The scatter plot for the correlation of weight and intelligence scores for 250 students would likely be very close to the origin, meaning that the majority of the points would be clustered around the point (0,0), with a very small range of points scattered further away.
This would indicate that there is no correlation between the two variables, which is reflected in the computed correlation coefficient of .00.
A scatter plot is a type of plot that displays data points on a two-dimensional graph. The data points are represented as dots or circles on the graph and show the relationship between two variables. The location of each data point is determined by the value of the two variables for that point. Scatter plots can be used to identify patterns in data, such as clusters, linear relationships, or nonlinear relationships. They can also be used to identify outliers or unusual data points.
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Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the function in standard form. Show your work.
0, 5, -5+sqrt8
The polynomial function is f(x) = x(x - 5)(x + 5)² - 8)
How to determine the polynomial from the zeros?From the question, we have the following parameters that can be used in our computation:
Zeros: x = 0, 5, -5 + √8
The polynomial can be repesented as
f(x) = product of (x - zeros)
using the above as a guide, we have the following:
f(x) = x(x - 5)(x - (-5 + √8))(x - (-5 - √8))
This can be expressed as
f(x) = x(x - 5)(x + 5)² - 8)
hence, the polynomial is f(x) = x(x - 5)(x + 5)² - 8)
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The range of 35, 40, 22, 17, 65, 31, 78, 33 is _____.
Answer:
56
The range is calculated by subtracting the lowest value from the highest value.
The highest value of the set is 78.
The lowest value of the set is 22.
78 - 22 = 56
Step-by-step explanation:
Hope it helps! =D
Answer:
56
Step-by-step explanation:
the average complexity a(n) of linearsearch for a list of size n assuming the list elements are distinct and the search element is equally likely to be found in any position is
The average complexity of linear search for a list of size n is O(n).
The average complexity of linear search for a list of size n is calculated by taking the sum of the number of comparisons for each possible position of the search element, and then dividing it by the total number of possible positions.
For example, if we have a list of size n = 10, and the search element is equally likely to be found in any position, then the number of comparisons to find the element in each position is as follows:
Position 1: 1 comparison Position 2: 2 comparisons Position 3: 3 comparisons Position 4: 4 comparisons Position 5: 5 comparisons Position 6: 6 comparisons Position 7: 7 comparisons Position 8: 8 comparisons Position 9: 9 comparisons Position 10: 10 comparisons
Therefore, the average number of comparisons to find the search element in the list is (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) / 10 = 5.5
This means that the average complexity of linear search for a list of size n is O(n).
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Given a graph, how would you identify continuous functions from discontinuous functions?
In order for a function to be continuous at a point, then,
The limit of f(x) as x approaches the x coordinate of the point from the left and the right equals the value of the function at that point.
What does the term "continuous function" mean?
A continuous function in mathematics is a function that causes the value of the function to continuously vary as a result of a continuous variation of the argument, or a change without a leap.
This indicates that there aren't any discontinuities, or sharp shifts in value.
What does it mean when a function is continuous or discontinuous?
If one can sketch a function without picking up a pencil, one can say that it is continuous. A function is considered discontinuous if it is not.
If there is no break in the graph of the given function at the point, then a function f(x) in calculus is continuous at x = c.
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3. Factor completely.
6x² - 31x+40
O (2x - 5)(3x-8)
O (2x-8)(3x - 5)
O (x - 5)(x-8)
O(x-31)(x+40)
6x² - 31 x + 40, after factorization we get: (2x - 5) (3x - 8).
correct option: a
What is factorization?Expanding brackets is done in reverse when factorising. By eliminating the most common factors, an expression is fully factored when it is enclosed in brackets. The simplest method of factorization is to identify the term in the equation with the largest common factor. The Grouping technique, the Difference in Two Squares, the Sum or Difference in Cubes, and the Greatest Common Factors (GCF) are the four primary methods of factoring.
Similar to this, factoring is a very useful technique in algebra that is utilised at all levels. Additionally to, of course, simplifying complex expressions, it offers a standard way for solving quadratic equations. Graphing functions also makes advantage of it.
= 6x² - 31 x+40
= 6x² - 15 x - 16 x +40
= 3x (2x - 5) - 8 (2x - 5)
= (2x - 5) (3x - 8)
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No recuerdo cómo hacer esto...
Para completar la piramide hay que ir sumando los polynomios que hay en cada bloque.
¿Como completar las piramides?Para construir las piramides, solo debes sumar los polinomios de los bloques inferiores para obtener los superiores.
