While looking at the critical points of a function f(x) is a useful first step in finding its maxima and minima, it is not enough by itself to determine all of them.
The statement is partially correct. If a function f(x) is continuous on a closed interval, it is possible to find its absolute maxima and minima by looking at the points where f'(x) = 0, but this is not enough to guarantee that you have found all of them.
The reason why this is the case is because the condition f'(x) = 0 only identifies critical points, which are points where the function may have an extremum (either a maximum or a minimum). To determine whether a critical point is indeed a maximum or a minimum, you need to analyze the behavior of the function near the critical point.
One way to do this is by using the second derivative test, which states that if f(x) is twice differentiable and f''(x) > 0 at a critical point x, then f(x) has a local minimum at x. Similarly, if f''(x) < 0 at a critical point x, then f(x) has a local maximum at x.
You also need to use additional tools, such as the second derivative test, to verify whether the critical points are indeed extrema.
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Order the following numbers from least to greatest: 3√2 , √3 − 1, √19 + 1, 6,
2√10 ÷ 5 and √14
can anyone help me with this answer please.
The order from least to greatest would be as follows:
√3 - 1 < 2√10 ÷ 5 < √14 < 3√2 < √19 + 1 < 6
How did we get the value?To order the numbers, we need to first simplify and evaluate each expression.
1. √3 - 1 = 1.73205080757 - 1 = 0.73205080757
2. 2√10 ÷ 5 = 1.265
3. √14 = 3.74166
4. 3√2 = 4.243
5. √19 + 1 = 5.359
6. 6 is simply 6
Therefore, the correct answer is as given above. It could then be concluded that the order from least to greatest is:
0.73205080757 < 1.265 < 3.74166 < 4.243 < 5.359 < 6
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If a vertex of a triangle is (7,-2) and the midpoints of two
sides are (3.5, -0.5) and. (3,1) find the other vertices of
the triangle.
The triangle has vertices A(7,-2), B(5.25, -1.25), and C(5, -0.5).
What is a triangle ?
Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.
Let's call the vertex we know A, and the midpoints of the other two sides B and C, respectively.
Using the midpoint formula, we can find the coordinates of the other two vertices, which are the endpoints of the sides that have B and C as midpoints
Coordinates of B:
x-coordinate: (7 + 3.5)/2 = 5.25
y-coordinate: (-2 - 0.5)/2 = -1.25
So, B is (5.25, -1.25)
Coordinates of C:
x-coordinate: (7 + 3) / 2 = 5
y-coordinate: (-2 + 1)/2 = -0.5
So, C is (5, -0.5)
Therefore, The triangle has vertices A(7,-2), B(5.25, -1.25), and C(5, -0.5).
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based on the data in the table, what is the probability that a randomly selected persons favorite restaurant is a deli?
Answer choices
8/25
2/5
1/10
9/50
The probability that a randomly selected persons favorite restaurant is a deli is 9/50
How to determine the probabilityFrom the question, we have the following parameters that can be used in our computation:
The table of values
On the table, we have
Total = 100
Deli = 18
So, the probability is
P = Deli/Total
Substitute the known values in the above equation, so, we have the following representation
P = 18/100
Simplify
P = 9/50
Hence, the probability is (d) 9/50
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The fourth term in an arithmetic sequence is 3 and the tenth term is 18. If the first term is a1, which is an equation for the nth term of this sequence?
The equation for the nth term of this sequence is an = -4.5 + 2.5(n - 1)
How to determine the equation for the nth term of this sequence?From the question, we have the following parameters that can be used in our computation:
a4 = 3
a10 = 18
An arithmetic sequence is represented as
an = a + (n - 1)d
Using the above as a guide, we have the following:
a + 3d = 3
a + 9d = 18
Subtract the equations
So, we have
6d = 15
Divide
d = 2.5
So, we have
a + 3 * 2.5 = 3
This gives
a = -4.5
So, the sequence is -4.5 + 2.5(n - 1)
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You start driving west for 3 miles, turn right, and drive north for another 2 miles. At the end of driving, what is your straight line distance from your starting point?
