The maximum number changes of direction (turning points) = 3
What is Direction?
The direction of an object's motion or tendency is indicated by its direction.
The main directions are East, South, West, and North.
Concept:
Not every cubic function has a definite turning point. but their are 3 turning point and depends upon the type of the cube
The first derivative of the function becomes zero and the second derivative might either be positive or negative at a turning point of the function.
The function would not have a turning point if the set of real numbers containing the roots of the first derivative of the function included none.
The point would not be a turning point but an inflexion point of the curve if the function has a root in the set of real numbers but its second derivative is zero at that location. Additionally, such a process would not have a turning point.
Think about the equation f(x)=x3. There isn't a turning point in this function. Rather, it has an inflection point at x=3.
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Using composition of functions, determine if the two functions are inverses of each other. A. No, because the functions contain different operations. B. Yes, for all values x ≥ 0. C. No, because the composition does not result in an answer of x. D. Yes, because F(x) is equal to –G(x).
Yes, for all values x ≥ 0. If the composition of the two functions is equal to the identity function for all values of x in their domain, then the two functions are inverses of each other.
What is composition of functions?Composition of functions is a mathematical operation that involves combining two functions to form a new function. To determine if two functions are inverses of each other using composition of functions, we need to first define the two functions and then determine if the composition of the two functions is equal to the identity function (f(x) = x).If the composition of the two functions is equal to the identity function for all values of x in their domain, then the two functions are inverses of each other. In this case, the correct answer is B: Yes, for all values x ≥ 0.To learn more about composite functions refer :
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question in screenshot (need help ASAP)
Delma finds that it takes 27 paces to walk from her current location to the rock. She also knows that each of her paces is 14 inches long. Explain how she can use this information to estimate the distance across the river.
To estimate the distance across the river, Delma can multiply the number of paces she takes by the length of each pace to find the total distance she walks.
For example, if Delma takes 27 paces and each of her paces is 14 inches long, she can estimate the distance she walks by performing the following calculation:
27 paces * 14 inches/pace = 378 inches
This means that Delma estimates the distance across the river to be 378 inches, or about 31.5 feet.
It's important to note that this is just an estimate, and the actual distance across the river may be slightly different due to factors such as the terrain or the accuracy of Delma's pacing.
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Question 5 of 25
Which inequality is true?
OA />2
OB. 107> 30
C. 8-n> 5
D. π+4<7
SUBM
The true inequality in the list of options is (a) 6π > 2
How to determine the true inequality?From the question, we have the following inequality that can be used in our computation:
6π > 2, 7π > 30, 8 - π > 5 and π + 4 < 7
The value of the constant π is 3.142
So, we solve for π in the inequality expressions
A.6π > 2
This gives
π > 2/6
Divide
π > 0.33 -- true
B. 7π > 30
Divide
π > 4.29 -- false
C. 8 - π > 5
This gives
π < 3 -- false
D. π + 4 < 7
This gives
π < 3 -- false
Hence, the true inequality is 6π > 2
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Complete question
Which inequality is true?
A. 6π > 2
B. 7π > 30
C. 8 - π > 5
D. π + 4 < 7
(redo) A mistake was made in the steps shown to simplify the expression. which step includes the mistake?? EDMENTUM
The step in which there was a mistake in the simplification of the expression is given as follows:
A. Step 5.
How to simplify the expression?The expression in this problem is defined as follows:
(1 + 3²)/5 + |-10|/2
The first step is applying the absolute value of -10, which is the distance of -10 from the origin of 0, hence it is of 10 and the expression is given then by:
(1 + 3²)/5 + 10/2.
Then the square is applied to 3², as 3 x 3 = 9, hence:
(1 + 9)/5 + 10/2
The parenthesis takes precedence, hence:
10/5 + 10/2.
The first quotient takes precedence, hence:
2 + 10/2.
Then in Step 5 there was the mistake, as the quotient takes precedence over the addition, meaning that the expression should have been simplified as follows:
2 + 5 = 7.
This means that option A is correct.