La primer piramide tiene los valores en los dos bloques de la izquierda:
2r - 3s y 5s - r
Si los sumamos, obtendremos:
(2r - 3s) + (5s - r) = (2r - r) + (-3s + 5s) = r + 2s
Entonces eso es lo que colocamos en el bloque que esta justo arriba.
Si vemos el segundo y el tercero son:
5s - r y 7r - 6s
Sumandolos obtenemos:
5s - r + 7r - 6s = 6r - s
Y eso va en el bloque que esta justo arriba, y asi de a poco vamos completando la piramide.
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Tracy evaluates the expression on a math test, and gets an answer of .
Is this a reasonable answer?
According to the linear equation, because 8.8 rounds to 9 and 2.7 rounds to 3, division rounds to 3. His solution of 4.14 equals 4. As a result, it is illogical.
What exactly is a linear equation?A linear equation is an equation having one or more variables, the maximum power of which is one. A linear equation is an algebraic equation with simply a constant and a first-order (linear) component of the form y=mx+b, where m is the slope and b is the y-intercept. The above is sometimes referred to as a "linear equation with two variables," where y and x are the variables.
The following expression is:
Given expression is:
8.8 ÷ 2.7
≈ 9 ÷ 3
= 3
His answer is 4.14 ≈ 4.
According to the linear equation, division rounds to 3 since 8.8 rounds to 9 and 2.7 rounds to 3. His solution of 4.14 equals 4. It is thus irrational.
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Answer:
Since 6/7 rounds to 1 and 4 4/5 rounds to 5, the sum rounds to 6. Her answer of 5 22/23 rounds to 6. So it is reasonable.
Step-by-step explanation:
find the solution of the differential equation ′()=2() with the initial condition (0)=⟨7,5,3⟩, where () is a vector‑valued function in three‑space.
The solution of the differential equation with the given initial condition is[tex]()=⟨7⋅e^2x, 5⋅e^2x, 3⋅e^2x⟩.[/tex]
Let () be a vector-valued function in three-space. Then the solution of the differential equation ′()=2() with the initial condition [tex](0)=⟨7,5,3⟩[/tex] can be found by solving the system of differential equations:
[tex]′1()=2⋅1()\\′2()=2⋅2()\\′3()=2⋅3()[/tex]
where 1(), 2(), and 3() denote the components of ().
Solving for the general solution of each equation yields:
[tex]1()=7⋅e^2x\\2()=5⋅e^2x\\3()=3⋅e^2x[/tex]
Therefore, the solution of the differential equation with the given initial condition is:
[tex]()=⟨7⋅e^2x, 5⋅e^2x, 3⋅e^2x⟩.[/tex]
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Mr. Dharmendra Yadav has a rectangular mango farm having length 1.4 km and width 600 m. If he wishes to fence the farm with four rounds over the wall by sharp pointed fencing wire at the rate of Rs 50 per meter. find the total cost of fencing.
what does the entry of 1.00 indicate on the diagonal of the matrix?
The matrix's entry of 1.00 on the diagonal denotes that it is an identity matrix, which means that all values besides 1 along the diagonal are 0.
The matrix is an identity matrix, as evidenced by the entry of 1.00 on its diagonal. A square matrix called an identity matrix is one in which the primary diagonal's elements are all ones and the other components are all zeros. The letter "I" stands for this particular sort of matrix. In several branches of mathematics, such as matrix theory and linear algebra, identity matrices are employed. Calculations and equations can also be made simpler by using identity matrices. An identity matrix, for instance, is created by multiplying it by any other matrix. This characteristic can be used for matrix inversion or to solve a set of linear equations. In group theory and abstract algebra, the identity element is also represented by identity matrices.
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a tangent is drawn from a point at a distance of 17 cm of circle
From a position 17 cm from the circle's center, the tangent to it is 8 cm long.
What is the length of A tangent from A point distance 17 cm?Distance from a circle's center to any point along its perimeter is known as the radius of the circle. R or r are frequently used to indicate it.
Almost every formula involving circles makes use of this amount.
A circle's radius is used to determine both its surface area and circumference.
Give the circle's radius, r.
Given:
PQ=8cm
PO=17cm
OQ=r
Since the radius across the point of contact is perpendicular to any point on a line, it follows that any point on a line must be.
According to Pythagoras' Theorem, in OPQ, OP 2 = PQ 2 + OQ 2.
(17) ² = (8) ² +r ²
⇒ r= √289−64 = √225 =15cm
Consequently, the circle has a 15 cm radius.
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Select ALL the statements about the number 2^−3 that are true.
2^−3 is greater than 3^−2.