Answer:
[tex]\sqrt{13}[/tex]
Step-by-step explanation:
[tex]L^{2}[/tex]=[tex]3^{2}[/tex]+[tex]2^{2}[/tex]=9+4=13
L=[tex]\sqrt{13}[/tex]
The diameter of a circle is 18 millimeters. What is the circle's circumference?
Answer:
he circumference of the circle is approximately 56.52 millimeters.
Step-by-step explanation:
The circumference of a circle is given by the formula:
C = πd
where C is the circumference, d is the diameter, and π is a mathematical constant approximately equal to 3.14.
Substituting the given value of the diameter, we get:
C = πd = π(18) = 56.52 mm (rounded to two decimal places)
Therefore, the circumference of the circle is approximately 56.52 millimeters.
9. Liam ran 12 miles total over the weekend. He
ran 5.5 miles on Saturday. Which equation can
be used to find m, the number of miles he ran
on Sunday?
A. 12 + 5.5 = m
B. 5.5m= 12
C. m-5.5 = 12
D. 5.5+ m = 12
Answer:
x=6.5
Step-by-step explanation:
I'm not sure if it's correct
Ted made a nut mixture that contains 52%
peanuts by mixing together 9 kg of mixed
nuts that contain 20% peanuts and 16 kg
of a different brand of mixed nuts. The
second brand of mixed nuts contained
what percent peanuts?
Let's call the added amount of kg of mixed nuts that contain
40
%
peanuts
m
a
d
d
e
d
. If the new mixture contains
34
%
peanuts, then:
m
peanuts
m
total
=
0.34
The bag of
6
kg
already contained
0.3
⋅
6
=
1.8
kg
of peanuts. Furthermore,
40
%
of
m
added
will be peanuts. This means that:
m
peanuts
=
0.4
m
added
+
1.8
The total mass will be the original
6
kg
plus the added mass, so
m
total
=
m
added
+
6
.
This gives us the following equation.
0.4
m
added
+
1.8
m
added
+
6
=
0.34
Multiply both sides with
m
added
+
6
.
0.4
m
added
+
1.8
=
0.34
(
m
added
+
6
)
Multiply out the brackets.
0.4
m
added
+
1.8
=
0.34
m
added
+
2.04
Subtract
0.34
m
added
from both sides.
0.04
m
added
+
1.8
=
2.04
Subtract
1.8
from both sides.
0.06
m
added
=
0.24
Divide both sides by
0.06
.
m
added
=
4
Therefore, Jenny must add
4
kg
.
drop-down menu.
An experiment is conducted in which a bead is randomly drawn from a bag, the color is recorded, and then the bead is replaced.
The results of the experiment are given in the table below.
Color
Red
Orange
Yellow
Green
Blue
Purple
Frequency
17
12
10
13
8
5
Which of the following lists would most likely have produced the given experimental results?
Color
List A
List B
Red
33
31
Orange
27
24
Yellow
22
18
Green
30
34
Blue
18
19
Purple
12
5
For the list selected above, what is the theoretical probability of selecting a red bead?
Using the experimental results, if 156 beads are drawn from a bag and returned, which color would have a frequency closest
to 24?
The theoretical probability of selecting a red bead is 0.28.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Given that,
Color Frequency
Red 17
Orange 12
Yellow 10
Green 9
Blue 8
Purple 5
Color List A List B
Red 33 31
Orange 27 24
Yellow 22 18
Green 30 34
Blue 18 19
Purple 12 5
Probability of selecting a red bead = 17/61
= 0.28
Orange color would have a frequency closest to 24.
Therefore, the theoretical probability of selecting a red bead is 0.28.
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I need help on this please
The values a and b should be replaced to rewrite the given expression as (x + a)(x - b).
What is a quadratic function?Generally speaking, the standard form of a quadratic function is given by this mathematical expression;
ax² + bx + c = 0
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
c represents the constant.
Next, we would solve the above quadratic function by using the factorization method;
x² + x - 72 = 0
x² - 8x + 9x - 72 = 0
x(x - 8) + 9(x - 8) = 0
(x + 9)(x - 8) = 0
(x + 9)(x - 8) = (x + a)(x - b).
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Need help???!!!! Please
Answer:
+5&-2
Step-by-step explanation:
Which statement is true about this equation??
y = 2^x + 4
A.
