a.
tx) = -9x^2 + 12x - 4
t"x) = -18x + 12
Entering these into a graphing calculator or software, we can examine the table.
b.
To find any critical values, we set the first derivative t'(x) = 0.
t'(x) = -18x + 12 = 0
Solving for x, we get x = 2/3.
We can check if this is a maximum or minimum by using the second derivative test. The formula for f"(x) is the derivative of t'(x), which is t"(x).
t"(x) = -18
t"(2/3) = -18, which is negative. This means that at x = 2/3, there is a local maximum.
Therefore, the answer is:
OB. The function has a critical number at 2/3. At this critical number, the second derivative is negative.
Hi! I understand that you want to find the critical numbers of the given function f(x) = -3x + 6x^2 - 4x - 1. Let's first find the first and second derivatives, and then analyze them to find the critical numbers.
a. The first derivative, f'(x), is found by taking the derivative of f(x) with respect to x:
f'(x) = d(-3x + 6x^2 - 4x - 1)/dx = -3 + 12x - 4
The second derivative, f''(x), is found by taking the derivative of f'(x) with respect to x:
f''(x) = d(-3 + 12x - 4)/dx = 12
b. To find critical numbers, set f'(x) = 0 and solve for x:
0 = -3 + 12x - 4
Combine the constants and simplify:
0 = 12x - 7
Now, solve for x:
x = 7/12
So, there is one critical number at x = 7/12. To determine the nature of this critical number, check the value of the second derivative, f''(x), at this point:
f''(7/12) = 12
Since the second derivative is positive, the function has a local minimum at this critical number.
In conclusion, the function has one critical number at x = 7/12, and there is a local minimum at this point.
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Please help me with trig I’d really appreciate
Answer:
2 root 10/ 7, or the second option.
Step-by-step explanation:
If a is 3, then b is root 40. (Pythagorean)
root 40= root 4x10, or 2 root 10
Tangent= opposite/hypotenuse
Tangent= 2 root 10/ 7
3 m
4 m
5 m
The length of the prism ism.
The width of the prism is m.
The height of the prism is
The prism holds a total of
The volume ism³.
✓m.
cubes.
Answer:
the volume of the prism is 60 cubic meters (m³).
Step-by-step explanation:
We can calculate the volume of the rectangular prism by multiplying its length, width, and height.
Given:
Length = 3 m
Width = 4 m
Height = 5 m
The volume of the rectangular prism is:
Volume = length x width x height
Volume = 3 m x 4 m x 5 m
Volume = 60 m³
Therefore, the volume of the prism is 60 cubic meters (m³).
What is a z score in statistics?
Answer:
Below
Step-by-step explanation:
Z score is the ± standard deviations from the mean
From your conclusions in part E, how many triangles can be constructed based on the given conditions?
What are the given conditions?
Hillary’s summer job at the frozen yogurt shop paid her the amounts shown in the table below in her first three days on the job (she got paid the same hourly rate every day).
Answer:
P=9.0h
Step-by-step explanation:
Divide the Paid amount by the hours worked and you'll get how much money she gained every hour which is 8.50$ And the question is telling you which of the following equations is GREATER than the amount she got paid per hour. So the answer would be P=9.0h
The required equation represents an hourly pay rate that is greater than Hillary's hourly pay rate p = 9.0h. Option D is correct.
Given,
Hillary’s summer job at the frozen yogurt shop paid her the amounts shown in the table below in her first three days on the job (she got paid the same hourly rate every day).
day = 1 2 3
Hours worked(h) = 5 4 6
Amount paid (p) = $42.50 $34 $51
The slope of the line is the tangent angle made by line with horizontal. i.e. m = tanx where x in degrees.
The slope of the data given,
m = 42.5/5
m = 8.5
the slope shows the hourly rate to get paid.
Required expression is
p = 8.5h
From the option, the slope of equations needs to compare greater the slope greater will the hourly rate.
Slope of equation A = 1/8, B =8, C = 8.5 and D = 9.0
hence, only slope D has a greater value by the existing slope of 8.5
Thus, the required equation that represents an hourly pay rate that is greater than Hillary's hourly pay rate p = 9.0h.
