The domain of the given function f(x) = 2x + 7 is -∞ < x < ∞.
What is a domain?The range of values that we are permitted to enter into our function is known as the domain of a function.
Consider the function y = f(x), which has the independent variable x and the dependent variable y.
A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.
So, the given function is:
f(x) = 2x + 7
To find the domain:
There are no undefined places or domain restrictions in the function. As a result, -∞ < x < ∞ is the domain.
Therefore, the domain of the given function f(x) = 2x + 7 is -∞ < x < ∞.
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Correct question:
Find the domains of the following function: f(x) = 2x + 7
Write v as a linear combination of u1, u2, and u3, if possible. (Enter your answer in terms of u1, u2, and u3. If not possible, enter IMPOSSIBLE.)v = (-1, 7, 2), u1 = (3, 2, 8), u2 = (-1, -3, -1), u3 = (-2, 1 , -3)
v = u1 - 2u2 + u3 This means that v can be expressed as a linear combination of u1, u2, and u3. Specifically, we can take one copy of u1, subtract two copies of u2, and add one copy of u3 to obtain v.
To write v as a linear combination of u1, u2, and u3, we need to find constants a, b, and c such that v = au1 + bu2 + c*u3.
We can set up a system of equations to solve for these constants:
3a - b - 2c = -1
2a - 3b + c = 7
8a - b - 3c = 2
We can solve this system using row reduction, which yields:
a = 1
b = -2
c = 1
Therefore, we have:
v = u1 - 2u2 + u3
This means that v can be expressed as a linear combination of u1, u2, and u3. Specifically, we can take one copy of u1, subtract two copies of u2, and add one copy of u3 to obtain v.
It's worth noting that not every vector can be expressed as a linear combination of a given set of vectors. However, in this case, we were able to find constants that satisfy the equation v = au1 + bu2 + c*u3, so it is possible to write v as a linear combination of u1, u2, and u3.
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of the following values, which is least important to today's college students according to the yearly values survey?
The least important value to today's college students according to the yearly values survey is Political involvement. So the option B is correct.
The survey found that only 32% of college students believed that political involvement was important. This is significantly lower than the other values surveyed such as Financial Success (86%) and Community Involvement (71%). As such, it can be concluded that Political Involvement is the least important value to today's college students.
This may be due to a variety of factors, such as a lack of understanding of the political system, a lack of interest in politics, or a sense that individual political action will not make a difference.
It is important to recognize, however, that political involvement is still an important part of civic engagement and an essential part of the democratic process. As such, college students should strive to become more informed about politics and to find ways to get involved in the political process.
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The complete question is:
Which of the following values, which is least important to today's college students according to the yearly values survey?
A. Career success
B. Political involvement
C. Healthy lifestyle
D. Social media presence
construct shear and bending diagrams for the following beams. show your equations used to create the plots. p p p p l/2 l/4 l/4 p p p l/3 l/3 l/3
The shear force and bending moment diagrams for the given beam will have multiple segments of different shapes and slopes, reflecting the variation of loads along the length of the beam.
To construct the shear and bending diagrams for the given beam, we need to analyze the beam for the different sections where the load is applied. We can break down the beam into five sections:
Leftmost section (0 ≤ x ≤ L/4)
Second section (L/4 < x ≤ L/2)
Third section (L/2 < x ≤ 5L/12)
Fourth section (5L/12 < x ≤ 7L/12)
Rightmost section (7L/12 < x ≤ L)
We can use the equations for shear and bending moments to create the plots:
For section 1: 0 ≤ x ≤ L/4
The shear force diagram will be constant since there is no load applied in this section. The bending moment diagram will be a sloping line, which will be zero at x = 0 and will increase linearly with x as we move toward the right end of the section.
For section 2: L/4 < x ≤ L/2
The shear force diagram will start from the value of P at x = L/4 and remain constant up to x = L/2. The bending moment diagram will be a parabolic curve, which will be zero at x = L/4 and L/2 and will reach a maximum value at the midpoint of the section.