It represents neither a relation nor a function.
B.
It represents a relation only.
C.
It represents a function only.
D.
It represents both a relation and a function.
Answer: The correct answer is C. It represents a function only.
A function is a special type of relation where each input value is associated with only one output value. In other words, for every x in the domain of the function, there is only one corresponding y in the range.
In this equation, y = 2^x + 4, for every value of x, there is a unique corresponding value of y. So, it satisfies the requirement of a function and represents a function only.
Step-by-step explanation:
Answer:
D. It represents both a relation and a function
Hope this helps!
Step-by-step explanation:
All functions are relations, but not all relations are functions. The equation given is an Exponential function.
Copy each statement. Insert , -, x, + or division symbol to make each statement true.
27 3 5 2 = 19
81 11 8 4 1 = 60
The Complete statement are:
1. 27/3 + 5 x 2
2. 81 + 1 - 8 x 4 x 1 = 60
What are Arithmetic Operations?Combining operands with a single arithmetic operator specifies an arithmetic operation. The ADD, SUBTRACT, DIVIDE, and MULTIPLY can also be used to specify arithmetic operations.
Given:
we have to apply the operation to make
27 3 5 2 = 19
81 11 8 4 1 = 60
so, first 27 3 5 2 = 19
1. 27/ 3 = 9
2. 5 x 2= 10
3. 9+ 10 = 19
For second,
1.81 + 11 = 92
2. 8 x 4 x 1 = 32
3. 92-32 = 60
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Marcus has 19 blueberry muffins that he wants to share equally with his two
friends. How many blueberry muffins will Marcus and his two friends receive?
Answer: 6 and 1/3
Step-by-step explanation:
Assuming that sweet generous little Marcus here wants some muffins too, he has to share 19 blueberry muffins between 3 people (Marcus + friend 1 + friend 2.)
Most unfortunately, 19 isn't divisible by 3 to create a whole number (ie. a whole muffin).
Therefore you have 2 options:
Option 1:
19/3 = 6.333....
This means that each person will get 6 and 1/3 of a muffin
Option 2:
19/3 = 6 (and 1 remainder)
This means that each person will get 6 muffins each, but there will be a leftover muffin to feed the birds or something.
(I personally prefer option 2, but I think your teacher is looking for option 1.)
Write an equation in slope-intercept form for the line that passes through each pair of points.
(-7, -3) (-3, 5)
The equation of line passes through the points (- 7, -3) and (-3, 5) will be;
⇒ y = 2x + 11
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (- 7, -3) and (-3, 5).
Now,
Since, The equation of line passes through the points (- 7, -3) and (-3, 5).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (5 - (-3)) / (-3 - (-7))
m = 8 / 4
m = 2
Thus, The equation of line with slope 2 is,
⇒ y - (-3) = 2 (x - (-7))
⇒ y + 3 = 2 (x + 7)
⇒ y + 3 = 2x + 14
⇒ y = 2x + 14 - 3
⇒ y = 2x + 11
Therefore, The equation of line passes through the points (- 7, -3) and
(-3, 5) will be;
⇒ y = 2x + 11
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Factor the trinomial 2x²
-
2x
3x - 9 using the box method
The factorization of 2x² - 2x - 3x + 9 using the box method is (2x - 3)(x - 3).
How to factor the trinomial using box methodTo factor the trinomial 2x² - 2x - 3x + 9 using the box method, we first draw a box and divide it into four sections:
| 2x -3 |
|--------|
| -2x 9 |
Then, we fill in the top left section with the coefficient of the leading term, 2x, and the bottom right section with the constant term, 9.
| 2x -3 |
|--------|
| -2x 9 |
Next, we find two numbers that multiply to 2x * 9 = 18 and add to the coefficient of the middle term, -2x - 3x = -5x.