2^−3 multiplied by −1 equals 2^3.
2^−3 is less than 1. 2^−3 raised to the third power equals 1.
2^−3 is equal to −8.
ALL the statements about the number 2⁻³that are true are:
2⁻³ is equal to −82⁻³ multiplied by −1 equals 2³ 2⁻³ is < 1What is an inequality?An inequality in mathematics is a relationship that compares two numbers or other mathematical expressions in an unequal way. It can be used most frequently by comparing the sizes of two numbers on a number line.
In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another. Therefore, inequality comes from an imbalance.
The phenomena of an unfair and/or unequal distribution of opportunities and resources among the people who make up a society is known as inequality.
Inequalities can be shown in the speed limits on roads, the minimum age for watching particular movies, or even in how long it takes to walk to the park. Inequalities don't represent a precise sum.
First
2⁻³ = -8
So, 2⁻³ is equal to −8 is true
2⁻³ is greater than 3⁻²
No, as negative odd exponent will result in negative number while negative even exponent would result in positive number.
2⁻³ multiplied by −1 equals 2³
Yes, -8 × -1 = 8 = 2³
2⁻³ is less than 1
As negative odd exponent is there
2⁻³ raised to the third power equals 1, Nope.
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suppose that accidents occur at a rate of 1 per hour from 3-5pm and 6-7pm, and 4 per hour from 5-6pm as poisson process. (a) what is the probability that there are less than 2 accidents occur between 3-7pm? (b) suppose that on day 1, there was an accident at 3pm and on day 2, at 5pm. what is the probability that the next accident occurred within 30 minutes on both days?
(a) The probability that there are less than 2 accidents occur between 3-7pm is 0.2465.
(b) The probability that the next accident occurred within 30 minutes on both days is 0.1358.
Suppose that accidents occur at a rate of 1 per hour from 3-5pm and 6-7pm, and 4 per hour from 5-6pm as Poisson process.
(a) We have to determine the probability that there are less than 2 accidents occur between 3-7pm.
We may use the Poisson distribution to determine the likelihood that there would be less than two accidents between 3 and 7 pm.
The total of the rates for each individual hour represents the rate of accidents during this time period, which is
= 1 + 1 + 4 + 1
= 7 accidents per hours
So the Poisson variable λ = 7
So the probability that there are less than 2 accidents occur between 3-7pm is:
P(X < 2) = P(X = 0) + P(X = 1)
P(X < 2) = [tex]e^{-7}[/tex] × (7^0/0!) + [tex]e^{-7}[/tex] × (7^1/1!)
After simplifying
P(X < 2) = 0.2465
(b) Suppose that on day 1, there was an accident at 3pm and on day 2, at 5pm, then we have to determine the probability that the next accident occurred within 30 minutes on both days.
Since accidents occur in a Poisson process, we may use the Poisson distribution to determine the likelihood that an accident will occur within the next 30 minutes.
Since there are 4 accidents every hour between 5 and 6 o'clock, the likelihood that one will happen in the next 30 minutes is:
P(X = 1) = [tex]e^{-1}[/tex] × (1^1 / 1!)
P(X = 1) = 0.3679
The likelihood that the following event will occur within 30 minutes on both days would thus be
= 0.3679 × 0.3679
= 0.1358
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Solve the equation. Then check your solution. 15 (negative 42 x + 40) = 15 (negative 8 x + 244) a. –6 c. 6 b. 0.7 d. 3 Please select the best answer from the choices provided A B C D
Answer:
C
Step-by-step explanation:
15 (-42 x + 40) = 15 (- 8 x + 244)
15 cancelled on each side
-42x+40= -8x+244
move all the x to one side & numbers to the other,
-34x =204
x=6
Of a group of patients having injuries, 28% visit both a physical therapist and a chiropractor and 8% visit neither. Say that the probability of visiting a physical ther apist exceeds the probability of visiting a chiropractor by 16%. What is the probability of a randomly selected person from this group visiting a physical therapist?
The probability of a randomly selected person from this group visiting a physical therapist is 0.68.
The probability is the extent to which an event is likely to occur, measured by the ratio of the favourable cases to the whole number of cases possible. Let A denote the event that the person visits a physical therapist, and let B denote the event that the person visits a chiropractor. Now, we need to use the laws of probability to arrive at each individual probability i.e. P(A) and P(B).