For section 3: L/2 < x ≤ 5L/12
The shear force diagram will start from the value of P at x = L/4 and remain constant up to x = L/2. At x = 5L/12, a load of P/3 is added, causing the shear force to increase suddenly. The bending moment diagram will be a cubic curve, which will be zero at x = L/4 and L/2, and will have a local minimum at x = 5L/12.
For section 4: 5L/12 < x ≤ 7L/12
The shear force diagram will start from the value of P + P/3 at x = 5L/12 and remain constant up to x = 7L/12. The bending moment diagram will be a cubic curve, which will be zero at x = L/4 and L/2, and will have a local maximum at x = 7L/12.
For section 5: 7L/12 < x ≤ L
The shear force diagram will start from the value of P + P/3 at x = 5L/12 and remain constant up to x = 7L/12. At x = L/3, a load of P/3 is added, causing the shear force to decrease suddenly. The bending moment diagram will be a parabolic curve, which will be zero at x = L/4 and L/2 and will reach a minimum value at the midpoint of the section.
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An inlet pipe on a swimming pool can be used to fill the pool in 16
hours. The drain pipe can be used to empty the pool in 24
hours. If the pool is 13
filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?
Answer:
Step-by-step explanation:
find all real numbers k for which there exists a nonzero 2 dimensional vector bold v such that begin bmatrix 2
The rectangle can be made to have rotation symmetry of order 2 by colouring one of the squares blue. Put a cross in the middle of the square which would have to be made blue.
To make a rectangle with a rotation symmetry of order 2, first draw the rectangle on a piece of paper. Then draw a cross in the middle of one of the squares in the rectangle. This is the square that needs to be coloured blue in order to create the rotation symmetry. Finally, colour the square with the cross blue to create the rotation symmetry.
Census data for a certain county shows that 19% of the adult residents are Hispanic. Suppose 92 people are called to jury duty and only 11 of them are Hispanic. Does this apparent underrepresentation of Hispanics call into question the fairness of the jury selection process? Again run a test using the PHANTOMS method to complete all parts of your problem.
Yes, the apparent under representation of Hispanics on the jury duty calls into question the fairness of the jury selection system, as the results of the hypothesis test suggest that the system may be systematically excluding Hispanics.
To determine whether the apparent underrepresentation of Hispanics on the jury selection system is statistically significant and calls into question its fairness, we need to perform a hypothesis test.
First, we set up the null hypothesis, which is the assumption that there is no difference between the proportion of Hispanics in the county population and the proportion of Hispanics in the jury pool. That is, the proportion of Hispanics in the jury pool is expected to be equal to 19%.
The alternative hypothesis is that there is a difference between the proportion of Hispanics in the county population and the proportion of Hispanics in the jury pool.
We can use a one-tailed z-test to test the null hypothesis, where the test statistic is calculated as:
z = (p - P) / sqrt(P(1-P)/n)
where p is the proportion of Hispanics in the jury pool, P is the proportion of Hispanics in the county population (0.19), and n is the sample size (72).
Plugging in the values, we get
z = (9/72 - 0.19) / sqrt(0.19*(1-0.19)/72) = -2.39
Assuming a significance level of 0.05, we compare the calculated z-value with the critical z-value of -1.645 (obtained from a standard normal distribution table). Since the calculated z-value is less than the critical z-value, we reject the null hypothesis and conclude that the proportion of Hispanics in the jury pool is significantly different from the proportion of Hispanics in the county population.
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The star Bellatrix is 1.4 × 1015 miles from Earth. Barnard’s star is 35,000,000,000,000 miles from Earth. Part A How far is Barnard’s star from Earth, in scientific notation? 3.5 × 1013 35 × 1013 3.5 × 1015 35 × 1015
In scientific notation the distance of the Barnard’s star from Earth, is given as 3.5 × 10^13
What is scientific notation?Scientific notation is a way of writing very large or very small numbers in a more compact form using powers of 10. In scientific notation, a number is expressed as a product of a coefficient and 10 raised to a power. The coefficient must be greater than or equal to 1 but less than 10. The power of 10 indicates the number of places the decimal point is moved to obtain the original number.
