Answer:
(a) 3.5
(b) x = 4
(c) -¹/₂
(d) -¹/₂
Step-by-step explanation:
Part (a)f(1) is the value of y when x = 1.
To find the value of y from a given value of x, find the position of x on the x-axis, then trace vertically until you meet the line. Once you meet the line, trace horizontally to the y-axis to find the corresponding value of y.
Therefore, f(1) = 3.5.
Part (b)To solve f(x) = 2, find the value of x when y = 2.
To find the value of x from a given value of y, find the position of y on the y-axis, then trace horizontally until you meet the line. Once you meet the line, trace vertically to the x-axis to find the corresponding value of x.
Therefore, the solution of f(x) = 2 is x = 4.
Part (c)The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
\(\dfrac{f(b)-f(a)}{b-a}\)
Given interval: 2 ≤ x ≤ 4
Therefore:
a = 2b = 4\(\implies \dfrac{f(4)-f(2)}{4-2}=\dfrac{2-3}{4-2}=-\dfrac{1}{2}\)
Part (d)The average rate of change between any interval of the given function will be the same as the graph is linear. Therefore, the average rate of change from 0 to 8 is the same as the rate found in part (c): -¹/₂.
Proof
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
\(\dfrac{f(b)-f(a)}{b-a}\)
Given interval: 0 ≤ x ≤ 8
Therefore:
a = 0b = 8\(\implies \dfrac{f(8)-f(0)}{8-0}=\dfrac{0-4}{8-0}=-\dfrac{4}{8}=-\dfrac{1}{2}\)
What is the area (what is the height)
Answer:
5 i think
Step-by-step explanation:
The trapezoid's height (h) is 4 mm(millimeters).
Formula to calculate a trapezoid's height;
2 x Area ÷ by A(short base) + B(large base)
What are the values of the function when x=-2 and when x=4
Answer:
g(-2) = 0
g(4) = -4
Step-by-step explanation:
The outputs of each inequality are the numbers directly next to the parentheses. If an "x" value lies within a particular inequality, the values of the function are the corresponding output.
Remember, the "greater than or equal to" sign (≤) indicates that the "x" value can be equal to the number on the left. The "greater than" symbol (<) indicates that the number to the right cannot satisfy the inequality.
x = -2 lies within the inequality -2 ≤ x < 4. All "x" values that fall within this range are g(x) = 0. Therefore, g(-2) = 0.
x = 4 lies within the inequality 4 ≤ x < 10. All "x" values that fall within this range are g(x) = -4. Therefore, g(4) = -4.
Find a linear function h given h(-1)=-2 and h(-7)=-9 The linear function is h(x)= (Simplify your answer. Use integers or fractions for any numbers in the expression.)
h(x) = -7/6x - 25/6.
Given h(-1)=-2 and h(-7)=-9
For linear function h(x), we can use slope-intercept form which is y = mx + b, where m is the slope and b is the y-intercept.
To find m, we can use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
h(-1) = -2 is a point on the line, so we can write it as (-1, -2).
h(-7) = -9 is another point on the line, so we can write it as (-7, -9).
Now we can find m using these points: m = (-9 - (-2)) / (-7 - (-1)) = (-9 + 2) / (-7 + 1) = -7/6
Now we can find b using one of the points and m. Let's use (-1, -2):
y = mx + b-2 = (-7/6)(-1) + b-2 = 7/6 + b
b = -25/6
Therefore, the linear function h(x) is:h(x) = -7/6x - 25/6
We can check our answer by plugging in the two given points:
h(-1) = (-7/6)(-1) - 25/6 = -2h(-7) = (-7/6)(-7) - 25/6 = -9
The answer is h(x) = -7/6x - 25/6.
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An investor bought 50 shares of stock for $98.40 per share when the value of the stock was $142.00 per share
The profit on the shares is $2180
How to determine the profit on the sharesFrom the question, we have the following parameters that can be used in our computation:
Number of shares = 50
Cost price = $98.40
Current price = $142.00
The profit on the shares is then calculated as
Profit = (Current price - Cost price) * Number of shares
Substitute the known values in the above equation, so, we have the following representation
Profit = (142 - 98.40) * 50
Evaluate
Profit = 2180
Hence, the profit is $2180
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C is a town.