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Question is incomplete, correct question has added below.
solve the following equation in terms of x.
20x - 3y = z
Answer:
(3y+z)/20
Step-by-step explanation:
Begin by moving 3y to the right side of your equation:
20x=3y+z
Then divide both sides by 20 isolating x on one side of your equation:
x=(3y+z)/20
The required solution of the following equation 20x - 3y = z is
x=(3y+z)/20
What is equation?
An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.
Given:
The following equation is
20x - 3y = z
According to given question we have
The equation is
20x - 3y = z
By simplifying we have to solve in terms of x
By move 3y to the right side of your equation:
20x=3y+z
Then divide both sides by 20 isolating x on one side of your equation:
x=(3y+z)/20
Therefore, the required solution of the following equation 20x - 3y = z is
x=(3y+z)/20
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Please help on this practice paper my parents couldn’t solve this either
We are given that ,
\({:\implies \quad \sf \dfrac{12+\sqrt{128}}{1-\sqrt{2}}=a+b\sqrt{2}}\)
Consider LHS;
\({:\implies \quad \sf \dfrac{12+\sqrt{128}}{1-\sqrt{2}}}\)
Can be further written as ;
\({:\implies \quad \sf \dfrac{12+8\sqrt{2}}{1-\sqrt{2}}}\)
Rationalizing the denominator we have ;
\({:\implies \quad \sf \dfrac{12+8\sqrt{2}}{1-\sqrt{2}}\times \dfrac{1+\sqrt{2}}{1+\sqrt{2}}}\)
\({:\implies \quad \sf \dfrac{(12+8\sqrt{2})(1+\sqrt{2})}{(1-\sqrt{2})(1+\sqrt{2})}}\)
\({:\implies \quad \sf \dfrac{12(1+\sqrt{2})+8\sqrt{2}(1+\sqrt{2})}{1-2}}\)
\({:\implies \quad \sf \dfrac{12+12\sqrt{2}+8\sqrt{2}+16}{-1}}\)
\({:\implies \quad \sf \dfrac{28+20\sqrt{2}}{-1}}\)
\({:\implies \quad \sf -28-20\sqrt{2}}\)
Hence, we can conclude that ;
\({\bf a=-28}\) \({\bf b=-20}\)Find the power set for the following sets (Write 3 examples of each)
a) Two sets A & B both having any 2 elements
b) Two sets A & B both having any 3 elements
c) Two sets A & B both having any 4 elements
Given statement solution is :- a) Power set for two sets A and B with any 2 elements:
Set A: {1, 2}, Set B: {3, 4}
Power set of A: {{}, {1}, {2}, {1, 2}}
Power set of B: {{}, {3}, {4}, {3, 4}}
b) Power set for two sets A and B with any 3 elements:
Set A: {1, 2, 3}, Set B: {4, 5, 6}
Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}
c) Power set for two sets A and B with any 4 elements:
Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}
Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}
Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},
a) Power set for two sets A and B with any 2 elements:
Set A: {1, 2}, Set B: {3, 4}
Power set of A: {{}, {1}, {2}, {1, 2}}
Power set of B: {{}, {3}, {4}, {3, 4}}
Set A: {apple, banana}, Set B: {cat, dog}
Power set of A: {{}, {apple}, {banana}, {apple, banana}}
Power set of B: {{}, {cat}, {dog}, {cat, dog}}
Set A: {red, blue}, Set B: {circle, square}
Power set of A: {{}, {red}, {blue}, {red, blue}}
Power set of B: {{}, {circle}, {square}, {circle, square}}
b) Power set for two sets A and B with any 3 elements:
Set A: {1, 2, 3}, Set B: {4, 5, 6}
Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}
Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}
Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}
Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}
Set A: {red, blue, green}, Set B: {circle, square, triangle}
Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}
Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}
c) Power set for two sets A and B with any 4 elements:
Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}
Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}
Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},
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help math pklz hekllo
Answer:
ইহেবে জেজে জেহব ইঞ্জিন জেবি জেজেবেজে jeiehbbr রুরুরব এভে
There are 180 puppies in the shelter with 9 kids. How many students puppies per kids?
The number of puppies per kids is 20 puppies.