Given: P(A∩B)=0.28
(ii) P(AC∩BC)=0.08
(iii) P(A)−P(B)=0.16
Required: P(A)
By the laws of inclusion/exclusion,
P(A∪B)=P(A)+P(B)−P(A∩B)
Therefore,
P(A)+P(B)=P(A∩B)+P(A∪B)
By DeMorgan's Law,
P(AC∩BC)=1−P(A∪B)
Therefore,
P(A)+P(B)=0.28+1−0.08=1.2
By adding the equation,
P(A)−P(B)=0.16
we get
2P(A)=1.36
Therefore, P(A)=0.68
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the sum of three consecutive numbers is 96 find the numbers
For f(x)=2/√10-6
Evaluate f (-6) = ?
The value of the function when evaluated is 1/2
How to evaluate the functionFrom the question, we have the following parameters that can be used in our computation:
f(x)=2/√10-6
Express properly
So, we have the following representation
f(x)=2/√(10-x)
Substitute the known values in the above equation, so, we have the following representation
f(-6)=2/√10+6
Evaluate the like terms
f(-6)=2/√16
So, we have
f(-6) = 1/2
Hence, the function value is 1/2
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Round 684 to the nearest hundred
Answer:
700
Step-by-step explanation:
Please help!
The area of parallelogram
ABCD is 24 square units.
Find x.
The value of x determined from the area of parallelogram is 6 units.
What is area of parallelogram?A parallelogram's area is the area that it occupies in a two-dimensional plane. A parallelogram is a four-sided, two-dimensional form in geometry. This particular quadrilateral example has equal and parallel opposing sides. The space bounded by a parallelogram's four sides is known as its area. A parallelogram's area is determined by multiplying its length by its height.
Given that the area of the parallelogram is 24 square units.
The area of the parallelogram is given by the formula:
A = (b)(h)
Substitute the value of A = 24, and b = 8 as given in the figure:
24 = 8(h)
h = 3
The measure of the height is 3 units.
For the triangle, we can observe that it is a right-angled triangle and the angle given is 30 degrees.
Using trigonometric functions, we have:
sin 30 = h / x
Substitute the values:
0.5 = 3 / x
x = 6
Hence, the value of x determined from the area of parallelogram is 6 units.
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if you are using a calculator to find the measure of an angle in degrees, what type of measure might make you question whether your calculator is actually in right mode? explain.
If a calculator displays an angle measure in radians instead of degrees, it would make you question whether the calculator is in the right mode. Radians and degrees are two different units of measuring angles, with radians being the standard unit in mathematics and degrees being more commonly used in everyday life and geography.
Calculator Angle Mode CheckBecause the range of values for angles in radians is between 0 and 2π, while the range for angles in degrees is between 0 and 360. So, if a calculator gives an angle measure in radians that is outside the range of 0 to 2π or gives an angle measure in degrees that is outside the range of 0 to 360, it would indicate that the calculator is not in the correct mode for the desired unit of measurement.
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P varies inversely as the square of W and W = 4 when P = 9, find the value of
P when W = 9.
Answer:
kaoajaoàwkwk2k2kwkw
Step-by-step explanation:
[tex] \boxed{ \sf \: \\ \\ \\ \\ \\ \\ \\ } \: \: \: \: \: \: \: \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \boxed{ \colorbox{blue}{ \: }}[/tex]
The digit in the ones place of 2^88 is 6. What is the digit in the ones place of 2^90?
The digit in the ones place of 2^90 is 4. The pattern of the digits in the ones place for powers of 2 follows a repeating cycle of 0, 2, 4, 6, 8, 0, 2, 4, 6, 8 and so on.
The digit in the ones place of 2^88 is 6 because the last digit of 2^88 is 6. The pattern of the digits in the ones place for powers of 2 is 0, 2, 4, 6, 8, 0, 2, 4, 6, 8, etc. Therefore, the digit in the ones place of 2^90 is 4 since the pattern starts over again at 0 after 8.
The pattern of the digits in the ones place for powers of 2 follows a repeating cycle of 0, 2, 4, 6, 8, 0, 2, 4, 6, 8 and so on. This pattern is a result of the fact that 2^n is divisible by 10 for all integers n greater than or equal to 0. Since 10 is divisible by 10, the remainder of 2^n divided by 10 will always be the same for certain powers of 2. The remainder for 2^0 is 0, 2^2 is 4, 2^4 is 6, 2^6 is 8 and 2^8 is 0. This pattern then repeats with 2^10 being 2 and so on. Therefore, the digit in the ones place of 2^90 is 4, since the pattern starts over again at 0 after 8.
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the digits {1,2,...,5} are randomly arranged in a row. how many ordered elements are in the sample space?
The digits {1,2,...,5} are randomly arranged in a row so total 5 ordered elements are in the sample space.