The bearing of C from A is 050°.
Find the bearing of A from C.
In the context of engineering and construction, a bearing point refers to a specific location or area. The bearing of A from C is 230°.
Which point is the bearing?The load from the structural element is transferred to the foundation at a bearing point, which is often a concentrated load point.
To avoid structural failure, settling, or excessive deflection of the part, it is crucial to make sure the bearing point is properly designed and supported.
Since the bearing of C from A is 050°, we can find the bearing of A from C by adding 180° to 50°, which gives us:
Bearing of A from C = 50° + 180° = 230°
Therefore, In the context of engineering and construction, a bearing point refers to a specific location or area. The bearing of A from C is 230°.
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Complete question -
A children's pony ride at a zoo has ponies attached to a carousel pole in the center of a circle. The diameter of a circle is 25 feet. How many feet does a pony walk to complete one trip around the circle?
A pony walks approximately 78.4 feet to complete one trip around the circular pony ride.
What is the distance around the circular pony ride?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The circumference of a circle or the distance around the circle is expressed mathematically as;
C = 2πr or C = πd
Where r is radius, d is diameter and π is constant pi ( π = 3.14 ).
The distance traveled by a pony to complete one trip around the circle is equal to the circumference of the circle.
Given that the diameter of the circle is 25 feet, we can calculate the circumference using the above formula as follows:
C = πd
C = 3.14 × 25 feet
C = 78.5 feet.
Therefore, the measure of the circumference is approximately 78.5 feet.
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IV Find the citical points at which profit (pie) is maximized given the total revenue TR=4700−302 and Total CostTC =320/10,500 (2pts) 1. Compute Marginal Revenue and Marginal Cost 2. Equate MR=MC to find Q
∗
3. Verify that Q* is a relative maximum point 4. Compute the maximum profit level (pie) )
∗
by establishing (pie)* =9( (pie) (Q
∗
)
To find the critical points at which profit is maximized given the total revenue TR = 4700 - 302 and total cost TC = 320/10,500, we need to compute the marginal revenue and marginal cost, equate MR = MC to find the optimal quantity Q∗, verify if Q∗ is a relative maximum point, and compute the maximum profit level (π) by evaluating π∗ = 9(π(Q∗)).
Marginal Revenue (MR) is the derivative of the total revenue function with respect to quantity (Q). In this case, MR = dTR/dQ. By taking the derivative of TR = 4700 - 302 with respect to Q, we can find the expression for MR.
Marginal Cost (MC) is the derivative of the total cost function with respect to quantity (Q). In this case, MC = dTC/dQ. By taking the derivative of TC = 320/10,500 with respect to Q, we can find the expression for MC.
To find the optimal quantity Q∗, we equate MR and MC by setting MR = MC and solve for Q. This is because profit is maximized when MR equals MC.
Once we have found Q∗, we need to verify if it is a relative maximum point. This can be done by checking the second derivative of the profit function and determining if it is negative at Q∗. If the second derivative is negative, it confirms that Q∗ is a relative maximum point.
Finally, to compute the maximum profit level (π∗), we evaluate π(Q∗) by substituting Q∗ into the profit function. In this case, we can multiply the value of π(Q∗) by 9 to obtain the maximum profit level (π∗).
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None of the answers I got is an answer choice
Answer:
N/A
Step-by-step explanation:
1. subtract 3 from both sides to isolate the square root and its coefficient
5√(5-x) = - 10
2. divide both sides by 5 to isolate the square root
√(5-x) = -2
this means that the square root of something would be negative, which is not possible
In the number 2,222.222, what is the difference between the 2 in the tens place and the 2 in the column to its left? a. the 2 in the tens place represents of what the 2 to its left represents. b. the 2 in the tens place represents of what the 2 to its left represents. c. the 2 in the tens place represents 100 times what the 2 to its left represents. d. the 2 in the tens place represents 10 times what the 2 to its left represents.
This questions is testing the knowledge on place value and total value.
The two to the left of the 2 in the tens place is 100 times larger than the 2 in the 100ths place in the value.
The total value of the 2 in the tens position is 20.
The total value of the 2 in the tenth position is 0.2.