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Given MN is perpendicular to MP, PQ is perpendicular to MP, and NR is congruent to OR. Prove triangle NRP is congruent to triangle QRM
1. [tex]\overline{MN} \perp \overline{MP}[/tex], [tex]\overline{PQ} \perp \overline{MP}[/tex] (given)
2. [tex]\angle NMP[/tex] and [tex]\angle MPQ[/tex] are right angles (definition of perpendicular lines)
3. [tex]\angle NMP \cong \angle MPQ[/tex] (all right angles are congruent)
4. [tex]\overline{NR} \cong \overline{QR}[/tex] (given)
5. [tex]\angle NRM \cong \angle QRP[/tex] (vertical angles)
6. [tex]\triangle PRQ \cong \triangle MRN[/tex] (AAS)
7. [tex]\overline{MR} \cong \overline{RP}[/tex] (CPCTC)
8. [tex]\angle NRP \cong \angle MRQ[/tex] (vertical angles)
9. [tex]\triangle NRP \cong \triangle QRM[/tex] (SAS)
what is the the difference between a repeating decimal and a nonstop decimal on the rational numbers chart
Repeating decimals are those numbers that, following the decimal point, continue to repeat the same value. The term "non-repeating rational numbers" refers to decimal numbers that do not repeat their value after the decimal point.
Repeating decimals are those numbers that, following the decimal point, continue to repeat the same value. Recurring numbers is another name for these figures. The term "non-repeating rational numbers" refers to decimal numbers that do not repeat their value after the decimal point.
A repeating decimal can be a rational number, and any integer is a rational number since it can be expressed as a fraction by simply assigning it a denominator of 1. Then, by multiplying and dividing the decimal according to its place values, we can also state that a terminating decimal can be expressed as a fraction.
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The length of a rectangle is four times its width.
If the perimeter of the rectangle is 100 m, find Its area.
Answer:4
Step-by-step explanation:
rectangular prism 1 829 equals the conterpostiive
The base of triangle exceeds the height by 4cm if the area is 30cm² then find the langth of base & hight of triangle
Answer:
Base = 10 cm
Height = 6 cm
Step-by-step explanation:
Here is the formula for the area of a triangle.
[tex]A=\frac{bh}{2}[/tex]
We are given
[tex]A=30[/tex]
[tex]b=h+4[/tex]
Replace all occurrences of [tex]b[/tex] with [tex]h+4[/tex] in each equation.
[tex](h+4)*\frac{h}{2} =30[/tex]
Apply the distributive property.
[tex]h(\frac{h}{2})+4(\frac{h}{2})=30[/tex]
[tex]\frac{h*h}{2}+4(\frac{h}{2})=30[/tex]
Use the power rule to combine exponents.
[tex]\frac{h^2}{2}+4(\frac{h}{2})=30[/tex]
Factor 2 out of 4 .
[tex]\frac{h^2}{2}+2(2)(\frac{h}{2})=30[/tex]
Cancel the common factor.
[tex]\frac{h^2}{2}+2h=30[/tex]
Solve for h.
Multiply each term in [tex]\frac{h^2}{2}+2h=30[/tex] by 2 to eliminate the fractions.
[tex]\frac{h^2}{2}*2+2h*2=30*2[/tex]
Simplify each term.
Cancel the common factor of 2.
[tex]h^2+2h*2=30*2[/tex]
[tex]h^2+4h=60[/tex]
Subtract 60 from both sides of the equation.
[tex]h^2+4h-60=0[/tex]
Factor using the AC method.
Consider the form [tex]x^2+bx+c[/tex] . Find a pair of integers whose product is [tex]c[/tex] and whose sum is [tex]b[/tex] . In this case, whose product is − 60 and whose sum is 4 .
−6, 10
Write the factored form using these integers.
[tex](h-6)(h+10)=0[/tex]
Set [tex]h-6[/tex] equal to 0 and solve for h.
Then add 6 to both sides of the equation.
[tex]h-6=0\\h=6[/tex]
Set [tex]h+10[/tex] equal to 0 and solve for h.
Then subtract 10 from both sides of the equation.
[tex]h+10=0\\h=-10[/tex]
The final solution is all the values that make [tex](h-6)(h+10)=0[/tex] true.
[tex]h=6,-10[/tex]
Given [tex]b=h+4[/tex]
Replace all occurrences of h with 6 in each equation.
[tex]b=6+4\\b=10\\h=6[/tex]
I need help with these
Answer:
[tex] = \frac{11}{10} \\ \\ [/tex]
this is the correct answer for first question
what is the product of all constants $k$ such that the quadratic $x^2 kx 15$ can be factored in the form $(x a)(x b)$, where $a$ and $b$ are integers?
The value of k as calculated from the information provided is -16 , -8 , 8 , 16.
The given equation is,
x² + kx + 15
= ( x + a ) (x + b)
= x² + (a + b ) x + ab
Therefore,
k = a + b
ab = 15
as known , a and b are integers,
15 = ( -1 x -15 ) , ( 1 x 15)
15 = (-3 x -5) , (3 x 5 )
Therefore,
k = -1 -15
= -16
and
k = -3 - 5
=8
The values of k are -16 , -8 , 8 , 16.