The digits {1,2,...,5} are randomly arranged in a row.
We have determine how many ordered elements are in the sample space.
The number of possible ways to choose items from a collection when the order of choice is irrelevant is determined using the combination formula. Combination, to put it simply, is the choosing of items or things from a bigger group when the order doesn't important.
So, we use the combination formula
[tex]^nC_{r} = \frac{n!}{r!(n-r)!}[/tex]
Total digits are 5. So,
Sample space = [tex]^5C_{1}[/tex]
Sample space = [tex]\frac{5!}{1!(5-1)!}[/tex]
Sample space = [tex]\frac{5!}{1!4!}[/tex]
Sample space = [tex]\frac{5\times 4!}{1\times 4!}[/tex]
Sample space = 5
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Solve this system of equations by graphing. First graph the equations, and then type the solution.
y=
7/2x –3
y=–3/2x +7
By graphing, the solution to the given system of equations is: (2, 4).
How to Solve a System of Equations by Graphing?To solve a system of equations by graphing:
Graph each equation on the same set of axes.Look for the point(s) at which the two graphs intersect.Check that the point(s) of intersection satisfy both equations.If there is only one point of intersection, it is the solution to the system. If there is no point of intersection, the system has no solution. If there are infinitely many points of intersection, the system has infinitely many solutions.The graph of y = 7/2x - 3 is the red line while that of y = –3/2x + 7 is the red line. They intersect at (2, 4).
Therefore, the solution of the system of equations is: .
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subtracting 12 inverse operation that will undo the given operation
Answer:
+ 12
Step-by-step explanation:
Inverse means the opposite of the operation, and if the operation is subtraction the inverse would be addition. Add 12 to undo the -12.
the class is made up of 13 boys and 9 girls. what percent of the class do the boys make up? what percent do girls make up?
Answer: 60% boys and 40% girls
Step-by-step explanation:
The total amount of kids in the class would be 13 + 9 = 22 kids.
Boys would make up 13 / 22 = 60% of the class,
Girls would make up 9 / 22 = 40% of the class
how do I solve
What is the equation for a line that passes through the points (5,-2) and (-10,10)?
Answer:
y=-4x+2
Step-by-step explanation:
y2-y1/x2-x1
= 10-(-2)/-10-5
=12/-15 (divide by 3)
= -4/5x ---(Slope)
y=mx+b
-2=(-4/5)(5)+b
-2=-4+b (Add 4 on both Sides)
2=b
Put it all together
y=mx+b
Therefore,the equation is : y=-4/5x+2
Find the general expression for the area of the shaded region
In most cases, the area of the shaded zone is obtained by deducting the area of a smaller inner form from the area of a larger outer shape.The expression for the area of the shaded region is x² - 23x - 49.
Find the general expression for the area ?In most cases, the area of the shaded zone is obtained by deducting the area of a smaller inner form from the area of a larger outer shape.The area of the shaded region is the difference between the total area of the polygon and the area of its unobscured interior.
There are two ways for polygons to have the area of the shaded region.
Depending on the shape of the polygon, the shaded area may be on one or both of its sides.
Area of a rectangle
area = lw
where
l = length
w = width
Therefore,
The area of the shaded region = area of the big rectangle - area of the small rectangle
Therefore,
area of the big rectangle = (x+10)(2x+5) = 2x² + 5x + 20x + 50 = 2x² + 25x + 50
area of the small rectangle = (x+1)(x+1) = x² + x + x + 1 = x² + 2x + 1
area of the shaded region = 2x² + 25x + 50 - ( x² + 2x + 1)
area of the shaded region = 2x² + 25x + 50 - x² - 2x - 1
area of the shaded region = x² - 23x - 49
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A metal bar weights 8.15 ounces 93% of the bar is silver how many ounces of silver or silver are in the bar
There are 7.58 ounces of silver are in the bar.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We have to given that;
A metal bar weights 8.15 ounces.
And, 93% of the bar is silver.
Now, Let the amount of silver in the bar = x
So, We can formulate;
⇒ x = 93% of 8.15
⇒ x = 93/100 × 8.15
⇒ x = 7.58
Thus, the amount of silver in the bar = 7.58 ounces
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Evaluate this expression for x = 5: 6+ (10 -x2-20
Salut/Hello!
Answer:
Step-by-step explanation:
x = 5 : 6 + (10 - 2x - 20)
x= 0,8(3) + 10 - 2x - 20
2x + x = 0,8(3) + 10 - 20
3x = 0,8(3) + 10 - 20
3x = -10,8(3)
x = -3.6(1)
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