One way to do this is to factor out 2 from the leading two terms, giving 2x² - 2x - 3x + 9 = 2x(x - 1) - 3(x - 3), and then finding the product of (x - 1) and (x - 3) using the AC method:
AC method:
- The product of A and C is -9- The sum of A and C is -4 (since B = -5, which is the sum of A and C)- Find two numbers that multiply to -9 and add to -4: -9 and 1- Rewrite B as the sum of these two numbers, using the distributive property:2x(x - 1) - 3(x - 3) = 2x(x - 1) - 3x + 9 - 3(-1)
We can then place these two numbers in the remaining two sections of the box:
| 2x -3 |
|--------|
| -2x 9 |
| 2x -3 |
|--------|
| -2x 9 |
|--------|
| -3 1 |
We can now factor the trinomial by taking the common factor out of each row and column of the box:
2x(x - 1) - 3x + 9 - 3(-1)
= (2x - 3)(x - 3)
Therefore, the factorization of 2x² - 2x - 3x + 9 using the box method is (2x - 3)(x - 3).
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What does 250 represent in the function y = 250(2.3)"?
250 in the function given represents the exponential constant.
What is function? What is expression?A function is a relationship between a dependent {y} and independent variable {x}.An expression is a combination of terms both constants and variables.Given is the exponential function as -
y = 250(2.3)ˣ
In the exponential function given, 250 represents the exponential constant.
An exponential function is of the form -
y = A(B)ˣ
Therefore, 250 in the function given represents the exponential constant.
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For the points P and Q do the following.
(a) Find the distance d(P,Q).
(b) Find the coordinates of the midpoint M of the segment PQ.
P (3√2,5√3), Q(√2,-√3)
The solution is, the distance = √116.
What is distance?The distance between two points is the length of the line joining the two points.
Formula: distance= √(x_2-x_1)²+(y_2-y_1)²
here, we have,
given that,
P (3√2,5√3), Q(√2,-√3)
so, the distance d(P,Q).
by using the formula we get,
the distance = √108 + 8
= √116
Hence, The solution is, the distance = √116.
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How does the formula for the sample mean differ from the formula for the Population mean?
The formulas are functionally the same, but 'n' (the sample size) is used instead of 'N' (the population size).
The sample mean is the average value for a set of observations which is derived from a population. While the population mean is the average value for the entire set of observation belonging to a particular study of interest.
The set of observation belonging to a population is denoted by 'N' ; while the sample size is denoted as 'n' :
The mean formula is written thus :
Population mean = Σx / N
Sample mean = Σx / n
Where, x = set of values.
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Please help. what is an equation of the line best fit. This is urgent
a. The line of the best fit is ŷ = -8.55485X + 118.39451.
b. The value of the correlation coefficient is -0.8619.
What is the line of best fit?A straight line that minimizes the gap between it and certain data is called a line of best fit. In a scatter plot containing several data points, a relationship is expressed using the line of best fit. It is a result of regression analysis and a tool for forecasting indicators and price changes.
Sum of X = 117.4
Sum of Y = 298
Mean X = 10.6727
Mean Y = 27.0909
The sum of squares (SSX) = 0.8618
The sum of products (SP) = -7.3727
Regression Equation = ŷ = bX + a
b = SP/SSX = -7.37/0.86 = -8.55485
a = MY - bMX = 27.09 - (-8.55*10.67) = 118.39451
ŷ = -8.55485X + 118.39451
X Values
∑ = 117.4
Mean = 10.673
∑(X - Mx)² = SSx = 0.862
Y Values
∑ = 298
Mean = 27.091
∑(Y - My)² = SSy = 84.909
X and Y Combined
N = 11
∑(X - Mx)(Y - My) = -7.373
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = -7.373 / √((0.862)(84.909)) = -0.8619
Therefore, the line of the best fit is ŷ = -8.55485X + 118.39451
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Q5. The volume of a cone is 128 cm³. The height of the cone is three time the length of the diameter of its base. Calculate the height of the cone.
The height of the cone in discuss as required to be determined is; 16.38 cm.
What is the height of the cone as described?Since the height of the cone is three times the length of the diameter of its base;
h = 3d;
d = h/3
Therefore, radius,
r = d/2
r = h/3 ÷ 2
multiply by the reciprocal of 2
r = h/3 × 1/2
r = h / 6.
Volume of a cone, V = (1/3) πr²h
128 = (1/3) × (22/7) × (h³/36)
h³ = 4398.55
h = 16.38 cm.
Ultimately, the height of the cone is; 16.38 cm.
