The dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 19 in. by 11 in. by cutting congruent squares from the corners and folding up the sides are 6.33 in. x 3.33 in. x 5.33 in. The volume of the box is 113.78 in³.
How to find the dimensions of the open rectangular box of maximum volume?The dimensions of the box can be found with the following steps:
First, determine the side length of the square that is to be removed from each corner of the cardboard box. Since this will be done uniformly on all four corners, let the side length be x. The dimensions of the cardboard box can then be written as:
Length = 19 in. - 2x
Breadth = 11 in. - 2x
Height = x
After folding the cardboard along the creases, the base of the rectangular box will be (19 - 2x) in. by (11 - 2x) in. with the height of the box being x in. The volume of the box can then be found by multiplying the base and height of the box, i.e.,
Volume = (19 - 2x) (11 - 2x) x
Let V(x) be the volume of the rectangular box in terms of x. Then:
V(x) = (19 - 2x) (11 - 2x) x
Simplifying,
V(x) = 4x³ - 60x² + 209x
The maximum value of V(x) can be found by differentiating V(x) with respect to x and equating the result to zero. Therefore,
V'(x) = 12x² - 120x + 209 = 0
Solving, V(x) has a maximum value when x = 19/3 - 2(2/3)√14 or x = 19/3 + 2(2/3)√14. The value x = 19/3 - 2(2/3)√14 is the maximum value because x must be less than 5.5, which is the minimum of 11/2 and 19/2 divided by 3, the upper bound for x. Therefore, the dimensions of the box are
Length = 19 - 2(19/3 - 2(2/3)√14) = 6.33 in.
Breadth = 11 - 2(19/3 - 2(2/3)√14) = 3.33 in.
Height = 19/3 - 2(2/3)√14 = 5.33 in.
Thus, the dimensions of the box are 6.33 in. x 3.33 in. x 5.33 in. The volume of the box is:
V = 6.33 x 3.33 x 5.33 = 113.78 in³.
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At times, the relationship between a dependent and an independent variable is expressed as a logarithmic equation: Given a positive constant € and the two equations below, what is the relationship between X and Y? Equation 1: Log(c) = X/2 Equation 2: Log(c^2) = Y 1 . X Y Submit
The relationship between a dependent and an independent variable expressed as a logarithmic equation is as follows X = Y/2
At times, the relationship between a dependent and an independent variable is expressed as a logarithmic equation. For this question, given a positive constant € and the two equations below, we can find the relationship between X and Y. Equation 1: Log(c) = X/2 Equation 2: Log(c^2) = Y.We can use the basic properties of logarithms to solve this problem. To do so, we need to understand what logarithms are first.Logarithms are the opposite of exponentials. They allow us to find the exponent needed to produce a given value. For instance, log base 2 of 8 is 3 since 2^3 = 8.
A logarithm is represented as log_bx where b is the base and x is the argument or the number being passed to the logarithm.In equation 1, we are given that log(c) = x/2. To isolate x, we need to exponentiate both sides with base e.e^(log(c)) = e^(x/2)This gives us c = e^(x/2).We can rewrite this expression as c^2 = e^x. Now we use equation 2 which states that log(c^2) = y. This is equivalent to 2log(c) = y.Using equation 1, we can substitute log(c) for x/2.2log(c) = y2(x/2) = yx = y/2So the relationship between X and Y is X = Y/2. Therefore, we can conclude that the relationship between a dependent and an independent variable expressed as a logarithmic equation is as follows: X = Y/2.
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a circular piece of glass has a radius of 2.1 meters the glass sells for $7.10 per square meter what is the cost of the glass
Answer:
Step-by-step explanation:
The area of a circle is given by the formula:
A = πr^2
where A is the area and r is the radius.
Substituting the given values, we get:
A = π(2.1 m)^2 = 13.85 m^2
So the total cost of the glass with a price of $7.10 per square meter is:
Cost = Price per square meter x Total area
Cost = $7.10/m^2 x 13.85 m^2 = $98.24
Therefore, the cost of the glass is $98.24.
What is the composition of linear transformation matrix?
A linear transformation matrix is a square matrix that represents a linear transformation of a vector space. The composition of linear transformation matrices is equivalent to the composition of linear transformations they represent.