For 35,000,000,000,000
you have to start counting the digits from the right. The decimal point would occur just before the first digit (that is the number 3)
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PLEASE HELP 30 POINTS!
Answer:
57
57
123
123
57
57
123
that's all.
Answer:
m<1 = 57°
m<2 = m<1 = 57°
m<3 = x = 123°
m<4 = x = 123°
m<5 = m<1 = 57°
m<6 = m<5 = 57°
m<7 = m<4 = 123°
Step-by-step explanation:
[tex]{ \tt{m \angle 1 + x = 180 \degree}} \\ { \colorbox{silver}{corresponding \: angles}} \\ { \tt{m \angle 1 = 180 - 123}} \\ { \tt{ \underline{ \: m \angle 1 = 57 \degree \: }}}[/tex]
a relation r is called circular if arb and brc imply that cra. if r is an equivalence relation, then would r be circular?
If a relation R is an equivalence relation, then R will be circular.
If a relation R is an equivalence relation, then it must satisfy three properties: reflexivity, symmetry, and transitivity.
(i) Reflexivity: For any element "a" in the set, "aRa" must be true.
(ii) Symmetry: For any elements "a" and "b" in the set, if "aRb" then "bRa" must be true.
(iii) Transitivity: For any elements "a", "b", and "c" in the set, if aRb and bRc then "aRc" must be true.
A Circular relation is where "aRb" and "bRc" imply "cRa".
This is a stronger condition than the transitivity property of an equivalence relation, which only requires that "aRb" and "bRc" together imply "aRc".
Therefore, a relation that is an equivalence-relation have to be circular.
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The given question is incomplete, the complete question is
A relation R is called circular if "aRb" and "bRc" imply that "cRa". if R is an equivalence relation, then would R be circular?
Jane has been practicing sewing, and she wants to make a rectangular blanket to give as a gift to her best friend. So that the blanket is not too small, Jane decides the blanket will have an area of approximately 40 square feet, or 5,760 square inches. She also wants the blanket to be 18 inches longer than it is wide to have room to embroider her friend's name along one edge.
To the nearest tenth of an inch, what is the width of the blanket?
The width of the blanket to the nearest tenth of an inch is approximately 67.4 inches.
What is width in rectangle ?
In a rectangle, the width refers to the measurement of the shorter side of the rectangle, which is perpendicular to its length.
Let x be the width of the blanket in inches. Then the length of the blanket is x + 18 inches.
The area of the blanket is given by:
Area = Length x Width
5760 sq inches = (x + 18) inches * x inches
Expanding the right-hand side and solving for x, we get:
[tex]x^2 + 18x - 5760 = 0[/tex]
We can solve this quadratic equation using the quadratic formula:
[tex]x = (-b \pm \sqrt{(b^2 - 4ac)}) / 2a[/tex]
where a = 1, b = 18, and c = -5760. Plugging in these values, we get:
[tex]x = (-18 \pm \sqrt{(18^2 - 4(1)(-5760))}) / 2(1)[/tex]
[tex]x = (-18 \pm \sqrt{(18^2 + 23040)}) / 2[/tex]
x ≈ 67.42 or x ≈ -85.42
Since the width cannot be negative, the width of the blanket to the nearest tenth of an inch is approximately 67.4 inches.
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Solve the system of equations x + y = 8; y = x ^ 2 - 4
The solution to the system of equations is (x, y) = (-4, 12) or (3, 5).
What are systems of equations?simultaneous equations, or system of equations Two or more equations in algebra must be solved concurrently (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a distinct solution. Even then, a solution is not assured.
