A method for determining whether a critical point is a relative minimum or maximum using concavity.
To determine whether a critical point is a relative minimum or maximum using concavity, we need to examine the second derivative of the function at the critical point.
If the second derivative is positive, then the function is concave up, meaning it is shaped like a bowl opening upwards. At a critical point where the first derivative is zero, this indicates a relative minimum, as the function is increasing on either side of the critical point.
On the other hand, if the second derivative is negative, then the function is concave down, meaning it is shaped like a bowl opening downwards. At a critical point where the first derivative is zero, this indicates a relative maximum, as the function is decreasing on either side of the critical point.
If the second derivative is zero, then the test is inconclusive and further analysis is needed, such as examining higher order derivatives or using other methods such as the first derivative test.
Therefore, the concavity test is a useful method for determining the nature of critical points and whether they represent a relative minimum or maximum.
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Complete question is:
What we need to examine for a method for determining whether a critical point is a relative minimum or maximum using concavity.
Convert 1.19rads to degree
Answer:
68.2 degrees
Step-by-step explanation:
\(1.19\frac{180}{\pi }\)
\(68.2\) degrees
The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. Use the constraints of the real-world situation to predict the height of the water balloon at 15 seconds. Use complete sentences to support your answer.
From the linear model we can see that the height of the balloon after 15 seconds is 0 feet.
Depending on the context, the phrase "linear model" is used differently in statistics.
The word is frequently used interchangeably with a linear regression model since it occurs most frequently in relation to regression models. The phrase has a different connotation when employed in time series analysis, though. The term "linear" is used in each instance to denote a subclass of models for which a significant decrease in the complexity of the underlying statistical theory is feasible.From the linear model we can see that the water balloon is thrown from a height of 40 feet upwards.
Now the balloon reaches a height of 70 feet and then falls back down on earth due to gravity.
At about 10 seconds the balloon falls on the ground and splashes.
Hence for further time the balloon is always at the ground.
Therefore at time of 15 seconds the height of the balloon is always 0 feet as represented in the linear model.
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Charlotte works in a department store selling clothing. She makes a guaranteed salary of $500 per week, but is paid a commission on top of her base salary equal to 30% of her total sales for the week. How much would Charlotte make in a week in which she made $1575 in sales? How much would Charlotte make in a week if she made
x
x dollars in sales?
Charlotte makes 500 pounds per week
30 % of 500 she has to pay to the commission per week
if she made 1575 one week how much would she get?
1575 divided by 30%=472.5
472.5 rounded = 473
x=473 or 472.5
Charlotte would make $972.50 in a week in which she made $1575 in sales and if Charlotte made x dollars in sales, she would make $500 + 0.3x in total earnings for the week.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
To calculate how much Charlotte would make in a week in which she made $1575 in sales
we first need to calculate her commission:
Commission = 30% × $1575
= $472.50
Total earnings = Guaranteed salary + Commission
= $500 + $472.50
= $972.50
Therefore, Charlotte would make $972.50 in a week in which she made $1575 in sales.
To calculate how much Charlotte would make in a week if she made x dollars in sales, we can use the same method.
Her commission would be:
Commission = 30% ×x
And her total earnings would be:
Total earnings = Guaranteed salary + Commission
= $500 + 0.3x
So, if Charlotte made x dollars in sales, she would make $500 + 0.3x in total earnings for the week.
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HELP THIS IS DUE TODAY
I'm stuck on this.
Step-by-step explanation:
couldn't find the answer but try to get photo math on your phone it would surely help
Answer:
x = 0, y = -4
x = 1, y = -1
x = 2, y = 2
x = 3, y = 5
Step-by-step explanation:
just plug in the x value to get the y smh
if u get it wrong its not on me
a triangle has sides with lengths of 6 kilometers, 7 kilometers, and 10 kilometers. is it a right triangle?
Answer:
Step-by-step explanation:
no because 6 , 7 and 10 doesn't add up to 180 so it is not
A triangle has sides with lengths of 6 kilometers, 7 kilometers, and 10 kilometers is not a right triangle.
To determine if a triangle is a right triangle, you can use the Pythagorean Theorem. The Pythagorean Theorem states that "In a right-angled triangle, the sum of the square of the two shorter sides is equal to the square of the longest side." It can be written as:
a² + b² = c², where 'a' and 'b' are the lengths of the two legs of a right triangle, and 'c' is the length of the hypotenuse.
In this triangle, the two shorter sides have lengths of 6 kilometers and 7 kilometers and the longest side is 10 kilometers.