In general, the composition of two linear transformations A and B can be represented by the matrix product AB. Therefore, the composition of two linear transformation matrices, say A and B, would be the matrix product AB.
Linear transformations are functions that map vectors from one vector space to another in a linear way. These transformations can be represented by matrices, which can be composed to represent the composition of linear transformations.
The composition of two linear transformations represented by matrices involves multiplying the matrices together. To perform this multiplication, we need to ensure that the number of columns in the first matrix matches the number of rows in the second matrix. The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.
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The stem-and-leaf plot below gives the number of minutes that customers waited for their orders at two restaurants. There were 13 wait times recorded for the first restaurant and 16 for the second. Use the plot to answer the questions.
Answer: The first restaurant had a greater median time
the range for the first restaurant is 35 minutes and the range for the second restaurant is 39 minutes
The second restaurant had more wait times from 30-39 minutes
16 A function is given.
f(x)= (2x-2)(x − 3)
-
Use the Add Point tool to plot the zeros and the maximum or minimum value of the function.
The zeros of the function are x=1 and x=3, and the minimum value of the function is at x=2.
What is the polynomial function?
A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.
To find the zeros, we set the function equal to zero and solve for x:
(2x-2)(x-3) = 0
This equation is true when either 2x-2=0 or x-3=0. Solving for x in each case, we get:
2x-2=0 => x=1
x-3=0 => x=3
So the zeros of the function are x=1 and x=3.
To find the maximum or minimum value of the function, we can take the derivative of the function and set it equal to zero:
f'(x) = 4x - 8
4x - 8 = 0 ----> x = 2
So the critical point of the function is x=2. To determine if this point is maximum or minimum, we can use the second derivative test:
f''(x) = 4
Since f''(2) > 0, the function has a minimum at x=2.
Therefore, the zeros of the function are x=1 and x=3, and the minimum value of the function is at x=2.
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B = 75*
C = 50*
A = ?*
Answer: A = 55* or 55 degrees
Step-by-step explanation:
The interior angles of a triangle always have a sum of 180 degrees.
75 + 50 + x = 180
Solve for x
FInal answer: 55 degrees
hope i explained it :)
William writes a function f(x) = 2x - 10. He uses an
input-output table to represent the function.
Input: 4
Output: -8
What is the output of William's function when the
input is 4?
Answer: -8
Step-by-step explanation:
When the input is 4, according to the input-output table, the output is -8.
Plugging 4 into the function f(x) = 2x - 10 directly also gives the same result:
f(4) = 2(4) - 10 = 8 - 10 = -2
So the output of William's function when the input is 4 is -8.
Thabo and his friend Amon shared a Job of cleaning Thabo's uncle yard He paid both of them R400. Thabo worked three hours and Amon worked for two hours. Use the information above to answer the questions that follow: 1.1 Determine the amount Thabo will receive, if they decide to share the R400 in a ratio of 3.2. 12 Thabo used 1/5 of his money towards a second hand video game. Calculate the cost of the video game. 13. Thibo's transport fare to school has increased from R800 to R1150. 1.3.1 Write R1150 in words. 1.3.2 Determine the percentage increase of the transport fare. You may use the formula: Percentage increase New amount-Old amount * 100% (2)
1.1) If Thabo and Amon decide to share the R400 in a ratio of 3.2, the amount Thabo will receive is R240.
1.2) If Thabo used 1/5 (a fraction) of his money towards a secondhand video game, the cost of the secondhand video game is R48.
1.3.1) If Thabo's transport fare to school has increased from R800 to R1,150, R1,150 written in words, is One Thousand, One Hundred and Fifty rupees.
1.3.2) If Thabo's transport fare to school has increased from R800 to R1,150, the percentage increase in the transport fare is 43.75%.
What is the ratio?The ratio refers to the relative size of one quantity compared to another.
Ratios are formally written using the ratio standard form (:). Ratios can also be expressed as decimals, percentages, and fractions.