According to the given information:We can solve this system of equations by substitution or elimination. Here, we will use substitution:
Substitute y in the first equation with its expression from the second equation:
x + (x^2 - 4) = 8
Now, we have a quadratic equation in x:
x^2 + x - 12 = 0
Factor the quadratic equation:
(x + 4)(x - 3) = 0
So, either x + 4 = 0 or x - 3 = 0:
x = -4 or x = 3
Substitute each value of x into either equation to find the corresponding value of y:
If x = -4, then y = (-4)^2 - 4 = 12
If x = 3, then y = 3^2 - 4 = 5
Therefore, the solution to the system of equations is (x, y) = (-4, 12) or (3, 5).
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PLS Answer help i will give 10 brainly points if you help
Answer:
12×2, 3×8, 4×6
Step-by-step explanation:
To find the area of a parallelogram, the formula is A = bh.
1. Height: 6 ft
Base: 2 ft
6 × 2 = 12 ft
So it does not work.
2. Height: 12 ft
Base: 2 ft
12 × 2 = 24 ft
So it does work.
3. Height: 10 ft
Base: 14 ft
14 × 10 = 140 ft
So it does not work.
4. Height: 3 ft
Base: 4 ft
3 × 4 = 12 ft
So it does not work.
5. Height: 3 ft
Base: 8 ft
3 × 8 = 24 ft
So it does work.
6. Height: 4 ft
Base: 6 ft
4 × 6 = 24 ft
So it does work.
Solve the equation.
Cos 9= sin 56.3
According to the problem the answer is cos 9 = sin 56.3.
What is cos?Cos is a mathematical function that returns the ratio of the side adjacent to a given angle of a right triangle to the hypotenuse of the triangle. It is one of the most commonly used trigonometric functions and is used in various mathematical calculations such as finding angles, distances, and wave lengths. Cos is often written as cosine and is typically abbreviated as "cos." It can also be written as COS or csc. Cos is typically used in conjunction with sin and tan to measure angles and distances in a triangle. Cos can also be used to calculate wave lengths in physics and to determine the magnitude of a vector in vector calculus. Cos is an important concept in mathematics and is used in many areas of science, engineering, and technology.
Use the identity sin(90°-x) = cos x:
sin 56.3 = cos (90° - 56.3)
cos 9 = cos (90° - 56.3)
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For cos 9°, angle lies between 0° and 90° (First Quadrant). Since cosine function is positive and in the first quadrant, thus cos 9° value = 0.9876883. Also Cos 9 = √(1-sin²(9°)).
What is cos?Cos is a mathematical function that returns the ratio of the side adjacent to a given angle of a right triangle to the hypotenuse of the triangle. It is one of the most commonly used trigonometric functions and is used in various mathematical calculations such as finding angles, distances, and wave lengths. Cos is often written as cosine and is typically abbreviated as "cos." It can also be written as COS or csc.
The value of cos 9 degrees in decimal is 0.987688340, since Cos 9 degrees can also be expressed using the equivalent of the given angle (9 degrees) in radians (0.15707)
Using degree to radian conversion, θ in radians is:
= θ in degrees × (pi/180°)
⇒ 9 degrees
= 9° × (π/180°) rad
= π/20 or 0.1570
∴ cos 9° = cos(0.1570)
= 0.9876883
Since the cosine is the periodic function, we can represent cos 9° as,
So, cos 9 degrees = cos(9° + n × 360°).
⇒ cos 9°
= cos 369°
= cos 729°, and so on.
Cos 9 = √(1-sin²(9°))
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Question 8 Suppose that W is random variable. Given that P(W ≤6)=0.935 find the probability of it complement, P(W>6)
The required probability of W being greater than 6 is 0.065 or 6.5%.
What is Probability?A probability value represents the likelihood that an occurrence will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place.
According to question:The complement of an event A is the event that A does not occur. In this case, the event A is "W ≤ 6", and its complement is "W > 6".
We are given that P(W ≤ 6) = 0.935. Using the complement rule of probability, we can find the probability of W > 6 as follows:
[tex]$$P(W > 6) = 1 - P(W \leq 6)$$[/tex]
Substituting the given value, we have:
P(W > 6) = 1 - 0.935 = 0.065
Therefore, the probability of W being greater than 6 is 0.065 or 6.5%.