To obtain the difference, divide the 20 in the tens position to the 2 in the tenths position.
20/0.2 = 100
the 2 in the tens place represents 100 times what the 2 to its left represents.
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Write an algebraic expression to represent the area of the triangle (Area = 1/2 ×base ×height) given that the length is 6 inches greater than the height. Then evaluate it to find the area when h=7 inches
The expression for area of triangle is 1/2x² + 3x.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Area = 1/2 × base × height
and, length is 6 inches greater than the height.
let the height of the triangle is x
length of triangle = x + 6
So, The Area of triangle
= 1/2 x base x height
= 1/2(x)(x+ 6)
= 1/2x² + 3x
Hence, the expression for area of triangle is 1/2x² + 3x.
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whats 17×3297÷47+70=
Answer:
1,262.5
according to the calculator lol
Answer:
17×3297÷47+70=
Step-by-step explanation:
1262.53191489
$80 gift marked up 60%
give me the answer after the markup
Answer:
128
Step-by-step explanation:
0.6 (the percentage) x 80.00= 48.00
48.00 + 80.00 = 128.00
Answer:
128
Step-by-step explanation:
60% + 100% (new price) = 160% = 1.6
80 x 1.6 = 128
1o Divide
$ 20,000 in the ratio 3:2
Answer:
30,000
Step-by-step explanation:
3/2 multiplied by 20k is
3 x 20000 over 2
which is 60000 over 2
which is 30000
I need help with this question yeah i know i am spamming but i have to get this done or my mom will make me live with my dad!!!1!!!!!
the larger the sample, the more ________ you have when you generalize your sample findings to the population facts.
the larger the sample, the more confidence you have when you generalize your sample findings to the population facts.
The larger the sample size, the more confidence you can have when you generalize your sample findings to the population facts. This is because larger sample sizes provide more accurate representation of the population facts due to the increased number of data points collected. As a result, the more data points you have, the more reliable your findings are in terms of representing the population facts. The larger the sample size, the more confidence you can have in generalizing the findings to the population facts.
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Use solver to solve the following LP
max 9x+5y+z
st.
2x+5y+4z<=8
2x-3y+5z<=9
2x-2y+12z>=10
Report the optimal objective value (do not round)
Set variable bounds: Set the bounds for variables x, y, and z as "Non-negative".
To solve the given linear programming problem using Solver, follow these steps: Define the objective function: Set the objective function as "Max 9x + 5y + z" in the Solver dialog box. Define the constraints: Add the constraint "2x + 5y + 4z <= 8" as a "≤" constraint. Add the constraint "2x - 3y + 5z <= 9" as a "≤" constraint. Add the constraint "2x - 2y + 12z >= 10" as a "≥" constraint. Set variable bounds: Set the bounds for variables x, y, and z as "Non-negative". Run Solver: Click "Solve" in the Solver dialog box to find the optimal solution.
After running Solver, it will provide the optimal objective value. The optimal objective value for this problem will depend on the specific values of x, y, and z obtained. Please run the Solver with the given LP problem to obtain the optimal objective value.
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Someone help me asappppp!!! Will mark brainliest if right hurry!!!!!!
Answer:
i cant see the angle at the bottom of the page. im assuming it is E.
1. BAE and BDC
2. BEA and BCD
Step-by-step explanation:
Which steps could be used to solve this story problem? Blake took flyers to the shopping center to advertise his car wash event. By the time he arrived 14 of the flyers had blown away. He ended up putting 50 flyers on blue cars, 26 flyers on white cars, and 32 flyers on silver cars. How many flyers did Blake start with?
Blake started with 94 flyers before 14 of them blew away.To solve this story problem, we can follow these steps:
1. Start by identifying the key information provided in the problem:
- 14 flyers had blown away by the time Blake arrived.
- Blake put 50 flyers on blue cars, 26 flyers on white cars, and 32 flyers on silver cars.
2. To find out how many flyers Blake started with, we need to determine the total number of flyers he distributed. Add the number of flyers on blue cars, white cars, and silver cars:
- 50 + 26 + 32 = 108 flyers were distributed.
3. Since 14 flyers blew away, we subtract this number from the total number of distributed flyers to find the initial number of flyers Blake had:
- 108 - 14 = 94 flyers.