Given that, there are 180 puppies in the shelter with 9 kids.
Number of puppies per kids = Total number of puppies/Number of kids
= 180/9
= 20 puppies
Therefore, the number of puppies per kids is 20 puppies.
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if n is a positive integer, how many integers from 0 through 2n must you pick in order to be sure of getting at least one that is odd? how many integers must be picked in order to be sure of getting at least one that is even?
To guarantee to select at least one odd integer, pick one from {1,3,5,...,2n-1}. To guarantee at least one even integer, pick two from {0,2,4,...,2n}.
To be sure of getting at least one odd integer, you need to pick just one integer from the set {1,3,5,...,2n-1}. Any integer in this set is odd, so selecting just one integer guarantees that you will get an odd integer.
On the other hand, to be sure of getting at least one even integer, you need to pick two integers from the set {0,2,4,...,2n}. If you pick only one integer from this set, it could be an odd integer, which means you didn't get an even integer. But if you pick two integers, at least one of them must be even. This is because if you pick two odd integers, their sum will be even, and if you pick an even integer and an odd integer, their sum will be odd.
In summary, to be sure of getting at least one odd integer, you need to pick one integer from {1,3,5,...,2n-1}, and to be sure of getting at least one even integer, you need to pick two integers from {0,2,4,...,2n}.
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An____is an outcome of a population that has some probability of being selected.
An "event" is an outcome of a population that has some probability of being selected.
In statistics, an event refers to a specific outcome or combination of outcomes of an experiment or random process. It represents a subset of the sample space, which is the set of all possible outcomes.
For example, let's consider rolling a fair six-sided die. The sample space consists of the numbers 1, 2, 3, 4, 5, and 6. An event could be rolling an even number, which consists of the outcomes 2, 4, and 6. Each of these outcomes has an equal probability of 1/6.
Events can also be combined using logical operators. For instance, the event of rolling a number greater than 3 and less than 6 would consist of the outcome 4 and 5. The probability of this event would be 2/6 or simplified, 1/3.
In summary, an event is a specific outcome or combination of outcomes from a population, and it has a certain probability of being selected.
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An "outcome" is an outcome of a population that has some probability of being selected.
An "outcome" refers to a specific result or observation that can occur in a given situation or experiment. In the context of a population, an outcome represents one possible result that could be selected or observed.
When we talk about a population, we are referring to a group of individuals or items that share a common characteristic. For example, a population could be all the students in a school, all the trees in a forest, or all the cars in a city.
In statistics, we often take samples from populations to make inferences or draw conclusions about the entire population. When selecting a sample from a population, each individual or item in the population should have some probability of being chosen. This ensures that the sample is representative of the population and provides reliable information.
For example, if we want to study the average height of all students in a school, we might randomly select a sample of students from the population (all students in the school). Each student in the population has some chance of being selected, which means each student represents a potential outcome of the sample.
In summary, an outcome in the context of a population refers to a specific result or observation that has some probability of being selected from the population.
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Evaluate the expression shown below and write your answer as a fraction in
simplest form.
3/4 - 3/10
Which of the following expressions represents the total earnings of a commissioned employee earning 9. 5% commission with sales of $8,540? a. (0. 0095)(8,540) b. (0. 095)(8,540) c. (0. 95)(8,540) d. (9. 5)(8,540).
Answer:
Option B
Step-by-step explanation:
So we should first convert 9.5% into decimal point: 9.5/100= 0.095match your value to the options: 0.095(8540) (option b)you could evaluate if you want: 0.095(8540)= $811.3 in commission salesPlease help me, I struggle the most in this class and this is the last question
What is 108 as a fraction of 648? Give your answer in its simplest form.
Answer:
The simplest form of 108/648 is 16
For the given condition 108 as a fraction of 648 will be 108/648.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have to write 108 as a fraction of 648, in simplified form.
p as the fraction of q in the simplified form can be written as,
=p/q
For the given condition we have to write the 108 as a fraction of 648 in the simplified form.
Write the fraction's numerator, hyphenate it, and then spell out the denominator to represent it verbally. The phrase p/q would be used to represent the fraction 108/648.
Thus, for the given condition 108 as a fraction of 648 will be 108/648.