The total amount received from the cleaning job = R400
The number of hours Thabo worked = 3 hours
The number of hours Amon worked = 2 hours
1.1) Sharing ratio = 3:2
The sum of ratios = 5
Thabo's share of R400 = R240 (R400 x 3/5)
1.2) The cost of the video game = R48 (R240 × ¹/₅)
1.3) Transport Fare:Old transport fare = R800
Current transport fare = R1,150
Increase in transport fare = R350 (R1,150 - R800)
Percentage increase in transport fare = 43.75% (R350/R800 x 100)
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Expresa en grados los siguientes radiantes:
1) π RAD=?
2) 3/2π RAD=?
3) π/6 RAD=?
4) π/18 RAD=?
Square root of За^2/10b^6
The simplified square expression for[tex]\sqrt{3a^2/10b^6}[/tex] is [tex]|3a| / (\sqrt{10} * b^{3})[/tex].
What is square root ?
In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 x 3 = 9.
The square root is denoted by the symbol √, also known as the radical symbol. For instance, the square root of 16 is written as √16 = 4.
The square root can be used to solve various types of equations, including quadratic equations and problems involving areas and volumes. It is also used in various fields such as physics, engineering, and finance.
According to the question:
To simplify the expression [tex]\sqrt{3a^{2}/10b^6}[/tex], we can first separate the numerator and denominator inside the square root:
[tex]\sqrt{3a^2/10b^6} = \sqrt{3a^2}/\sqrt{10b^6}[/tex]
Next, we can simplify the square root of the numerator:
[tex]\sqrt{3a^2} = |3a|,[/tex] where |За| represents the absolute value of За.
Finally, we can simplify the square root of the denominator by factoring out the perfect square[tex]b^2[/tex]:
[tex]\sqrt{10b^6} = \sqrt{10} * \sqrt{b^6} = \sqrt{10} * b^{3}[/tex]
Substituting these values back into the original expression, we get:
[tex]\sqrt{3a^2/10b^6} = |3a| / \(sqrt{10} * b^3[/tex]
Therefore, the simplified expression for[tex]\sqrt{3a^2/10b^6}[/tex] is [tex]|3a| / (\sqrt{10} * b^{3})[/tex].
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three potential employees took an aptitude test. each person took a different version of the test. the scores are reported below. kaitlyn got a score of 74.5 ; this version has a mean of 68.5 and a standard deviation of 12 . kiersten got a score of 244.8 ; this version has a mean of 210 and a standard deviation of 29 . rebecca got a score of 7.24 ; this version has a mean of 6.7 and a standard deviation of 0.3 . if the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job?
Step-by-step explanation:
kaitlyn score is 6 points above the mean
z-score = 6 / 12 = .5
kiersten score is 34.8 above the mean z-score = 34.8/29 = 1.2
rebecca score is .54 above the mean z -score = .54/ .3 = 1.8
rebecca scored the highest percentile (highes z-score) of the three....the best
Select the reason why these triangles are
similar. If they are not, select "Not similar."
A. SAS
C. Not similar
B. AA
D. SSS
109⁰
41°
30⁰
30°
The triangles are similar by the AA similarity criterion since they have two pairs of congruent angles (41° and 109°, and 30°). Therefore, the answer is B. AA.
What is triangle?A triangle is a polygon that has three sides, three vertices, and three angles. It is the simplest polygon in Euclidean geometry and one of the most studied shapes in mathematics. The sum of the three angles in a triangle is always 180 degrees, and the length of one side of a triangle is always less than the sum of the other two sides. There are many different types of triangles, including equilateral triangles (where all sides are equal), isosceles triangles (where two sides are equal), and scalene triangles (where no sides are equal). Triangles are used in many areas of mathematics and science, including trigonometry, geometry, and physics.
Here,
To determine whether the two triangles are similar using AA similarity, we need to compare the angles of both triangles.
Triangle 1 has angles 41°, 30°, and 109°.
Triangle 2 has angles 30°, 41°, and 109°.
We see that the two triangles have two pairs of congruent angles, namely 41° and 41°, and 109° and 109°. Therefore, the two triangles are similar by the AA similarity criterion.
Note that the order of the angles does not matter when comparing triangles for similarity.
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QS and TV areparallellines. P Q R S T U V W Which angles are vertical angles?
The required angles ∠SRP and ∠TUW are alternate exterior angles.