The collection of whole numbers and negative numbers is known as an integer in mathematics. Integers, like whole numbers, do not include the fractional portion. Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions.
On integers, we can carry out all arithmetic operations, including addition, subtraction, multiplication, and division. Integer examples include 1, 2, 5, 8, -9, -12, etc. "Z" stands for an integer.
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a young rattlesnake grows at a rate of about 20 centimeters per year. Write an expression to represent how much ghe rattlesnake grows in y years
The exponential function to show the growth in y years is P(1.2)^y
Exponential FunctionAn exponential function is a mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
In this problem, this is an exponential growth since the rate increases.
Let;
P = Initial lengthA = Length in y yearsr = rate of growthThe exponential function to represent this will be;
A = P(1 + r)^y
A = P(1 + 0.2)^y
A = P(1.2)^y
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Given that a line has a y-intercept of 3 and a slope of 4, write an equation for the line in slope intercept form.
a. y=3x+4
b. y=4x+3
c.y=(-3/4)x+3
d.y=(4/3)x+4
Answer:
equation of the line should be y=3x+4.
Step-by-step explanation:
I apologize if i'm wrong :)
can anyone help me with 17, 18, or 20? i’ll make you a brainliest if you can answer all of them but i need help!!
(17) The value of x would be 20 degrees.
(18) The value of x would be 21.25 degrees.
(20) The value of x would be 6 degrees.
What is the sum of the angles of a triangle?
The sum of the angles of a triangle is 180 degrees. This is a fundamental property of triangles and is known as the triangle sum theorem.
(17)
By using the property of the sum of angles of a triangle, we get
(x+6) + (3x+9) + (4x+5) = 180
Simplifying the left side of the equation gives:
8x + 20 = 180
Subtracting 20 from both sides of the equation gives:
8x = 160
Dividing both sides of the equation by 8 gives:
x = 20°
(18) In a right triangle, one angle is a right angle, which measures 90 degrees. If we know the measures of the other two angles in the triangle, we can use the fact that the sum of the measures of the angles in a triangle is 180 degrees to find the value of x.
(2x-4) + (6x+14) + 90 = 180
Simplifying the left side of the equation gives:
8x + 10 = 180
Subtracting 10 from both sides of the equation gives:
8x = 170
Dividing both sides of the equation by 8 gives:
x = 21.25
(20) To find the value of x, we can use the fact that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. We can write an equation using this fact and the measures of the three angles given in the problem:
(2x+13) + (15x+19) = (7x+92)
Simplifying the left side of the equation gives:
17x + 32 = 7x + 92
Subtracting 7x from both sides of the equation gives:
10x + 32 = 92
Subtracting 32 from both sides of the equation gives:
10x = 60
Dividing both sides of the equation by 10 gives:
x = 6
Hence,
(17) The value of x would be 20 degrees.
(18) The value of x would be 21.25 degrees.
(20) The value of x would be 6 degrees.
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a) what is the cube root of 729
b) describe how to construct a cube root of 729
Answer:
9
Step-by-step explanation:
a.) cube root of 729
³√729
= 9
b.) look for a number that you will multiply thrice to get 729
which is 9 or u will use your calculator
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Word Problems: (please write out the equations and solve it)
1. David is going out for a pizza. The Pizza costs $10.50 plus $1.50 for each extra
topping ,x. Write an equation to represent the total cost of the pizza, t.
Dependent variable:
Independent variable:
Equation:
Use your equation to determine the total cost of the pizza with 3 extra
toppings.
The total cost of the pizza is
Dependent variable: t (total cost of the pizza)
Independent variable: x (number of extra toppings)
Equation: t = 10.50 + 1.50x
To determine the total cost of the pizza with 3 extra toppings, plug in x = 3 into the equation:
t = 10.50 + 1.50(3)
t = 10.50 + 4.50
t = 15.00
So the total cost of the pizza with 3 extra toppings is $15.00.
What is Dependent Variables?
The dependent variable is the variable that is being measured or studied in a statistical or scientific research study. It is called the dependent variable because it is believed to depend on the value of one or more other variables, known as the independent variables.
What is Independent Variables?
Independent variables are variables that are manipulated or controlled by the researcher in a scientific or statistical study. They are called independent variables because they are believed to have an effect on the dependent variable, which is the variable being measured or studied.