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c. The expression ax² + 11x + 3 can be factorised. List the possible values of a given that a is a positive integer.
Step-by-step explanation:
If the polynomial 3x^3+ax^2-11x+3 is exactly divisible by (x – 1), then find the value of a. Hence, factorize the polynomial. can anyone help
please help !! Given l, m, n, find the value of x.
(7x-2)° (5x+14)°
Answer:
Step-by-step explanation:
7x - 2 = 5x + 14
2x - 2 = 14
2x = 16
x = 8
6x³+4xy²+3y³+13xy+8÷x+2 Divide polynomials
The quοtient is [tex]6x^2 - 8xy + 17y^2 - 34y + 70[/tex], and the remainder is [tex]8y^3 - 40.[/tex]
What is polynomial?A polynomial is a mathematical expression made up of variables (like x, y, and z) and coefficients (constants multiplied by the variables), as well as addition, subtraction, and multiplication operators. The variables and coefficients are raised to n-negative integer powers, also known as degrees.
We can use long division to divide fractions. Divide 6x³ + 4xy² + 3y³ + 13xy + 8 by x + 2 as shown:
[tex]6x^2 - 8xy + 17y^2 - 34y + 70[/tex]
-------------------------------------
[tex]x + 2 | 6x^3 + 4xy^2 + 3y^3 + 13xy + 8[/tex]
[tex]- 6x^3 - 12x^2[/tex]
---------------
[tex]12x^2 + 4xy^2[/tex]
[tex]- 12x^2 - 24x[/tex]
--------------
[tex]4xy^2 + 24x[/tex]
[tex]- 4xy^2 - 8y^3[/tex]
--------------
[tex]24x - 8y^3 + 8[/tex]
[tex]- 24x - 48[/tex]
------------
[tex]8y^3 - 40[/tex]
Therefοre, the quοtient is [tex]6x^2 - 8xy + 17y^2 - 34y + 70[/tex], and the remainder is [tex]8y^3 - 40[/tex].
Thus, we can express the οriginal pοlynοmial as:
[tex]6x^3+4xy^2+3y^3+13xy+8[/tex]
[tex]= (x + 2)(6x^2 - 8xy + 17y^2 - 34y + 70) + (8y^3 - 40) \div (x + 2)[/tex]
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question 1 write an inequality and a word sentence that represent the graph. let x represent the unknown number.
The inequality is X > 0 and a word sentence represent the graph is X the graph of a number line with an open circle on zero and an arrow pointing to the right.
The inequality X > 0 represents the graph of a number line with an open circle on zero to left and an arrow pointing to the right. This means that any value of X that is greater than zero is a valid solution for the inequality.
In other words, X can be any positive number, such as 1, 2, 3, and so on. However, X cannot be zero or any negative number, as those values do not satisfy the inequality. Therefore, the word sentence that represents this inequality is "X is greater than zero."
This means that X must be a positive number, and it can be any value that is greater than zero.
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A human head can be approximated as a sphere with a circumference of 60
centimeters. What is the approximate volume of a human head, rounded to the nearest 1,000
cubic centimeters?(GEOMETRY HELP)
The approximate volume of a human head is 4000 cubic centimeter.
What is the approximate volume of a human head?A sphere is simply a geometrical object that is a three-dimensional analogue to a two-dimensional circle.
The circumference of a sphere is given by the formula:
C = 2πr
Where r is the radius of the sphere. In this case, we are given that the circumference of the sphere (which approximates the human head) is 60 cm, so:
60 cm = 2πr
Solve for r
r = 60/2π
r = 30/π
The volume of a sphere is given by the formula:
V = (4/3)πr³.
Substituting the value we found for r, we get:
V = (4/3) × π × ( 30/π )³
V = (4/3) × π × ( 30/π )³
V = 3647.566 cm³
V = 4000 cm³
Therefore, the volume to the nearest 1,000 cubic cm is 4000 cm³.