What is alternate exterior angles?Alternate exterior angles are a pair of angles that lie on opposite sides of a transversal line that intersects two other lines. Specifically, the angles are exterior to the two intersecting lines and lie on opposite sides of the transversal.
More formally, if two parallel lines are intersected by a transversal, then alternate exterior angles are the pair of angles that are:
On opposite sides of the transversal line.
Outside of the two parallel lines.
Congruent to each other.
These angles are called "alternate" because they are on opposite sides of the transversal and "exterior" because they are outside of the two parallel lines. The congruence of the angles is a result of the parallel lines creating equal corresponding angles.
So,∠SRP and ∠TUW are alternate exterior angles.
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Please help with these Formal Logic questions;
8.1 Some cashmere sweaters are fashionable garments, so some cashmere sweaters are not suede jackets, for some suede jackets are not fashionable garments.
Which of the following correctly expresses the form of this argument?
a. Some C are F.
Some C are not S.
Some S are not F.
b. Some S are not F.
Some C are F.
Some C are not S.
c. Some C are not F.
Some C are not S.
Some C are F.
d. Some F are not S.
Some F are C.
Some S are not C.
e. Some C are F.
Some F are not S.
Some S are not S.
8.2 Some cashmere sweaters are fashionable garments, so some cashmere sweaters are not suede jackets, for some suede jackets are not fashionable garments.
Which of the following substitutions proves the argument invalid?
a. C = animals, F = cats, S = mammals.
b. C = dogs, F = animals, S = mammals.
c. C = dogs, F = mammals, S = fish.
d. C = mammals, F = animals, S = dogs.
e. C = cats, F = mammals, S = animals.
8.3 If cell phone companies screen text messages, then freedom of speech is threatened. Thus, freedom of speech is not threatened, because cell phone companies do not screen text messages.
Which of the following substitutions proves the argument invalid?
a. C = Abraham Lincoln was assassinated, F = George Washington was assassinated.
b. C = Joe Smith was beheaded, F = Joe Smith is dead.
c. C = Abraham Lincoln was beheaded, F = Abraham Lincoln is dead.
d. C = Abraham Lincoln was assassinated, F = Abraham Lincoln is dead.
e. C = Abraham Lincoln was beheaded, F = Abraham Lincoln is not dead.
8.4 If cell phone companies screen text messages, then freedom of speech is threatened. Thus, freedom of speech is not threatened, because cell phone companies do not screen text messages.
Which of the following correctly expresses the form of this argument?
a) If C then F.
C.
F.
b) Not F.
Not C.
If C then F.
c) All C are F.
C.
F.
d) If C then F.
Not C.
Not F.
e) If C then F.
Not F.
Not C.
8.5 All container ships that are ocean-going are air polluters. Hence, all container ships are air polluters.
Which of the following correctly expresses the form of this argument?
a) All C are A.
All C are O.
b) All C are A.
All C that are O are A.
c) All CS are O.
All CS are A.
d) All C are O.
All C are A.
8.6 All container ships that are ocean-going are air polluters. Hence, all container ships are air polluters.
Which of the following substitutions proves the argument invalid?
a. C = husbands, O = married, A = men.
b. C = men, O = humans, A = mammals.
c. C = men, O = married, A = husbands.
d. C = wives, O = divorced, A = women.
e. C = cats, O = animals, A = dogs.
8.17 All A are B. (T) Contrary
a. No A are B. (Und.)
b. All B are A. (Und.)
c. Some A are B. (T)
d. No A are B. (F)
e. No A are non-B. (T)
8.18 Some A are not non-B. (F) Contradiction
a. Some A are non-B. (T)
b. All A are non-B. (T)
c. Some B are not non-A. (F)
d. Some A are non-B. (T)
e. Some A are B. (T)
8.19 Some non-A are not B. (T) Subcontrary
a. Some non-A are B. (Und.)
b. No non-A are B. (Und.)
c. All non-A are B. (F)
d. Some A are B. (T)
e. Some non-B are not A. (T)
The answers for the questions given are mentioned below respectively.
Define the term expression?In mathematics, an expression is a combination of numbers, variables, and mathematical operations that are arranged in a specific way.