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A storage box with a square base has a length of 2 feet and a height of 2 1/2 feet what is the volume of the storage box
Answer:
10
Step-by-step explanation:
Using this equation,
l × w × h = v
We can simply substitute the numbers into the equation.
2 × 2 × 2 1/2 =?
(We know that the width is equal to 2 because it is a square.)
2 × 2 = 4,
4 × 2 1/2 = 10
The volume of the storage box is equal to 10.
Consider the equation y = negative 2 x + 5. Create a table of five ordered pairs that satify the equation. What is the slope of the line represented by the equation? a. M = 2 b. M = 5 c. M = negative 2 d. M = negative 5.
Answer: C
Step-by-step explanation:
Slope is the number right in front of x, which in this case would be -2. So C is the answer.
Creating a table is hard, so I'll try my best. Just pretend the vertical line is connected.
x|y
0|5
1|3
2|1
3|-1
4|-3
Graph the inequality on the axes below.
3x + y ≤ -3
Answer:
y ≤ -3x - 3
Step-by-step explanation:
The graph crosses the y axis at -3. The slope is -3. (0, -3) . From that point do down vertical 3 spaces and horizontally 1 space. You will be at the point (1,-6) Draw a line to join those 2 points. The inequality is ≤ that means the solutions are the points on the line and below the line. This is shown in the pink shading.
y ≤ -3x - 3
Step-by-step explanation:
The graph crosses the y-axis at -3. The slope is -3. (0, -3) . From that point do down vertical 3 spaces and horizontally 1 space. You will be at the point (1,-6) Draw a line to join those 2 points.
The inequality is ≤ which means the solutions are the points on the line and below the line. This is shown in the pink shading.
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Find the inverse of the function f(x) = 3x + 2. State the answer in slope-intercept form.
Round 24.07 to the nearest tenths. It’s for an app it got a number line
24.07 rounded to the nearest tenth is 24.1
For fixed population standard deviation and level of significance, the minimum sample size needed to guarantee a given margin of error ......... as the margin of error increases.
stays the same
increases
decreases
Population standard deviation, level of significance are same.
Margin of error increased.
With increase in margin of error sample size decreases.
By dividing the population's standard deviation by the sample size and then multiplying the resulting number by the crucial factor, the margin of error—a statistical expression used to estimate how much a result will deviate from the value of the full population—can be determined.
The standard deviation of the sample statistics, if we could take several samples of the same size, is the standard error.
Population standard deviation, level of significance are same.
Margin of error increased.
Margin of error increases leads to decrease in the sample size
as the margin of error is in denominator position in sample size formula. Hence with increase in margin of error sample size decreases.
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Hello can someone help me out with these two questions!?!?! This will help me a lot thank you! :D
The solution to the first inequality is x ≥ -2. Option 1 is correct. The solution to the second inequality is x ≤ -7. Option 1 is correct.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.
A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R." It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.
The inequalities are,
2( x +6 ) > -6( x +1) +2
2x + 12 > -6x - 6 + 2
2x + 6x > -12 - 6 +2
8x > -16
x > -2
-3x - 1 ≥ 20
-3x ≥ 21
x ≥ -7
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Sam wants to build a wooden deck on his patio, which is in the shape of a parallelogram. The
area of the patio is 350 ft2. Find the base. Round your answer to the nearest foot.
Hint : Use A = bh.
We may calculate our answer using fractions and the fact that the base is 18.3 feet.
What are fraction ?The components of a whole or group of items are represented by fractions. A fraction consists of two components.
The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection.
The denominator is the figure that appears below the line. It displays the total number of identical objects in a collection or the total number of equal sections the whole is divided into.
There are three different methods to express a fraction: as a fraction, as a percentage, or as a decimal. Let's examine each of the three representational styles.
According to our question-
The patio is 280 square feet in size. locate the base.
Height = 5x Area = 280 feet square
Base = 6x
The parallelogram A's area can be expressed mathematically as;
Base + height equals area.
A = b×h
the values of area, base, and height are substituted.
280 = 5x × 6x = 30x^2 \sx^2 = 280/30 \sx = √(280/30)
Given that the base is 6x,
swapping out x's value.
Base = 6x = 6(√(280/30))
Base=18.3 feet
18.3 ft tall is the base
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Answer:
At short 18.7 ft is the answer
question 5: on a given day, there is a car accident reported at the intersection of victory blvd and richmond avenue with a probability 0.05. what is the probability that there are at most 2 car accidents reported thoughout a month?