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The chart below shows the distribution of the number of books in a library.
A circle graph titled Types of Books. The largest proportion is Literature, then Fantasy, then non-fiction, then children's.
Sahira chooses a random sample from the library and records the type of books in the chart below.
Type of Book
Number
Fantasy
10
Literature
25
Children’s
4
Nonfiction
11
Which explains whether or not Sahira’s sample is representative?
No, it is not representative because literature books were chosen much more often than the other types.
Yes, it is representative because each type of book was chosen a unique number of times.
Yes, it is representative because each type of book was represented in the approximate proportion that exists in the library.
Yes, it is representative because each type of book was selected as part of the sample.
Mark this and return
Answer:
Yes, it is representative because each type of book was represented in the approximate proportion that exists in the library.
Step-by-step explanation:
Given is a chart, showing the distribution of the number of books in a library.
Also given that Sahira chooses a random sample from the library and records the type of books in the chart below.
Sahira's sample can be said to be representative because given that books are taken at random. So just because literacy books were more we cannot say it is not representative II option is not right, because each book was not chosen uniquely, just random books were drawn
Lastly The Answer is C) Yes, it is representative because each type of book was represented in the approximate proportion that exists in the library is right, because each book selected represents the sample from population of full library books.
Answer:
it is c
Step-by-step explanation:
just did it
solve for x: (1/3)(x+3)=-(x-1)
Step-by-step explanation:
your answer
have nice day
Dr. peterson works 178 hours each month.how many hours dose she work each year?
Answer:
2,136
Step-by-step explanation:
Okay so, Dr. Peterson works 178 hours per month
You multiply 178 times 12 (the months in a year)
Please help! I don’t understand. Thank you! (10 points) you went to the mall with $45. you spent 40% of your money on a new hat. of the remaining money, you spent 15% on a snack. how much did you spend on the snack? show your thinking.
Answer:
$4.05
Step-by-step explanation:
40% of $45 =
(45 x 40)/100
= $18
Remaining money after spending on a hat
= $45 - $18 = $27.
15% of $27 spent on a snack
= (27 x 15) / 100 = $4.05
so
$4.05 was spent on the snack
if a vector a has components ax < 0, and ay > 0, then the angle that this vector makes with the positive x-axis must be in the range group of answer choices 180° to 270° 0° to 90° 270° to 360° it cannot be determined without additional information. 90° to 180°
The angle vector 'a' makes with the positive x-axis is 90° to 180°.
What is a vector?A vector is a quantity that has magnitude as well as direction one such example of this is velocity where we describe speed and direction also.
Given a vector a with two components one in the x direction and another one in the y direction.
The x component of the vector ax < 0 which is on the 2nd quadrant and the y component of the vector is ay > 0 which we join to the tail of the component ax.
∴ The angle it makes with the positive x-axis is 90° to 180° as it is on the second quadrant.
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Find the measure of
=======================================================
Explanation:
The angles SPT and TPU marked in red are congruent. They are congruent because of the similar arc markings.
Those angles add to the other angles to form a full 360 degree circle.
Let x be the measure of angle SPT and angle TPU.
86 + 154 + 60 + x + x = 360
300 + 2x = 360
2x = 360-300
2x = 60
x = 60/2
x = 30
Each red angle is 30 degrees.
Then,
angle SPQ = (angle SPT) + (angle TPU) + (angle UPQ)
angle SPQ = (30) + (30) + (86)
angle SPQ = 146 degrees
--------------
Another approach:
Notice that angles QPR and RPS add to 154+60 = 214 degrees, which is the piece just next to angle SPQ. Subtract from 360 to get:
360 - 214 = 146 degrees
Which statement is true about this equation? 3(-y 7) = 3(y 5) 6.