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19
The diagram shows a sector OBC of a circle with centre O and radius (6 + x) cm.
B
A
es 50°
6 cm
DX
find the value of x.
Give your answer correct to 3 significant figures.
x cm
A is the point on OB and D is the point on OC such that OA = OD = 6 cm
Angle BOC= 50°
Given that
Diagram N
accurately
the perimeter of sector OBC= 2 x the perimeter of triangle OAD
The value of the variable, x, obtained using the formula for the perimeter of a sector of a circle is; x = 6 cm
What is a sector of a circle?A sector of a circle is the region of the circle that has two radii of the circle and the arc between the two radii as the boundary of the region.
The perimeter of a sector of a circle can be obtained using the formula;
Perimeter = 2·r + (θ/360°) × (2·π·r)
The radius of sector OAD, r = 6 cm
Therefore;
The perimeter of sector OAD = 2 × 6 + (50/360) × 2 × π × 6 = 12 + 5·π/3
The perimeter of sector OBC = 2 × The perimeter of sector OAD
Therefore;
The perimeter of sector OBC = 2 × (12 + 5·π/3) = 24 + 10·π/3
Which indicates;
The perimeter of sector OBC = 2 × (6 + x) + (50/360) × 2 × π × (6 + x)
2 × (6 + x) + (50/360) × 2 × π × (6 + x) = (5·π·x + 30·π + 36·x + 216)/18
24 + 10·π/3 = (5·π·x + 30·π + 36·x + 216)/18
432 + 60·π = 5·π·x + 30·π + 36·x + 216
432 - 216 + 60·π - 30·π = x·(5·π + 36)
216 + 30·π = x·(5·π + 36)
6 × (5·π + 36 ) = x·(5·π + 36)
x·(5·π + 36) = 6 × (5·π + 36 )
x = 6 × (5·π + 36 )/(5·π + 36 ) = 6
x = 6 cm
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Por favor, necesito ayuda con esto es de estadística. Muchas gracias
Las calificaciones de 20 alumnos que presentaron exámen de admisión a cierta facultad, utilizando la escala de 0 a 100, fueron:
83 64 51 46 82 91 73 82 65 61 74 64 75 81 94 65 42 81 56 61 72 65 54 39 70 93 42 46 54 72
•Elaborar: diagrama de tallo y hoja
•Calcular: coeficiente de variación
•Realizar un diagrama de caja
•Percentil 85, decil 2
Therefore, the coefficient of variation for the given data is approximately 24.71%.
What is box plot?A box plot, also known as a box-and-whisker plot, is a graphical representation of a data set that shows the distribution of the data using quartiles. It is a standardized way of displaying the distribution of data based on the five-number summary: minimum, first quartile, median, third quartile, and maximum. The box represents the middle 50% of the data, with the median marked by a line inside the box. The whiskers extend from the box to the minimum and maximum values, or to a certain range if there are outliers. Box plots are useful for comparing the distributions of different data sets and identifying potential outliers.
Here,
1. Stem-and-Leaf Plot:
A stem-and-leaf plot is a way to display data that separates the tens digit of each number from the ones digit. Here is the stem-and-leaf plot for the given data:
3 | 9 9
4 | 2 2 6 6
5 | 1 4 4 6
6 | 1 4 5 5 5 5 5 5
7 | 0 2 3 4
8 | 1 2 2 3 5
9 | 3 4
In this plot, the stem represents the tens digit and the leaves represent the ones digit.
