. do the same to 980. (click minus, then 2, then percent, then equals). you get 960.4. do the same to 960.4. you get 941.192. do the same one more time since it says t=4 and you get 922.36816 which rounded to the nearest ten-thousandths is 922.3682.
hope this helped!
(Please help me!!!)
2. A solid has volume 7 cubic units. The equation k = 3^√V/7 scale factor of k by which the solid must be dilated to obtain an image with
volume V cubic units. Select all points which are on the graph representing this equation.
(A.) (0, 0)
(B.) (1, 1)
(C.) (1,7)
(D.) (7,1)
(E.) (14, 2)
(F.) (49, 2)
(G.) (56, 2)
(H.) (27,3)
Answers
We can see that the points (1,0), (3,7), and (7,29.74) are on the graph of this equation. Therefore, the correct answers are (C.) (1,7), (G.) (56,2), (H.) (27,3).
Describe Equation?An equation is a mathematical statement that shows the equality between two expressions. It is made up of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and roots. An equation is represented by an equal sign (=) which means "is equal to".
Equations are used in various fields of mathematics and science to represent relationships between variables and to solve problems. They can be linear or nonlinear, and may involve one or more variables.
Solving an equation involves finding the value(s) of the variable(s) that make the equation true. This may involve algebraic manipulation, substitution, or other techniques depending on the complexity of the equation.
First, let's simplify the given equation:
k = 3^(√(V/7))
We know that k is the scale factor by which the solid must be dilated, so let's solve the equation for V in terms of k:
k = 3^(√(V/7))
log3(k) = √(V/7)
(log3(k))^2 = V/7
V = 7*(log3(k))^2
Now, we can use this equation to find the values of V for different values of k:
For k = 1, V = 7*(log3(1))² = 0
For k = 2, V = 7*(log3(2))² ≈ 4.83
For k = 3, V = 7*(log3(3))² = 7
For k = 4, V = 7*(log3(4))² ≈ 12.11
For k = 5, V = 7*(log3(5))² ≈ 17.67
For k = 6, V = 7*(log3(6))² ≈ 23.57
For k = 7, V = 7*(log3(7))² ≈ 29.74
Based on these values, we can see that the points (1,0), (3,7), and (7,29.74) are on the graph of this equation. Therefore, the correct answers are:
(C.) (1,7)
(G.) (56,2)
(H.) (27,3)
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We can see that the points (1,0), (3,7), and (7,29.74) are on the graph of this equation. Therefore, the correct answers are (C.) (1,7), (G.) (56,2), (H.) (27,3).
Describe Equation?An equation is a mathematical statement that shows the equality between two expressions. It is made up of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and roots. An equation is represented by an equal sign (=) which means "is equal to".
Equations are used in various fields of mathematics and science to represent relationships between variables and to solve problems. They can be linear or nonlinear, and may involve one or more variables.
Solving an equation involves finding the value(s) of the variable(s) that make the equation true. This may involve algebraic manipulation, substitution, or other techniques depending on the complexity of the equation.
First, let's simplify the given equation:
k = \(\sqrt[3]{}\)(V/7))
We know that k is the scale factor by which the solid must be dilated, so let's solve the equation for V in terms of k:
k = \(\sqrt[3]{}\)(V/7))
log3(k) = √(V/7)
(log3(k))² = V/7
V = 7*(log3(k))²
Now, we can use this equation to find the values of V for different values of k:
For k = 1, V = 7*(log3(1))² = 0
For k = 2, V = 7*(log3(2))² ≈ 4.83
For k = 3, V = 7*(log3(3))² = 7
For k = 4, V = 7*(log3(4))² ≈ 12.11
For k = 5, V = 7*(log3(5))² ≈ 17.67
For k = 6, V = 7*(log3(6))² ≈ 23.57
For k = 7, V = 7*(log3(7))² ≈ 29.74
Based on these values, we can see that the points (1,0), (3,7), and (7,29.74) are on the graph of this equation. Therefore, the correct answers are:
(C.) (1,7)
(G.) (56,2)
(H.) (27,3)
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use the second fundamental theorem of calculus to find f'(x). f(x) = x 1 9 t csc t dt
Answers
Applying second fundamental theorem to the given function, f(x) = ∫[1 to 9x] t csc(t) dt, we can find its derivative, f'(x), by evaluating the integrand at the upper limit of integration, which is 9x.
The second fundamental theorem of calculus states that if we have a function defined as the integral of another function, then its derivative can be found by evaluating the integrand at the upper limit of integration. The derivative of f(x) is given by f'(x) = 9 csc(9x). This result comes from applying the second fundamental theorem of calculus. The integrand of the given function is t csc(t), and by evaluating it at the upper limit of integration, 9x, we obtain the derivative. The 9 outside the csc function is due to the fact that the derivative of 9x with respect to x is 9. Therefore, the derivative of f(x) with respect to x is simply 9 csc(9x).
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Find the function f, if: f'(x)=2/(x^3) + 4e^x + 5, f(-1)=1, f(1)=-1 (Note: Consider the domain and write the answer in ascending order of the variable).
Answers
Answer:
f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)
Step-by-step explanation:
We can find the function f(x) by integrating f'(x) with respect to x:
â«f'(x) dx = â«(2/(x^3) + 4e^x + 5) dx
f(x) = -1/x^2 + 4e^x + 5x + C
To find the constant C, we can use the given initial conditions:
f(-1) = 1 = -1/(-1)^2 + 4e^(-1) - 5 + C
C = 1 + 1/1 - 4e^(-1)
f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)
Therefore, the function f(x) is:
f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)
A, B and C are points on the circumference of a circle, centre O.
ECD is a tangent to the circle at C.
Angle AOB 2x +46°
Angle OBC-37°
Angle ACD-3xr
Work out the value of x.