The formula for the cumulative probability of a Poisson distribution can be used to calculate the likelihood that there will be at most 2 reported car accidents over the course of a month:
Cumulative probability is equal to (number of events * e)/(average number of events per time period).
(Number of events / (-average number of events per time period)!)
In this instance, there are typically 0.05 events per time period (the likelihood that a car accident is reported at the intersection on any given day), and there are typically between 0 and 2 events per time period (at most 2 car accidents). With these values entered into the formula, we obtain:
Cumulative probability is equal to (0.05 * e(-0.05)) / 0, (0.05 * e(-0.05)) / 1, and (0.05 * e(-0.05)) / 2, respectively.
That amounts to:
Probability total = 1 + 0.05 + 0.0025
which translates to 1.0525 percent, or 105.25%. It's crucial to keep in mind that this probability exceeds 1, which is impossible. This is because the formula for cumulative probability makes the assumption that each event is independent, which means that the occurrence of one event has no bearing on the probability of the occurrence of another. The cumulative probability calculated using this formula may not accurately reflect the probability of at most 2 car accidents occurring throughout a month because in reality, the probability of a car accident occurring on a given day may be influenced by the number of car accidents that have already occurred. You would need to account for the dependencies between the events in order to calculate this probability precisely.
Annapurna suppliers sold construction materials of
Rs. 4,40,000 to Angel suppliers making 10% profit
and adding 13% VAT. Angel suppliers spent Rs. 5,000
for transportation cost and made 10% profit on the
purchased price excluding VAT and levied local tax Rs.
2500 and sold to constructor. What VAT amount should
be paid by the constructor?"
Ans: Rs. 70187
First, we need to find the price that Angel suppliers paid for the construction materials, including the profit made by Annapurna suppliers and the VAT.
The price that Annapurna suppliers sold the materials for was Rs. 4,40,000 + Rs. 4,40,000 * 10% = Rs. 4,84,000.
The VAT that Annapurna suppliers added was Rs. 4,84,000 * 13% = Rs. 62,820.
So, the total price that Angel suppliers paid was Rs. 4,84,000 + Rs. 62,820 = Rs. 5,46,820.
Next, we need to find the price that the constructor paid for the materials, including the profit made by Angel suppliers, the transportation cost, the local tax, and the VAT.
The profit that Angel suppliers made was Rs. 5,46,820 * 10% = Rs. 54,682.
The total price that the constructor paid was Rs. 5,46,820 + Rs. 54,682 + Rs. 5,000 + Rs. 2,500 = Rs. 6,58,002.
The VAT that the constructor should pay is Rs. 6,58,002 * 13% = Rs. 70187.
Therefore, the answer is Rs. 70187.
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Can someone help me.
I need to solve for y=mx+b
My problem is 2y-3x=10 can you give me steps to help me understand how to solve for the slope and y-intercept.
I need to know what p is 12.4 - p =7.9
Answer: p = 4.5
Step-by-step explanation:
12.4 - 4.5 = 7.9
Answer: p=4.5
Step-by-step explanation:
You do it like this: 12.4=7.9+p
12.4-7.9=p
p=4.5
suppose you are trying to classify a variable where 96%of its observations equal 0 and only 4% equal 1. you run a logistic reg-ression, and the classification table shows that 97% of the classifications are correct. why might this large percentage still not be cause for celebration?
The large percentage obtained above will still not be a cause for celebration, because the observations demand a higher precision in the calculation results being obtained after running a logistic reg-session.
A precise calculation can be referred to or considered as a type of calculation, wherein the final results obtained are completely true and correct. Unlike approximate results, there is no scope of true and fair results in a precise calculation. Usually, rounding-off shall be avoided to obtained precise solutions at the end.
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a plane, 50 miles away from its destination, is flying toward the airport at an altitude of 30,500 feet. later, this same plane is 20 miles from the airport and has descended to an altitude of 18,000 ft. how far has the plane flown?
Using the geometry from the question and using the Pythagorean theorem with the distance provided, The answer is 30.09 miles.
What is unit conversion?By definition, unit conversion refers to the division or multiplication operation used to convert measurements of the same quantity between various units.
What is Pythagorean theorem and it's formula?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.
It's formula is:
[tex]h^{2} = p^{2} +b^{2}[/tex]
h1=30500 feet = 5.77 miles
d1= 50 miles
h2= 18000 feet = 3.4 miles
d2= 20 miles
for right angle triangle,
height = h1-h2 = 2.37 miles
distance = 50-20 = 30 miles
plane flown = [tex]\sqrt{2.37^{2}+30^{2}}[/tex]
=30.09 miles
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