2. Coefficient of Variation:
The coefficient of variation is a measure of the relative variability of a data set. It is calculated as the ratio of the standard deviation to the mean, expressed as a percentage. Here is how to calculate the coefficient of variation for the given data:
Calculate the mean of the data:
Mean = (83+64+51+46+82+91+73+82+65+61+74+64+75+81+94+65+42+81+56+61+72+65+54+39+70+93+42+46+54+72)/20 = 68.25
Calculate the standard deviation of the data:
Standard deviation = sqrt((1/20) * ((83-68.25)^2 + (64-68.25)^2 + ... + (72-68.25)^2))
Standard deviation ≈ 16.88
Calculate the coefficient of variation:
Coefficient of variation = (Standard deviation / Mean) * 100
Coefficient of variation ≈ 24.71%
3. Box Plot:
A box plot is a way to visualize the distribution of data. It displays the minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value of the data. Here is the box plot for the given data:
| +----------+
94 | |
| +----------+
93 | |
| +-----+-----+
82 | | |
| | |
81 | | |
| +-----+ |
80 | | |
| | |
79 | | |
| | |
78 | | |
| | |
77 | | |
| | |
76 | | |
| | |
75 | | |
| | |
74 | | |
| | |
73 | | |
| | |
72 | +-----------------+
|
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
In this plot, the horizontal line inside the box represents the median, the bottom and top edges of the box represent the first and third quartiles (Q1 and Q3), respectively, and the vertical lines extending from the box represent the minimum and maximum values, excluding outliers.
4. To find the 85th percentile, we need to arrange the data in order from smallest to largest:
39, 42, 42, 46, 46, 51, 54, 56, 61, 61, 64, 64, 65, 65, 65, 70, 72, 72, 73, 74, 75, 81, 81, 82, 82, 83, 91, 93, 94
There are a total of 20 scores, so the 85th percentile would be the score at the 0.85(20) = 17th position:
85th percentile = 72
To find the 2nd decile, we first need to calculate the number of scores in each decile. Since there are 20 scores, each decile would have 2 scores. The 2nd decile would be the score at the 0.2(20) = 4th position:
2nd decile = 46
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Complete question:
Please, I need help with this, it's about statistics. Thank you very much. The grades of 20 students who took an admission exam to a certain faculty, using a scale of 0 to 100, were: 83 64 51 46 82 91 73 82 65 61 74 64 75 81 94 65 42 81 56 61 72 65 54 39 70 93 42 46 54 72
• Make: stem-and-leaf plot
• Calculate: coefficient of variation
• Create a box plot
• 85th percentile, 2nd decile.
What is the meaning of "invertible n x n matrices"?
Answer: A matrix A of dimension n x n is called invertible if and only if there exists another matrix B of the same dimension, such that AB = BA = I, where I is the identity matrix of the same order.
Step-by-step explanation:
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Last night, Roberto spent 90 minutes doing homework, two-thirds of an hour reading, and 540 seconds making his lunch for the next day. How many more minutes did Roberto spend doing homework than he did reading and making his lunch?
The answer is 41 minutes.
explaination:
540 secs = 9 minutes
2/3 of 60 mins= 40 mins
(to find a fraction of a number you divide it by the denominator and times it after by the numerator)
9+40= 49
homework: 90 mins
reading and making lunch: 49 minutes
we want the difference so:
90-49= 41
Roberto spent 41 more minutes doing his homework than reading and making lunch.
Slope of the tangent line=?
m=?
b=?
The function for this problem is given as follows:
[tex]f(x) = \sqrt{57 - x}[/tex]
The derivative of the function is given as follows:
[tex]f^{\prime}(x) = -\frac{1}{2\sqrt{57 - x}}[/tex]
The slope of the tangent line at point (8,7) is given by the numeric value of the derivative of f(x) at x = 8, hence:
[tex]f^{\prime}(8) = -\frac{1}{2\sqrt{57 - 8}}[/tex]
m = f'(8) = -1/14.
Hence the equation of the tangent line, which is a linear function, is given as follows:
y = -x/14 + b.
When x = 8, y = 7, hence the intercept b is obtained as follows:
7 = -8/14 + b
b = 7 + 8/14
b = 49/7 + 4/7
b = 53/7.
Hence the equation is given as follows:
y = -x/14 + 53/7.
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point $p$ lies inside square $abcd$ such that triangle $abp$ is equilateral. find $\angle pcd$ in degrees.