The square of 6 kilometers is 36 kilometers and the square of 7 kilometers is 49 kilometers.
The sum of 36 kilometers and 49 kilometers is 85 kilometers.
The longest side of the triangle has a length of 10 kilometers, and the square of 10 kilometers is 100 kilometers.
Since 85 kilometers is not equal to 100 kilometers, this triangle is not a right triangle.
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james has saved $200 to purchase
some skateboarding equipment. Can he spend
less than 50% of his savings on skateboarding
shoes and knee pads? Explain
Answer:
Question Cannot Be Answered.
Step-by-step explanation:
In order to answer this question, we would need to know the price of shoes and knee pads.
If you receive a 20% DISCOUNT off an item costing $20.00, how much money do you save?
5. Write two expressions for the area of the big rectangle.
Answer:
Two expressions for the area are;
i) x/3 + 2·y + 6
ii) (1/3) × (x + 6·y + 18)
Step-by-step explanation:
The given dimension of the rectangle are;
The height of the rectangle, h = 1/3
The width of the smallest rectangle, w₁ = x
The width of the med sized rectangle, w₂ = 6·y
The width the large rectangle, w₃ = 18
The area, 'A', of the entire rectangular figure, the big rectangle, can be expressed as follows;
A = A₁ + A₂ + A₃
Where;
A₁ = The area of the smallest rectangle
A₂ = The area of the mid sized rectangle
A₃ = The area of the large rectangle
∴ A = (1/3) × x + (1/3) × 6·y + (1/3) × 18 = x/3 + 2·y + 6
The area of the big rectangle. 'A', can also be found as follows;
A = (1/3) × (x + 6·y + 18)
Therefore, two expressions for the area of the big rectangle are;
x/3 + 2·y + 6 and (1/3) × (x + 6·y + 18).
HELP. Please answer my question, picture below
The polynomial equation that represents the perimeter of the frame is determined as 18x + 2.
What is the perimeter of the frame?The perimeter of the frame is the distance round the frame, and the polynomial equation that represents the perimeter of the frame is calculated as follows;
The given dimension of the frame;
width of the frame = 6x + 3
length of the frame = 2x - 4
The perimeter of the frame is calculated as;
P = 2 (6x + 3) + 2x - 4
P = 12x + 6 + 2x - 4
P = 18x + 2
Thus, the polynomial equation that represents the perimeter of the frame is determined as 18x + 2.
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John took 8 hours to drive 385 miles. He believes that at this same rate he will need at least 17 hours to drive 1000 miles which is the best estimate of the total amount of time he will need to drive 1000 miles
A- 17
B- 19
C-21
D-15
Answer:
Step-by-step explanation:
Step one:
give data
time= 8hours
distance=385mile
speed=?
Step two:
let us solve for the speed
Speed= distance/time
Speed=385/8
speed=48.125miles per hour
Step three:
let's find the time taken to cover 1000mile at the speed of 48.125 mi per hour
speed=distance/time
time=distance/speed
time=1000/48.125
time=20.779hours
approximately 21 hours
10 records in her collection. Now she has 12 records. What is the percent increase of her collection?
10 records in her collection. Now she has 12 records. The percentage increase of her collection is by 20%.
Percentage:
In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is usually represented by the percent sign "%", although 'it is abbreviated "pct.", "pct.", and sometimes "pc". Percentage is a dimensionless number (pure number); it is unmeasured Unit.
Example :
If 50% of the total number of pupils in a class are boys, this means that 50 out of 100 pupils are boys. If there are 500 students, 250 of them are men.
According to the Question:
We can use the rule of three to solve this problem.
If 100% is 10 records, the percentage of 12 records:
= 12 × 100%/10
= 120%
Then if subtracted 120% -100%, there will be a difference of 20%, i.e. 12 is 20% more, i.e. his collection has increased by 20%.
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What is the equation of the line in the accompanying graph?
Answer:
I think its y=-2+2x
Can someone please help me with math
Help pleaseeee I don’t understand it’s for a test and it’s timing me
Answer:
-2: 6^2
-1: 6
2: 1/36
Step-by-step explanation:
Say that you see a consumer loan at 15% and you know that this lender borrows at 10%. What probability of repayment is this loan company expecting?
Determining the probability of repayment is not solely determined by the interest rate spread, but also relies on factors such as borrower creditworthiness, loan terms, and the lender's risk assessment methods.
To determine the loan company's expected probability of repayment, we can analyze the interest rate spread between what they charge (15%) and what they borrow at (10%).
The interest rate spread represents the lender's profit margin and accounts for various factors such as default risk, operating costs, and desired return on investment.