It can be a single number or variable, or a combination of them, along with mathematical operations like addition, subtraction, multiplication, division, exponents, and parentheses.
8.1 - The correct expression of the form of this argument is: a. Some C are F. Some C are not S. Some S are not F.
8.2 - The substitution that proves the argument invalid is: b. C = dogs, F = animals, and S = mammals.
8.3 - The substitution that proves the argument invalid is: e. C = Abrahamm Lincoln was beheaded, F = Abraham Lincon is not dead .
8.4 - The correct expression of the form of this argument is: d. If C then F. Not C. Not F.
8.5 - The correct expression of the form of this argument is: b. All C's are A. All C that are O are the A.
8.6 - The substitution that proves the argument invalid is: c. C=men, O=married, A=husbands.
8.17 - The correct truth value of the statement is: c. Some A are B. (T)
8.18 - The correct truth value of the statement is: e. Some A are B. (T)
8.19 - The correct truth value of the statement is: a. Some non-A are B. (Und.)
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Can some one solve this and show their work plssss
Answer:
For WXYZ to be a parallelogram, both pairs of opposite sides must be parallel.
So, we have 7m + 4 = 9m and 5y + 13 - (2n - 1) = 6y - 8 - (n + 6).
Solving the first equation, we get m = 2.
Solving the second equation, we get y - n = 4.
Thus, for WXYZ to be a parallelogram, m = 2 and y - n = 4, so option B is correct.
Sgr A has a diameter of about 27.3 million miles; that's roughly the same distance from Mercury to:
Venus
Jupiter
Earth
The Sun
Sgr A has a diameter of about 27.3 million miles; that's roughly the same distance from Mercury to The Sun.
What is distance?Distance is a measurement of how far apart two objects or points are, either numerically or rarely qualitatively. Distance can relate to a physical length in physics or to an estimate based on other factors in everyday language (e.g. "two counties over"). The term is frequently used metaphorically to refer to a measurement of the difference between two similar objects (such as statistical distance between probability distributions or edit distance between strings of text) or a degree of separation, as spatial cognition is a rich source of conceptual metaphors in human thought (as exemplified by distance between people in a social network). The concept of a metric space is used in mathematics to formalize the majority of these ideas of distance, both literal and figurative.
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which of the following is most likely a population as opposed to a sample? a) respondents to a newspaper survey. b) the first 5 students completing an assignment. c) every third person to arrive at the bank. d) registered voters in a county.
The option that is most likely a population as opposed to a sample is registered voters in a county. The correct answer is Option D.
A population is a group of individuals, objects, or events whose properties are being studied. A sample is a smaller subset of the population that is selected to represent the whole population.
The four options given in the question are all sets of individuals who are being studied, but the difference is how they were selected. Respondents to a newspaper survey, the first 5 students completing an assignment, and every third person to arrive at the bank are all examples of samples because they are subsets of a larger group.
However, registered voters in a county are most likely a population because they are the entire group that is being studied, and there is no need for a subset of this group since the entire population is available. Therefore, option d) registered voters in a county is the most likely population as opposed to a sample.
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Can you help me with this question
The length of the side x is equal to √22 using the trigonometric ratio of sin45° for the isosceles triangle.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
The triangle is an isosceles so the other two angles are the same and each equal to 45°
using the trigonometric ratio of sin 45°
{recall that sin 45°° = √2/2}
sin 45° = √11/x {opposite/hypotenuse}
√2/2 = √11/x
x = (√11 ×2)/√2 {cross multiplication}
x = 2√11/2 × √2/√2 {rationalize}
x = 2√22/2
x = √22
Therefore, the length of the side x is equal to √22 using the trigonometric ratio of sin 45° for the isosceles triangle.
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In the figure here, a small block is sent through point A with a speed of 6.8 m/s. Its path is without friction until it reaches the section of length L=14 m, where the coefficient of kinetic friction is 0.78. The indicated height are h1=5.4 m and h2=2.8 m. What are the speeds of the block at (a) point B and (b) point C? (c) Does the block reach point D? (d) If, so what is its speed there; if not, how far through the section of friction does it travel?