Answers
The value of x based on the circumference of a circle and the tangent to the circle is 11.5.
How to calculate x value?We know that angle OBC = -37° and angle AOB = 2x + 46°. Therefore, angle AOC is:
angle AOC = (angle AOB) / 2
angle AOC = (2x + 46) / 2
angle AOC = x + 23
Since angle AOC and angle ACD are opposite angles, they are equal. Therefore,
x + 23 = 3x
2x = 23
x = 11.5
Therefore, the value of x is 11.5.
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8. Maximize p=x+2y subject to 30x+20y
0.1x+0.4y
0.2x+0.3y
x≥0,y≥0
Answers
Answer:5.97
Step-by-step explanation.
you have to look at the question.
you have to look around the question
The very last step is you have to answer it
which is greater 3.65x10-8 or 3.65x10-7
Answers
Answer:
the second one is your answer
Step-by-step explanation:
hope this helped mark me brainlest pls and thank you
5th grade math. Correct answer will be marked brainliest.
Answers
Answer:
407.4
Step-by-step explanation:
Answer:
Partial product 1: 194
Partial product 2: 388
Answer: 407.4
Customers arrive at a video rental desk at the rate of 12 per minute(Poisson).Each server can handle 8.15 customers per minute(Poisson). If there are 3 servers, determine the average time it takes to rent a video tape. a. 0.085 minutes b. 0.219 minutes C. 0.018 minutes d. 0.141 minutes
Answers
The average time it takes to rent a video tape is 0.141 minutes.
Given data:Customers arrive at a video rental desk at the rate of 12 per minute(Poisson).
Each server can handle 8.15 customers per minute(Poisson). If there are 3 servers, we need to determine the average time it takes to rent a video tape.
Let us assume λ = 12 and μ = 3 × 8.15 = 24.45
Average time it takes to rent a video tape = 1 / (μ - λ/n)
Where, n = number of servers⇒ Average time it takes to rent a video tape = 1 / (24.45 - 12/3)⇒ Average time it takes to rent a video tape = 1 / 8.45⇒ Average time it takes to rent a video tape = 0.1185 minutes = 0.141 rounded to three decimal places.
Thus, the average time it takes to rent a video tape is 0.141 minutes.
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The ratio of the angle measures in a triangle is 1:2:3. What is the measure of the largest angle?
Answers
Answer:
Step-by-step explanation:
Let the 3 angles be x , 2x , and 3x
notice x:2x:3x = 1:2:3
we know x+2x+3x = 180
6x = 180
x = 30
so the largest angle is 3(30) or 90 degrees
1. The temperature in Hawaii on Thursday was 85°F. The temperature in Colorado on Thursday was
5°F. Which expression(s) represent this situation using the absolute value of the difference
Answers
Answer: See explanation
Step-by-step explanation:
From the question, we are informed that the temperature in Hawaii on Thursday was 85°F while thee temperature in Colorado on Thursday was 5°F.
The expression(s) that represent this situation using the absolute value of the difference will be:
= 85°F - 5°F
= 80°F
What is the solution to this linear system? Enter a value in each box to create an ordered pair. ill put brianly if u answer asap
Answers
Answer:
(-1,5)
Step-by-step explanation:
The function g(x) is a transformation of the parent function f(x). Decide how
f(x) was transformed to make g(x).
A. Horizontal or vertical reflection
B. Horizontal or vertical stretch
C. Horizontal or vertical shift
D. Reflection across the line y
(Graphs attached)
Answers
Answer:- a
Step-by-step explanation:
Natalie is competing in the javelin throw event at her school. in order to qualify for the final round, the mean length of her javelin throws in the first round must be at least 195 feet. she has 1 more throw left in the first round. this list shows the length, in feet, of natalie's first 7 javelin throws. 188, 204, 194, 195, 187, 201, 199 question what is the minimum length, in feet, that natalie must throw the javelin on her next throw in order to qualify for the final round? enter the answer in the box.
Answers
The minimum length = 192ft, that Natalie must throw the javelin on her next throw in order to qualify for the final round.
Based on the given conditions,
The length of her javelin throws in the first round must be at least 195 feet.
She has 1 more throw left in the first round.
This list shows the length, in feet, of Natalie's first 7 javelin throws.
= 188, 204, 194, 195, 187, 201, 199
The minimum length is,
= 188 + 204 + 194 + 195 + 187 + 201 + 199
= 1368
Let us assume,
Final length = x
So,
We can write,
( x + 1368 ) / 8 ≥ 195
x + 1368 ≥ 195 * 8
We can multiply the coefficient,
x + 1368 ≥ 1560
x ≥ 1560 - 1368
We can sum or difference the coefficient,
x ≥ 192
This is Inequality function.
Equations and inequalities are mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are supposed to be equal and shown by the symbol =. Whereas in inequality, the two expressions are not necessarily equal and are indicated by the symbols: >, <, ≤ or ≥.
Therefore,
The minimum length = 192ft, that Natalie must throw the javelin on her next throw in order to qualify for the final round.
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Find the most general real-valued solution to the linear system of differential equations.
Answers
To provide a general real-valued solution to a linear system of differential equations, specific equations need to be provided. Without the specific equations, it is not possible to determine the exact solution.
In general, a linear system of differential equations can be written in matrix form as follows:
dY/dt = AY,
where Y is a vector of functions, t is the independent variable, and A is a constant matrix.
To solve this system, one can use methods such as matrix diagonalization, eigenvalues, and eigenvectors, or the method of variation of parameters. These methods allow you to find the general solution of the system, which represents a family of solutions that satisfy the given equations.
It is important to note that the specific form of matrix A and the initial or boundary conditions if provided, will determine the exact solution to the system of differential equations.
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