In this case, with an interest rate spread of 5% (15% - 10%), the loan company expects to cover its costs and generate profit by lending money to consumers. The wider the interest rate spread, the greater the lender's expected profit.
However, the exact probability of repayment cannot be determined solely based on the interest rate spread. It also depends on other factors like the creditworthiness of borrowers, loan terms, and risk assessment methods employed by the lender.
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Which number is an integer?
А
1
B
-1
C
0
D
all of the above
Answer: D. ALL OF THE ABOVE
Step-by-step explanation:
AN INTEGER IS A WHOLE NUMBER THAT IS NOT A FRACTION
Answer:
D.) All of the above.
Step-by-step explanation:
An integer is defined as: a colloquially defined number that can be written without a fractional component. All of the above numbers apply.
Use estimation or fraction multiplication to determine if your answer is reasonable. Calculate the product. 78.93 x 32.45
Answer:
2561.2785
Step-by-step explanation:
All you gotta do is calculate and times 78.93 x 32.45
Simplify the square root of negative 18
Answer:
\(3i\sqrt{2}\)
Step-by-step explanation:
If we have the expression \(\sqrt{-18}\), we can divide -18 by 2.
\(\sqrt{2\cdot-9}\)
The square root of 9 is 3, and since we’re finding the square root of a negative number, we append the “i” to the term: so 3i.
This goes outside the root, making the expression \(3i\sqrt{2}\).
Hope this helped!
ANSWER ASAP PLEASE PICTURE BELOW
can you please explain it more clearly
Step-by-step explanation:
how many liters of 10% salt solution must be added to 5 liters of 25% salt solution to obtain a 15% salt solution?
Answer: 10 liters
Step-by-step explanation:
Let the number of liters of 10% solution be \(x\).
\(0.10x+5(0.25)=0.15(x+5)\\\\0.10x+1.25=0.15x+0.75\\\\1.25=0.05x+0.75\\\\0.05x=0.50\\\\x=10\)
rework problem 29 from section 1.4 of your text, involving the flipping of a coin. a coin is flipped. if a heads is flipped, then the coin is flipped 5 more times and the number of heads flipped is noted; otherwise (i.e., a tails is flipped on the initial flip), then the coin is flipped 3 more times and the result of each flip (i.e., heads or tails) is noted successively. how many possible outcomes are in the sample space of this experiment?
The sample space of this experiment consists of 24 possible outcomes, 32 if the initial flip is a heads and 8 if the initial flip is a tails.
The sample space of this experiment consists of 24 possible outcomes, 32 if the initial flip is a heads and 8 if the initial flip is a tails.
There are 24 possible outcomes in the sample space of this experiment. If a heads is flipped on the initial flip, then the 5 additional flips would yield 2^5 = 32 possible outcomes. If a tails is flipped on the initial flip, then the 3 additional flips would yield 2^3 = 8 possible outcomes. Therefore, the total number of possible outcomes is 32 + 8 = 24.
The sample space of this experiment consists of 24 possible outcomes, 32 if the initial flip is a heads and 8 if the initial flip is a tails.
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plzz helpp again pick one and wright it down and how u did it
Answer:
-23
Step-by-step explanation:
\( - 5 - 6 - 2 - 10 \\ - (5 + 6 + 2 + 10) \\ - (11 + 2 + 10) \\ - (13 + 10) \)
\( = - 23\)
an inverted cylindrical cone, 44 ft deep and 22 ft across at the top, is being filled with water at a rate of 11 ft3/min. at what rate is the water rising in the tank when the depth of the water is:
The rate of the water rising in the tank when the depth of the water is 1 ft is 56.05 ft/min.
Explain the term rate of change?The term "rate of change" (ROC) describes the rate at which something changes over time.The rate of change of volume is-
dV/dt = 11 ft3/min.
Volume of cylindrical cone = (1/3)πr²h
As we're trying to find dh/dt, we need to calculate the volume within terms of just one variable, h.
Diameter = 22 ft
Thus, radius is 11 ft
By using height and radius of a water in the tank, we may calculate h using similar ratios.
11/44 = r/h
1/4 = r/h
r= h/4
Put into volume;
V = (1/3)π(h/4)h²
V = (1/3)(π)h³ / (16)
dV/dt = [(1/3)(3)(π)(h)² / 16](dh/dt)
V = [(π)(h)² / 16](dh/dt)
Solve for (dh/dt) ;
dh/dt = (dV/dt)(16) / [((π)(h)²]
Now, the change in volume is dV/dt = 11 ft³/min
dh/dt = (11 ft³/min)(16) / [((π)(h)²]
For h = 1 ft,
dh/dt = (11 ft³/min)(16) / [((π)(1 ft)²]
dh/dt ≈ 56.05 ft/min
Thus, the rate of the water rising in the tank when the depth of the water is 1 ft is 56.05 ft/min.