Therefore, Blake started with 94 flyers before 14 them blew away.
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if the divining rod is completely useless for locating water, what is the probability that the expert will correctly identify (by guessing) both of the cans containing water?
a) The sample space for this experiment:
S = { E1E2, E1W2,E2W2, E1W1, E2W1, W1W2 }
b) The probability that the expert will correctly identify (by guessing) both of the cans containing water is: 1/6
Probability :Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
Now, According to the information:
Let E1 and E2 represent the empty cans and W1 and W2 be the cans filled with water.
S = { E1E2, E1W2,E2W2, E1W1, E2W1, W1W2 }
By merely guessing, the events are equally likely. Since there are 6 possible outcomes,
The probability that the expert will correctly identify (by guessing) both of the cans containing water is:
Since there are 6 possible outcomes,
probability = 1/6
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The given question is incomplete, complete question is:
According to Webster’s New Collegiate Dictionary, a divining rod is "a forked rod believed to indicate [divine] the presence of water or minerals by dipping downward when held over a vein." To test the claims of a divining rod expert, skeptics bury four cans in the ground, two empty and two filled with water. The expert is led to the four cans and told that two contain water. He uses the divining rod to test each of the four cans and decide which two contain water. a List the sample space for this experiment. b If the divining rod is completely useless for locating water, what is the probability that the expert will correctly identify (by guessing) both of the cans containing water?
Find the equation of the line.
Use exact numbers.
y=
Answer:
y = -2x + 5
Step-by-step explanation:
y = mx + b points on the graph: (0,5) (1,3)
y = mx + 5
\(\frac{5-3}{0-1}\) = \(\frac{2}{-1}\) = -2
y = -2x + 5
A particular antibiotic is eliminated from the blood with a half-life of 16 hours. how many hours does it take for 100-milligram dose to decrease to 30-milligrams in the blood?
Using the decay formula, the particular antibiotic with half-life of 16 hours, will decrease to 30-milligrams in the blood after 27.79 hours.
We can use the decay formula to solve the problem:
A(t) = A(0) . (0.5)^(t/T)
Where:
A(t) is the remaining quantity at time t
A(o) is the initial quantity
t is the time interval
T is the half-life rate
In the given problem:
A(0) = 100 milligram
T = 16 hours
A(t) = 30 milligram
We need to find t such that the remaining quantity of this antibiotic is 30 mg.
Substitute the given parameters into the formula:
A(t) = A(0) . (0.5)^(t/T)
30 = 100 . (0.5) ^(t/16)
Taking the logarithm:
log (30) = log [100 . (0.5) ^(t/16)]
Use the logarithm property, log(A.B) = log A + log B
log (30) = log (100) + log [(0.5) ^(t/16)]
Use the logarithm property, log(Aⁿ) = n.log A
log (30) = log (100) + (t/16) . log (0.5)
log (30) = 2 + (t/16) . log (0.5)
(t/16) . log (0.5) = log (30) - 2
t/16 = 1.737
t = 1.737 . (16) = 27.79 hours
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What is the pH of 0.2L of blood? Is it acidic or basic?
Answer:its acidic
Step-by-step explanation:
There are about 2.54 centimeters in 1 inch. if a segment is 2.7 centimeters long, how many inches is it, rounded to the nearest hundredth?
Answer: 1.06 cm
Step-by-step explanation:
Take 2.7 divided by 2.54 = 1.062cm
Rounded the nearest hundredth, so it will be 1.06 cm
HELP I NEED HELP ASAP
Answer:
i think its; there all inequalities
Step-by-step explanation:
Describe the type of solutions to the quadratic equation below.
x²-3x-28=0
Select the correct answer below:
1.Two real rational solutions
2.Two real irrational solutions
3.One repeated real rational solution
4.Two complex solutions
The quadratic equation x² - 3x - 28 = 0 has two real rational solutions. Therefore the correct option is 3. Two real rational solutions
To determine the type of solutions to the quadratic equation x² - 3x - 28 = 0, we can use the discriminant, which is the term b² - 4ac in the quadratic formula.