The measurement of angle PCD in equilateral triangle is 67.38°.
Let $s$ be the side length of the square $abcd$, and let $O$ be the center of the square. Then $OP = s/\sqrt{2}$.
Since triangle $ABP$ is equilateral, we have $\angle ABP = 60^\circ$ and $AP=BP=s$. Let $E$ be the foot of the perpendicular from $P$ to $AB$. Then $AE=BE=s/2$ and $EP=s\sqrt{3}/2$.
Since $EP$ is perpendicular to $AB$ and $AB$ is parallel to $CD$, we have $\angle PCD = \angle ACE$.
Since $OP$ is perpendicular to $AB$, we have $\angle OEP = \angle AEP = 30^\circ$. Also, $OE=OP/\sqrt{2}=s/2$.
Using the Pythagorean theorem in triangle $OCE$, we have
CE= [tex]\sqrt{(OE)^{2} + (OC)^{2}} = \sqrt{(s/2)^{2} + s^{2}} = s\sqrt{5}/2[/tex]
Therefore, $\sin \angle ACE = CE/CP = \sqrt{5}/2$. Thus,
∠PCD = ∠ACE = arcsin(√5/2) ≈ 67.38°
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I will mark you brainiest!
SSS is used to prove two triangles are congruent.
A) False
B) True
Answer:
A
Step-by-step explanation:
because___________________________________
Answer:
B) True
Step-by-step explanation:
SSS or Side-Side-Side is used to prove two triangles are congruent.
The cost C (in dollars) of supplying recycling bins to p% of the population of a rural township is given by C=25000p/100-p, 0 ≤ p ≤ 100, Use a graphing utility to graph the cost function.
Here's a graph of the cost function C = 25000p / (100 - p), using graphing utility. The graph shows that the cost function is continuous and defined for all values in its domain.
The domain of the function is restricted to 0 ≤ p ≤ 100, since it doesn't make sense to supply recycling bins to more than 100% of the population, or to a negative percentage of the population.
As p approaches 100%, the cost of supplying recycling bins becomes very large, since it becomes increasingly expensive to provide bins to a large portion of the population. As p approaches 0%, the cost also approaches 0, since there are fewer bins needed for a smaller population.
The function has a vertical asymptote at p = 100, since the denominator of the fraction approaches 0 as p approaches 100 from the left. This means that the cost becomes infinitely large as the percentage of the population approaches 100%.
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the graph shows the preimage shaded in grey and the image outlined in black. what is the scale factor of the dilation?
The scale factor of dilation of the shaded in gray to the shaded in black is 3
Calculating the scale factor dilationGiven that
The preimage = shaded in gray
The image = shaded in black
From the graph, we have the following values on the image and the preimage
The preimage = shaded in gray = 4
The image = shaded in black = 12
The scale factor of dilation is then calculated as
Scale factor = shaded in black/shaded in gray
So, we have
Scale factor = 12/4
Evaluate
Scale factor = 3
Hence, the scale factor dilation is 3
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The volume, V , of a sphere in terms of its radius, r , is given by V(r)=4/3πr^3 . Express r as a function of V , and find the radius of a sphere with volume of 100 cubic feet.
Round your answer for the radius to two decimal places.
A sphere with volume 100 cubic feet has radius ??
So the radius of the sphere is approximately 2.88 feet (rounded to two decimal places).
What is volume?Volume is the amount of space occupied by a three-dimensional object as measured in cubic units. It is the measure of the amount of material or substance that a container, object, or shape can hold.
Here,
To express r as a function of V, we can rearrange the equation V = 4/3πr³ to solve for r:
V = 4/3πr³
V / (4/3π) = r³
r = ³√(V / (4/3π))
r = ³√(3V / 4π)
To find the radius of a sphere with volume 100 cubic feet, we can substitute V = 100 into the equation:
r = ³√(3V / 4π)
= ³√(3(100) / (4π))
≈ 2.88 units
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