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fifteen hours is what part of the day. Write the answer as a fraction in simpliest form
Answer:
\(\frac{5}{8}\)
Step-by-step explanation:
There are 24 hours in 1 day, thus 15 hours is
\(\frac{15}{24}\) = \(\frac{5}{8}\) of a day in simplest form
How many followers will Tina and Frank have after 5 weeks?
The number of followers that Tina and Frank have after 5 weeks will be 3,829 and 9,750, respectively.
Given that:
Functions, T(x)=3000 × 1.05ˣ and F(x) = -50x+ 10000
The number of followers after 5 weeks for Tine is calculated as,
T(5) = 3000 × 1.05⁵
T(5) = 3,829
The number of followers after 5 weeks for Frank is calculated as,
F(5) = -50(5)+ 10000
F(5) = 9,750
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The complete question is given below.
Tina and Frank are tracking your followers. Tina creates the equation T(x)=3000 × 1.05ˣ to track her followers, where x is the number of weeks and T(x) is the total number of followers. Frank creates the equation F(x) = -50x+ 10000 to track his followers, where x is the number of weeks and F(x) is the total number of followers.
How many followers will Tina and Frank have after 5 weeks?
A horizontally thrown dart falls 5 cm before it travels 2. 5 m to hit the dart board. how fast was it thrown?
The dart player throws a dart horizontally at a speed of 24.75 m/s.
In this question,
The horizontal distance traveled by the dart, x = 2.5 m
The dart hits the board 5 cm below the height from which it was thrown.
⇒ 5 cm = 0.05 m
Let the time taken by the dart to hit the board is t.
The time taken can be calculated using the Newton's second law of motion,
\(y = ut+\frac{1}{2}at^{2}\)
Put, u = 0, a = -g and g = 9.8
On substituting the above values, we get
⇒ \(-0.05 = 0-\frac{1}{2}(9.8)t^{2}\)
⇒ \(0.05(\frac{2}{9.8}) = t^{2}\)
⇒ \(t^{2} =0.0102\)
⇒ \(t=\sqrt{0.0102}\)
⇒ t = 0.1010 s
Now, the velocity (speed) can be calculated as
displacement = speed × time
⇒ 2.5 = speed × 0.1010
⇒ speed = \(\frac{2.5}{0.1010}\)
⇒ speed = 24.7524 m/s
Hence we can conclude that the dart player throws a dart horizontally at a speed of 24.75 m/s.
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Keith wrote the expression shown to determine the cost in dollars for an upcoming trip. (127.50 - 23.50) + 3(86.50 + 4) Which expression is equivalent to the one Keith wrote?
Answer:
104 + 3(90.50)
Step-by-step explanation:
Given the cost expression :
(127.50 - 23.50) + 3(86.50 + 4)
Equivalent expression :
(127.50 - 23.50) + 3(86.50 + 4)
104 + 3(90.50)
skiing eight people compete in a downhill ski race. assuming that there are no ties, in how many different orders can the skiers finish?
Eight people skiing downhill in a race can finish in 40,320 different orders.
Calculating probabilities for a set of possibilities keeping in account the order they are in is called permutation (\({n}_P_{r}\)).
If we overlook the order, it becomes a problem of combination (\({n}_C_{r}\)).
Permutation plays an important role in probability problems where the order of the possible outcomes is concerned. It does not allow repetition of outcomes.
Mathematically, permutation can be represented as:
\({n}_P_{r}=\frac{n!}{(n-r)!}\)
where 'n' represents the total objects/values/instances and 'r' represents our selected number of objects/values/instances.
In this case, we have total 8 drivers (n=8) and 8 positions we are selecting i.e. the order skiing people finish in (r=8);
\({n}_P_{r}=\frac{8!}{(8-8)!}=\frac{8!}{0!}=\frac{40320}{1}\)
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Need help asap!
1. sin theta =
-15/17
8/17
15/17
-8/17
2. cos theta =
-8/17
15/17
-15/17
8/17
3. tan theta =
8/15
15/8
-15/17
-15/8
4. csc theta =
-17/8
-17/15
17/15
17/8
5. sec theta =
17/15
-17/8
-17/15
17/8
6. cot theta =
15/8
-15/17
-15/8
8/15