In this case, the coefficients are:
a = 1 (coefficient of x²)
b = -3 (coefficient of x)
c = -28 (constant term)
The discriminant is calculated as follows:
Discriminant = b² - 4ac
Discriminant = (-3)² - 4(1)(-28)
Discriminant = 9 + 112
Discriminant = 121
Now, let's analyze the value of the discriminant:
1. If the discriminant is positive (greater than zero), there are two real solutions.
2. If the discriminant is zero, there is one repeated real solution.
3. If the discriminant is negative (less than zero), there are two complex solutions.
In this case, the discriminant is 121, which is positive. Therefore, the quadratic equation x² - 3x - 28 = 0 has two real rational solutions.
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13. Zahra likes to go rock climbing with her friends. In the past, Zahra has climbed to the top of the
wall 7 times in 28 attempts. Determine the odds against Zahra climbing to the top.
A. 3:1
B. 4:1
C. 3:11
D. 3:4
Answer:
the odds against Zahra climbing to the top are,
B. 4:1
Step-by-step explanation:
Since she has climbed 7 times in 28 attempts,
the probability of a successful climb is,
P = 7/28
P = 1/4
So, the odds against Zahra climbing to the top are 4:1
Ferdinand is playing golf. He hits a shot off the tee box that
has a height modeled by the function h(t) = –16t2 + 80t,
where h(t) is the height of the ball, in feet, and t is the time
in seconds it has been in the air. The graph that models
the golf ball's height over time is shown below.
When does the ball reach its maximum height?
What is the maximum height of the ball?
Answer:
Maximum height of the ball = 100 m
Time to reach the maximum height = 2.5 seconds
Step-by-step explanation:
Function that models the height h(t) of the ball and time 't',
h(t) = -16t² + 80t
Convert this equation into vertex form,
h(t) = -16(t²- 5t)
= -16[t² - 2(2.5t) + (2.5)² - (2.5)²]
= -16[[t² - 2(2.5t) + (2.5)²] + 16(2.5)²
= -16(t - 2.5)² + 16(6.25)
= -16(t - 2.5)² + 100
By comparing this equation with,
g(t) = a(x - h)² + k
Here, (h, k) is the vertex of the parabola.
Vertex of the given parabola will be → (2.5, 100)
Therefore, maximum height of the ball = 100 m
Time taken by the ball to reach the maximum height = 2.5 seconds
PLEASE HELP ASAP!!!!!
Given:
The side lengths of two cubes are 2.5 yd and 2 yd.
To find:
The side length of third cube.
Solution:
From the given figure it is clear that the cubes are inclined to each other in such a way so that they form a right angle triangle and side length of third cube is the base.
Let x be the side length of the third cube.
Using Pythagoras theorem, we get
\(Hypotenuse^2=Base^2+Perpendicular^2\)
\((2.5)^2=(x)^2+(2)^2\)
\(6.25=x^2+4\)
\(6.25-4=x^2\)
\(2.25=x^2\)
Taking square root on both sides, we get
\(x=\pm\sqrt{2.25}\)
\(x=\pm 1.5\)
Side cannot be negative. So,
\(x=1.5\)
Therefore, the side length of the third cube is \(x=1.5\) yd.
In Mrs. Ramon's class, the ratio of boys to girls is 2 to 3. The class has 30
students. How many girls are in Mrs. Ramon's class?
Answer:
10 girls
Step-by-step explanation:
Because 2/3 of 30 is 20 making the other 10 girls
The arcs in the photo at the right appear to
be paths of stars rotating about the North Star, To produce this effect, the
photographer set a camera on a tripod and left the shutter open for an
extended time. If the photographer left the shutter open for a full 24 hours,
each are would be a complete circle. You can model a star's rotation" in the
coordinate plane. Place the North Star at the origin. Let P(1, 0) be the position
of the star at the moment the camera's shutter opens. Suppose the shutter is
left open for 2 h 40 min, with the arc ending at P. a. What angle of rotation
maps Ponto P? b. What are the x and y coordinates of P to the nearest
thousandth? c. What translation rule maps P onto P?
Answer:
a. What angle of rotation maps Ponto P?
30.25 degrees
b. What are the x and y coordinates of P to the nearest thousandth?
(83.3, 33.3)
c. What translation rule maps P onto P?
Rotation