The statement that is true about the equation 3(-y + 7) = 3(y + 5) + 6 is;
Statement A; The equation has one solution, y = 0
The given equation is;
3(-y + 7) = 3(y + 5) + 6
Expanding the brackets gives us;
-3y + 21 = 3y + 15 + 6
-3y + 21 = 3y + 21
Using subtraction property of equality, subtract 21 from both sides to give;
-3y = 3y
Using addition property of equality, add 3y to both sides to give;
-3y + 3y = 3y + 3y
6y = 0
Using division property of equality, divide both sides by 6 to get;
y = 0
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The missing statements are;
A. The equation has one solution, y = 0.
B. The equation has one solution, y = -1.
C. The equation has no solution.
D. The equation has infinitely many solutions.
COMPUTE THE AREA PARALLELOGRAM DETERMINED BY U= (4,-1) AND V = (-6,-2).
To compute the area of a parallelogram determined by two vectors U = (4, -1) and V = (-6, -2), we can use the formula that states the area of a parallelogram is equal to the magnitude of the cross product of the two vectors. Therefore, the area of the parallelogram determined by U = (4, -1) and V = (-6, -2) is 28 square units.
The formula to compute the area of a parallelogram determined by two vectors U and V is given by:
Area = |U x V|
To calculate the cross product U x V, we can use the following determinant:
| i j k |
| 4 -1 0 |
|-6 -2 0 |
Expanding the determinant, we get:
i * (0 * -2 - 0 * -2) - j * (4 * -2 - 0 * -6) + k * (4 * -2 - (-1) * -6)
= -12i + 24j + 8k
Taking the magnitude of the cross product, we have:
|U x V| = √((-12)^2 + 24^2 + 8^2) = √(144 + 576 + 64) = √784 = 28
Therefore, the area of the parallelogram determined by U = (4, -1) and V = (-6, -2) is 28 square units.
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the mean and the standard deviation of a normal population are called statistics . the mean and the standard deviation of a random sample from a population are called .
The mean and standard deviation of a normal population are called parameters, and the mean and standard deviation of a random sample in the population are called statistics.
Normally distributed data:
In a normal distribution, data is distributed symmetrically without asymmetry the data are probabilities whose distribution is symmetrical with respect to the mean.
The normal distribution is symmetric, unimodal and asymptotic, and the mean, median and mode are all equal.
In statistics, standard deviation is a measure of the amount of variation or distribution of a set of values. A low standard deviation indicates that the values tend to be close to the ensemble mean (also called the expected value), while a high standard deviation indicates that the values are spread over a wide range.
For solving the problems are :
The average of the data is the average of the given data. The standard deviation of the data is half the difference between the highest value in the data set and the mean.
These numbers that summarize information about a sample are called statistics.
The numbers that summarize information about a population are called parameters.
Numbers that summarize information about a sample are called statistics.
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Answer:
(B) Parameters
(A) Statistics
Step-by-step explanation:
egg 2023
Determine the perimeter of the athletic track
Answer:
418.2477796 m
Step-by-step explanation:
You divide it in to a rectangle and 2 half circles (which will make a whole circle if added together) and solve them.
RECTANGLEP= 2( L + W) - - > 2 ( 102 + 60)= 324
Circle (has a circumference not a perimeter)Cf= 2лr^2 - - - > 2л(30)^2=30л
Together324 + 30л = 418.2477796 m
AM= 2x+6, MB= 4x-2, and AB= 22, by solving for x, determine whether or not M is the midpoint of AB
Answer:
Step-by-step explanation:
Please help me with this
Answer:
.3 repeating
Step-by-step explanation:
Answer:
b=-4/21
Step-by-step explanation:
Which point on the number line represents the product (5)(-2)(-1)?ABСD-11 -10 -93 -7 -6 -5 4 -3 -2 -1012345 6 7 8 9 10 11Point AO Point BO Point CPoint D
In order to determine which point represent the given expression (5)(-2)(-1), you first calculate the result of such operation:
(5)(-2)(-1) = 10
Then, the point is 10:
The red circle is the required point.
-1 over 5 divided by 7 over 4
Answer:-0.00714
Step-by-step explanation: STEP
1
:
1
Simplify —
5
Equation at the end of step
1
:
1
0 - — ÷ 7 ÷ 4
5
STEP
2
:
1
Divide — by 7
5
Equation at the end of step
2
:
1
0 - —— ÷ 4
35
STEP
3
:
1
Divide —— by 4
35
Equation at the end of step
3
:
1
0 - ———
140
STEP
4
:
Final result :
-1
——— = -0.00714
140