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2x + 3y = 12
2x - y = 4
Answer:
The point of intersection between 2x+3y=12 and 2x-y=4 is (3,2)
Step-by-step explanation:
I NEED HELP ON THIS ASAP!!
The solution of both inequalities is (-1, 2).
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
We have the inequalities
x+ y >1.........(1)
-x+ y <3.........(2)
The graph for x+ y >1 is shown by the red shaded region.
and, the graph for -x+ y <3 is shown by the blue shaded region.
Also , the Inequality intersect at (-1, 2) which shows the solution of both inequalities.
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Which graph represents data points that have no correlation?
Answer:
bottom-right
Step-by-step explanation:
the points on the graph are scattered and have no correlation whereas the others all remain in a relatively similar shape
What are the x and y coordinates of the following equations?
y = x - 3
y = 2x + 2
Answer: The coordinates where the two lines intersect are (-5, -8).
Step-by-step explanation:
To find the coordinates where the two lines intersect, we need to solve the system of equations simultaneously. We can do this by substitution or elimination, but we'll use substitution here:
First, we set the two equations equal to each other:
x - 3 = 2x + 2
Next, we solve for x:
x - 2x = 2 + 3
-x = 5
x = -5
Now that we have the value of x, we can substitute it into one of the original equations to find the corresponding value of y. Let's use the first equation:
y = x - 3
y = (-5) - 3
y = -8
The sides of a triangle measure 32 inches, 22 inches, and 19 inches. What is the area of the triangle? Round intermediate results to 3 decimal places and the final answer to 1 decimal place. The area of the triangle is?
The area of the given triangle is approximately 204.2 square inches.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.
To calculate the area of a triangle with given side lengths, we can use Heron's formula:
Area = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter of the triangle (half of the perimeter), and a, b, and c are the lengths of the sides.
In this case, the lengths of the sides are a=32, b=22, and c=19. Therefore, the semi-perimeter is:
s = (a + b + c) / 2 = (32 + 22 + 19) / 2 = 36.5
Now we can plug in these values into the formula and simplify:
Area = √(36.5(36.5-32)(36.5-22)(36.5-19)) ≈ 204.16
Rounding this to 1 decimal place, the area of the triangle is approximately 204.2 square inches.
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You want to save up to buy a car. You currently have $500 saved and are going to work this summer cleaning house for your grandma. She will pay you $50 every time you clean her house. Write an equation for this situation. Make sure you define your variables. (How many times will you need to clean her house to have $4,500 for the car you want to buy?
I need answer by 2/25/2023
80 times, the house should be cleaned to buy the car.
Equation for the amount is y = 50t + 500
What is linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.
Given,
Amount in the savings = $500
Amount to get the car = $4500
Grandma pays $50 for every time after cleaning
then, after t times, the amount will be
y = 50 t + 500
here, y is the total amount after working
t is number of times of cleaning the house
For $4500
4500 = 50t + 500
50t = 4500 - 500
50t = 4000
t = 4000/50
t = 80
Hence, we have to clean the house 80 times to have $4500.
equation for the amount is y = 50t + 500
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This graph represents the amount of milk in a bottle in the fridge. Tell a story of the amount of milk in the bottle.
The milk bottle, item is the best example of an artifact from the passage that reveals something about sign. Thus, option (a) is correct.
What is passage?The term “passage” refers to the explanation and description of a sentence in relation to a topic. The passage aimed to describe those details related to the theme of the story. The different passage is to justify to the different things as to clarify. The passage is to define the important terms.
The milk bottle sat on the central shelf, as mentioned in the passage. The artifact is a completely empty milk bottle. The section gives information regarding signs. The passage was Sig's refrigerator, which had been opened. A milk bottle sat on the middle shelf, its cap missing and no milk inside.
As a result, the milk bottle, item is the best example of an artifact from the passage that reveals something about sign. Therefore, option (a) is correct.
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A car travels at an average speed of 80 km/h for 2 hours. What distance does the car travel? c) A car travels a distance of 330 km at an average speed of
If the tire height is 5.2 in. and the rim diameter is 17 in., what is the tire diameter?
Answer:
Circumference = (3.14)(15) = 47.1 in
Step-by-step explanation: