A function that will match the given graph is; f(x) = 2(x - 5)²(x + 2)
How to interpret Polynomial Graphs?In polynomial graphs, we know that the roots are the points where the graph crosses or touches the x-axis.
In this given graph, we see that the graph touches the x-axis at x = 5 and then crosses the x-axis at x = -2. Thus;
The roots of the equation are -2 and 5.
However, when the graph changes sign at a point on the x-axis, it means that point represents double roots. Thus, we will now have three roots which are -2, 5 and 5. The factors of the polynomial are;
(x + 2), (x - 5)²
Now, we see that when x = 0, y = 100 from the graph. Thus;
a(0 + 2)(0 - 5)² = 100
a(50) = 100
a = 100/50
a = 2
Thus, the equation would now be;
f(x) = 2(x - 5)²(x + 2)
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Multiply.
17.22(−2.4)
Enter your answer in the box.
Answer:
-41.328
Step-by-step explanation:
Answer:
-41.328
Step-by-step explanation:
Addition multiplied by subtraction gets you subtraction. +-=-
so now, ()= multiplication
so now all you have to do is 17.22 times 2.4 which gets us 41.328
then, add the negative sign which gives you -41.328
yw :)
i need help divided 4/7 by 3
Answer:
0.1904
Step-by-step explanation:
4/7 ÷ 3 is = 0.1904
Answer: I hope this helps
Step-by-step explanation:
4/7 divided by 3
Dividing is equivalent to multiplying by the reciprocal
4/7 times 1/3 or 4/7•1/3
Multiply the fractions
And you get
4/21 or 0.190476
Answer to this required:
Answer:
9
Step-by-step explanation:
3.4^0 = 1
9^1 = 9
1 * 9 = 9
For rhombus LMNO, m∠LON = 102° and NP = 5 units.
Rhombus L M N O is shown. Diagonals are drawn from point L to point N and from point M to point O and intersect at point P. All sides are congruent.
Use the diagram of rhombus LMNO to find the missing measures.
The measure of ∠LPM is
°.
The measure of ∠PMN is
°.
The length of LN is
units.
the measure of ∠LPM is 90°
the measure of ∠PMN is 102°
the length of LN is 10 units.
Define Rhombus.
A rhombus is a special case of a parallelogram, and it is a four-sided quadrilateral. In a rhombus, opposite sides are parallel and the opposite angles are equal.
For a Rhombus, LMNO
∠LON = 102°
NP = 5 units
By the properties of Rhombus, we know that
All sides of a rhombus are congruent (equal)
So, LM = MN = NO = OL
and
Opposite angles are equal and the opposite sides are parallel.
So, ∠LON = 102° = ∠LMN
Since Adjacent angles add up to 180°.
Therefore ∠L + ∠M = 180°
∠M + ∠N = 180°
∠N + ∠O = 180°
∠O + ∠L = 180°
So, ∠N = 180° - ∠O = 180° - 102° =78°
∠L = 180° - ∠O = 180° - 102° =78°
∠M = 180° - ∠L = 180° - 78° =102°
Diagonals bisect each other at 90° or we can also say that each of the two diagonals in a rhombus is the perpendicular bisector of the other.
So, ∠LPM = ∠NP0 = ∠MPN = ∠LPO =90°
Thus, the measure of ∠LPM is 90°
the measure of ∠PMN is 102°
the length of LN is 10 units.
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Answer:
Lpm= 90
PMN=51
LN= 10
Step-by-step explanation:
write the mixed number as an improper fraction
Answer:
[tex]\frac{19}{6}[/tex]
Step-by-step explanation:
3[tex]\frac{1}6}[/tex]
[tex]\frac{6}{6}[/tex] + [tex]\frac{6}{6}[/tex] + [tex]\frac{6}{6}[/tex] + [tex]\frac{1}{6}[/tex] [tex]\frac{6}{6}[/tex] is another name for 1 How many 6th's do we have?
[tex]\frac{19}{6}[/tex]
expressions equivalent to 9 2/3
The equivalent expression for the given expression is 29/3.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given mixed fraction [tex]9\frac{2}{3}[/tex].
There are equivalent improper fractions for all mixed numbers. By multiplying the integer by the denominator and then adding the numerator, they are transformed. The numerator will not change.
Convert mixed fraction to improper fraction as follows
Improper fraction = [(Numerator × Denominator)+Numerator]/Denominator
[(9×3)+2]/3
=[27+2]/3
= 29/3
Therefore, the equivalent fraction for the given mixed fraction is 29/3.
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Find the measure of one exterior angle in each regular polygon. Round your answer to the
nearest tenth if necessary.
3)
45°
27.7°
51.4°
Which coordinates are the best estimate of the solution to the system of equations. -3x+y=2 -4x+7y=1
The best estimate of the solution to the system of linear equations is the point are (x,y) will be (0.76, 4.30).
What is linear equations?A linear equation in two variables is one that is written in the form axe + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero.
Given:
as x,y are variables,
-3x + y = 2 ..............(1)
- 4x + 7y = 1 ...........(2)
We know that,
The solution of the system of linear equations is the intersection point of both graphs
Multiply equation (1) by 7 on both sides and then subtract it from eq (2)
- 4x + 7y = 1 ...........(2)
-21x + 7y = 14 ..............(1)
⇒- 17 x = -13
⇒ 17 x = 13
⇒ x =[tex]\frac{13}{17}[/tex]
⇒ x = 0.76
Now on putting value of x = 0.76 in eq (1) we get
- 3x + y = 2 ............ (1)
⇒- 3(0.76) + y = 2
⇒y = 4.30
The best estimate of the solution to the system of linear equations is the point (x,y) will be (0.76, 4.30).
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Which variable has a binomial distribution?
When tiles are drawn, with replacement, from a bag of lettered tiles, X is the number of vowels in 5 draws.
When tiles are drawn, without replacement, from a bag of lettered tiles, X is the number of times it takes to get a vowel.
When tiles are drawn, without replacement, from a bag of lettered tiles, X is the number of vowels in 5 draws.
When tiles are drawn, with replacement, from a bag of lettered tiles, X is the number of times it takes to get a vowel.
When tiles are drawn, with replacement, from a bag of lettered tiles, X is the number of vowels in 5 draws variable has binomial distribution
The possibility that a value would take one of two independent values given a particular combination of factors or assumptions is summarised by the statistical distribution known as the binomial distribution.
The basic presumptions of the binomial distribution are:
each trial has a single possible outcome each trial has an equal chance of success each trial is either independent of the others or mutually exclusive.As opposed to a continuous distribution, like the normal distribution, the binomial distribution is a frequent discrete distribution used in statistics.
The probability of success raised to the power of the number of successes and the probability of failure raised to the power of the difference between the number of successes and the number of trials are multiplied to create the binomial distribution.
The result is then multiplied by the sum of the number of attempts and the number of successes.
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Select all of the zero(s) of f(x)
Answer:
B, F
Step-by-step explanation:
[tex]2x^2(x-4)^2=0 \\ \\ \implies x^2=0, (x-4)^2=0 \\ \\ \implies x=0,4[/tex]
What is the length of the missing side of the triangle below to the nearest tenth of a centimeter?
4^2 + 6^2 = C^2
Answer:
7.2 cm
Step-by-step explanation:
You want the value of C to the nearest tenth centimeter, given that 4^2 + 6^2 = C^2.
SolutionSimplifying gives ...
4^2 + 6^2 = C^2
16 +36 = C^2 = 52
C = √52 ≈ 7.2
The length of the missing side is about 7.2 cm.
List from least to greatest! ( WILL GIVE BRANILIST IF CORRECT)
Answer:
need the numbers to do it
Help me!!!
Graph the equation:
y - 2 = 3 (x - 2)
Answer:
See below and attached graph
Step-by-step explanation:
If you are using a graphing calculator it is a breeze. You write down the equation as it is and it should plot it, depending on what calculator you use.
If you are doing this manually here are the steps
We are given y - 2 = 3(x-2)
Expand the brackets on the right hand side
3(x - 2) = 3x - 6
So the original equation becomes
y - 2 = 3x - 6
Adding 2 to both sides
y - 2 + 2 = 3x -6 + 2
y = 3x - 4 [1]
This form of equation is known as a slope-intercept form of the line
We need two points to plot a line. This can be done by choosing a value for x, finding the y value which gives one point. Then repeat for another value of x to get y for that value giving another point. Draw a straight line through both points
Point 1
Let's choose x = 2 and plug this into the equation [1]
y = 3·2 - 4 = 6- 4 = 2.
So (2, 2) is one point on the graph
Point 2
Choose another value for x, say x = 4
y = 3·4 - 4
y = 12-4
y = 8
So (4, 8) is another point
Draw a line through these two points
1.
Kim's age to her sister's age, you get 36. How old is each
Kim's age is twice that of her sister. When you add
sister?
(a) Write an equation that represents the situation. Explain any variable used.
(b) Solve the equation from Part (a). Show your work. State your solution as a complete sentence.
Sister's age will be equal to 12 and Kim's age is 24.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Consider that x is sister's age, Kim's age is twice that of her sister
Thus Kim's age = 2x
Kim’s age + Sister’s age = 36
The equation:
x + 2x = 36
Now solve the equation;
x + 2x = 36
3x = 36
x = 36 / 3
x = 12
Therefore, Kim's age = 2x = 2(12) = 24
Hence, Sister's age is 12 and Kim's age is 24.
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A professor wanted to know what proportion of college students believe in ghosts. She polled 200 students and found that 58% said they believe in ghosts. Create a 99% confidence interval for the true proportion of college students believing in ghosts. a. (0.5116, 0.64840 b. (0.2074, 0.3727) c. (0.4901, 0.6699) d. (0.2271,0.3529)
A 99% confidence interval for the true proportion of college students believing in ghosts is Option(c) (0.4901, 0.6699)
According to the question,
A professor wanted to know what proportion of college students believe in ghosts.
For that he drawn a sample from the college.
Sample size : n = 200
Proportion of students that believed in ghosts in sample = 58%
=> p = 0.58
Proportion of students who does not believe in ghost : q = 1 - p
=> q = 0.42
We have to create a 99% confidence interval for a true proportion of college students believing in the ghosts
Formula of C.I = [tex]p \pm ( z_{\alpha} \sqrt{\frac{pq}{n}})[/tex]
Where p and q is sample proportion , z is value of CI at given α level of significance and n is sample size
C.I at 99% = 0.58 ± 2.576 √0.58×0.42/200
=> 0.58 ± 2.576 √0.001218
=> 0.58 ± 2.576 × 0.035
=> 0.58 ± 0.08958
C.I = ( 0.58 - 0.08958 , 0.58 + 0.08958)
=> C.I = (0.4901, 0.6699)
Hence, Option (c) is correct
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Answer:
41%
Step-by-step explanation:
Find tan(0), if cot(0) = -2.6
According to Trigonometric Identity , tan(theta) = -5 / 13
What are Trigonometric Identities ?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. The relationship between a triangle's side length and angle is expressed by a variety of specific trigonometric identities.
Sin, cos, and tan are the three fundamental trigonometric ratios. The reciprocals of sin, cos, and tan are represented by the three additional trigonometric ratios sec, cosec, and cot in trigonometry, respectively.
According to the given information
We know that
tan(theta) = 1/cot(theta)
= 1 / -2.6
= -1 / 2.6
= -10 / 26
= -5 / 13
According to Trigonometric Identity , tan(theta) = -5 / 13
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Solve ABC using diagram and the given measurement A=64 a=7.4
Answer:
Hope this helps!
The distances between Dry Gulch, Wet Creek, and Soggy River can be represented by a triangle.
The distance between Dry Gulch and Wet Creek is 530 miles and the distance between Dry Gulch and Soggy River is 721 miles. Circle ALL the possible distances below between Wet Creek and Soggy River: SHOW YOUR WORK
The distance between Wet Creek and Soggy will be 894.03 miles.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The distances between Dry Ravine, Wet Rivulet, and Saturated Waterway can be addressed by a triangle.
The distance between Dry Ravine and Wet Rivulet is 530 miles and the distance between Dry Gorge and Saturated Waterway is 721 miles.
The distance between Wet Creek and Soggy will be given as,
d² = 530² + 721²
d² = 280,900 + 518,400
d² = 799,300
d = 894.03 miles
The distance between Wet River and Soaked will be 894.03 miles.
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What is the end behavior of the graph of the polynomial function f(x) = –x5 + 9x4 – 18x3?
The end behavior of the graph of the polynomial function:
As x approaches ∞, y approaches -∞
As x approaches -∞, y approaches ∞
What is an end behavior?
The behavior of the function graph at the "ends" of the x-axis is known as the end behavior of a function, or f.
Here, we have
f(x) = –x⁵ + 9x⁴ – 18x³
F(x) is a fifth-degree (odd function ) with a negative leading coefficient
If the exponent is odd and the leading coefficient is negative then the end behavior is
As x approaches ∞, y approaches -∞
As you go on the right, f(x) goes down
As x approaches -∞, y approaches ∞
As you go on the left, f(x) goes up.
Hence, the end behavior of the graph of the polynomial function: As x approaches ∞, y approaches -∞
As x approaches -∞, y approaches ∞
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Use a sign chart to solve the inequality. Express the solution in inequality notation and in interval notation. X2 - 5x - 36 < 0 The solution expressed in inequality notation is.
The solution in inequality notation and in interval notation is (-∞ . -√5]∪[√5,36)
The term inequality refers the a relationship between two expressions or values that are not equal to each other is called 'inequality.
Here we have given the inequality (x² - 5)/ (x - 36) < 0
And we need to find the solution in inequality notation and in interval notation.
In order to find the inequality notation, we have to solve the given inequality, then we get.
(x² - 5)/ (x - 36) < 0
(x² - 5) < 0
x² < 5
x < √5
While we looking into the inequality we must know that the denominator must not be 0.
So, the interval notation can be written as,
=> (-∞ . -√5]∪[√5,36)
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Here is a linear equation: y= 1 4x+2. What is the x-intercept of the graph of the equation?
As per the linear equation, the x-intercept of the graph of the equation will be (-8, 0).
What is slope?It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.
As per the information given in the question,
The given equation is,
y= -1/4 x + 2
Now, let's take y = 0 for x- intercept,
So, the equation will be,
0 = 1/4x + 2
1/4x = -2
x= -8
The x-intercept is (-8, 0).
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The question sees incomplete, your question may be:
Here is a linear equation: y = 1/4x + 2 What is the x-intercept of the graph of the equation?
The cost of three pens and one rubber is 2.25 the cost of two pens and two rubbers is 1.90 work out how much one pen costs and how much one rubber costs
Answer:
0.65 pens
2.25 rubber
Step-by-step explanation
You can make two equations with the information given and solve them simultaneously to find x and y. Assume x is pens and y is rubber.
Which ordered pair lies on the graph of the function y = -2x + 1? (0, -2) (2, -2) (3, -5) (5, 2
So, the ordered pair which lies on the graph of the function y = -2x + 1 is (3,-5)
We will use the substitution method and check for all the ordered pair which are given
If the ordered pair lies on the graph, then it should satisfy the function.
So,
Given,
y = -2x+1
First check for (0,-2)
x=0, y=-2
Substitute the values,
y = -2x+1
-2=-2(0)+1
-2=1
It is false.
Next check for (2,-2)
x=2, y=-2
Substitute the values,
y = -2x+1
-2=-2(2)+1
-2=-3
It is false.
Next check for (3,-5)
x=3, y=-5
Substitute the values,
y = -2x+1
-5=-2(3)+1
-5=-5
It is true.
Next check for (5,2)
x=5, y=2
Substitute the values,
y = -2x+1
2=-2(5)+1
2=9
It is false.
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Can someone help me?
Answer:
Y=6x-12
Step-by-step explanation:
whenever the X is at zero the number across from it is the Y-intercept. and to find the slope just count how much they are increasing or decreasing by.
Do not understand this question
Answer:
A, C
Step-by-step explanation:
You want all the shapes that are enlargements of shape X, which is 1 unit high and 3 units wide.
EnlargementAn enlargement of shape X multiplies each of its dimensions by the same factor. When it is enlarged by a factor of 2, the dimensions become ...
high : wide = 1 : 3 = 2 : 6 . . . . . . matches shape C
When it is enlarged by a factor of 3, the dimensions become ...
high : wide = 1 : 3 = 3 : 9 . . . . . . . matches shape A
The 2-high shape B is too short, being 4 1/2 wide instead of 6. Shape F is too long, being 7 wide instead of 6.
The 3-high shapes D and E are too short, being 8 and 5 wide instead of 9.
__
Additional comment
An enlargement preserves the aspect ratio of the shape, the height to width ratio. Here, that is 1:3. Any shape with a different aspect ratio is not an enlargement of X.
Select the best answer. The central limit theorem is important in statistics because it allows us to use the Normal distribution to find probabilities involving the sample mean (a) if the sample size is reasonably large (for any population). (b) if the population is Normally distributed and the sample size is reasonable large. (c) if the population is Normally distributed (for any sample size). (d) if the population is Normally distributed and the population standard deviation is known (for any sample size). (e) if the population size is reasonably large (whether the population distribution is known or not).
The central limit theorem's not needed when the original distribution is normal, the distribution of the sample mean is always normal in that case. So, option (a) is correct. If the sample size is reasonably large (for any population) is correct.
Given that,
The central limit theorem is important in statistics because it allows us to use the Normal distribution to find probabilities involving the sample mean,
In layman's words, the theorem asserts that regardless of the form of the initial population distribution, the sampling distribution of the mean tends to resemble a normal distribution as the sample size rises.
Statistics benefits from the Central Limit Theorem because it makes it safe to assume that the sampling distribution of the mean will be typically normal. As we will see in the next section, this means that we can benefit from statistical methods that presume a normal distribution.
The distribution of people's heights within a population is one illustration of how the central limit theorem is put to use. Even though the population's distribution of heights is not normal, when we sample this population, the distribution of the sample averages will be roughly normal.
Therefore,
The central limit theorem's not needed when the original distribution is normal, the distribution of the sample mean is always normal in that case. So, option (a) is correct. If the sample size is reasonably large (for any population) is correct.
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it has been (mathematically) proven that there is no polynomial time algorithm for any np-complete problem.
It has been (mathematically) proven that there is no polynomial time algorithm for any np-complete problem. the given statement is false.
In order to solve previously unsolvable issues, Leonid Khachiyan developed a polynomial-time method, in which the number of processing steps increases as a power of the number of variables rather than exponentially.
Determining whether NP-complete problems are tractable or intractable remains one of the most crucial concerns in theoretical computer science since it is unknown if any polynomial-time algorithms will ever be developed for them.
So, it is unknown if any polynomial-time algorithms will ever be developed for them.
By applying different constraints, a linear function is maximized or reduced in linear programming, a mathematical modelling approach. In commercial planning, industrial engineering, and—to a lesser extent—the social and physical sciences, this method has proven helpful for directing quantitative decisions.
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The number line below is divided into 4 equal parts. Fill in the missing fractions and percentages.
Note that your fractions don't need to be in simplest form.
We can fill in the remaining fractions and percentages.
as
0 1/4 2/4 3/4 1
|--------------|--------------|--------------|--------------|
0% 25% 50% 75% 100%
What is a number line?
A number line is a straight line that is used to represent real numbers. The numbers are usually represented as points on the line, and the distance between the points corresponds to the magnitude of the numbers. The numbers can be positive or negative and are typically marked at regular intervals.
The missing parts are
0 1/4 2/4 3/4 1
|--------------|--------------|--------------|--------------|
0% 25% 50% 75% 100%
This is how we can fill in the remaining fractions and percentages.
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Customers at a gas station pay with a credit card (A), debit card (B), or cash (C). Assume that successive customers make independent choices with P(A) = 0.6, P(B) = 0.3, and P(C) = 0.1. (a) Among the next 100 customers, what are the mean and variance of the number who pay with a debit card? mean customers variance customers2 (b) Answer part (a) for the number among the 100 who don't pay with cash. mean customers variance customers^2
Variance of customers who pay by card = 16
Mean number of customers = 20
Given that,
Customers at a gas station pay with a credit card (A), debit card (B), or cash (C). Assume that successive customers make independent choices with
P(A)=0.4,
P(B)=0.2,
and
P(C)=0.4
Because we are interested in whether or not a debit card was used, we can use the binomial distribution.
Let X= the number of customers who use a debit card.
Here, probability of customers who pay with debit card (or success) is
p=0.2
(a) Mean and variance of the number of customers who pay with a debit card:
The mean number of customers who pay with a debit card can be calculated as given below:
μ=np =100×0.2
=20
The variance of the number of customers who pay with a debit card can be calculated as given below:
σ²=np(1−p) =100×0.2(1−0.2)
=16
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What is true about machine learning algorithms? A/Model is fitted using training dataset B/Performance of the model is assessed using test data C/Model is validated on validation dataset D/Model is calibrated on test dataset E/Validation dataset is used to minize model overfitting Select all what applies to traditional classification tree model: A/Group of answer choices B/Unsupervised learning method C/Requires categorical output(target) variable D/Does not require any output variables E/None of the above F/Supervised learning method
A. Model is fitted using training dataset and E. Validation dataset is used to minimize model overfitting are true about machine learning algorithms
The process by which an AI system completes its task—generally, forecasting output values from provided input data—is known as a machine learning algorithm. Classification and regression are the two key operations of machine learning algorithms.
Simple linear regression, decision trees, logistic regression, the KNN algorithm, and other well-known supervised learning techniques are some examples.
Machine learning is crucial because it helps businesses identify trends in customer behaviour and operational patterns and facilitates the creation of new goods.
According to the question,
Option A and option E are correct about the machine learning algorithms
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