A small block is sent through point A with a speed of 6.8 m/s. Its path is without friction until it reaches the section of length L=14 m, where the coefficient of kinetic friction is 0.78. The indicated height are h₁ =5.4 m and h₂=2.8 m. The speeds of the block at (a) Point B is 108m/s and (b) Point C is 7.6m/s
The velocity of an object (usually denoted v) is the amount of its position change over time ; therefore it is a scalar quantity. The average speed of an object over a time interval is the distance traveled by the object divided by the duration of the interval; the instantaneous speed remains zero.
(a) At B the speed is :
V = [tex]\sqrt{V^{2}+2gh_1 }[/tex]
⇒ V = [tex]\sqrt{(6.8m/s)+ 2(9.8m/s^2) (5.4)}[/tex]
⇒ V = 108.44 m/s
⇒ V = 108 m/s
(b) Here, matters is the difference in heights (between A and C):
[tex]V = \sqrt{V_0^{2}+2g(h_1+h_2) }[/tex]
⇒ [tex]V = \sqrt{(6.8)+2 (9.8) (5.4- 2.8) }[/tex]
⇒ [tex]V = \sqrt{6.8 +2(9.8)(2.6)}[/tex]
⇒ √57.76 = 7.6m/s
(c) Using the results from part (b), we see that its kinetic energy is just at the beginning of its "rough glide" (horizontally to D) is:
1/2 m(7.6m/s)² = 28.88m (with SI units understood).
We note that this kinetic energy will turn entirely into thermal energy
28.88m = μₙ mgd
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Given
Δ
ΔACE with vertices A(2, 1), C(2, 4), and E(5, 1)
and
Δ
Δ BCD with vertices B(2, 3), C(2, 4), and D(3, 3)
a) Find each length in simplest form
AC =
BC =
CE =
CD =
b) < C
≅
≅ < C because
c)
Δ
ΔACE
Δ
ΔBCD because
d) < CBD
< A
a) the lengths of each side:
AC = 3, BC = 1, CE = 3, CD = √2.
b) < C ≅ < C, corresponding angles of congruent triangles.
c) ΔACE ≅ ΔBCD by Side-Angle-Side (SAS) criterion,
d) ∠CBD ≅ ∠A, vertical angles.
What is the similarity of a triangle?
If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both triangles are equal, then two triangles are said to be similar.
a)
AC = √[(2-2)² + (4-1)²] = √9 = 3
BC = √[(2-2)² + (4-3)²] = 1
CE = √[(5-2)² + (1-1)²] = 3
CD = √[(3-2)² + (3-4)²] = √2
b) < C ≅ < C because they are corresponding angles of congruent triangles ΔACE and ΔBCD.
c) ΔACE ≅ ΔBCD by Side-Angle-Side (SAS) criterion, since AC = BC, CE = CD and < C ≅ < C.
d) < CBD < A because the point B lies on AC, and therefore < A and < CBD are vertical angles, and by definition, vertical angles are congruent.
Hence, a) the lengths of each side:
AC = 3, BC = 1, CE = 3, CD = √2.
b) < C ≅ < C, corresponding angles of congruent triangles.
c) ΔACE ≅ ΔBCD by Side-Angle-Side (SAS) criterion,
d) ∠CBD ≅ ∠A, vertical angles.
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Polynomial question
I don't understand this working
Why is b = d = 0 if the function is even?
Please explain the steps to solve a question like this.
To understand why b = d = 0 if the function is even, we need to consider the definition of an even function.Therefore If P(x) is an even function, then b = d = 0.
What is Polynomial?A polynomial is a mathematical expression that consists of variables and coefficients, combined using the operations of addition, subtraction, and multiplication. It can have one or more terms and can be of any degree.
An even function is a function that satisfies the condition f(x) = f(-x) for all x in the domain of the function.
If P(x) is an even function, then we have P(x) = P(-x) for all x. Substituting -x for x in the expression for P(x), we get:
P(-x) = a(-x)⁴ + b(-x)³ + c(-x)² + d(-x) + e
= a(x⁴) - b(x³) + c(x²) - d(x) + e
Since P(x) = P(-x), we can equate the two expressions for P(x) and P(-x) to get:
a(x⁴) + b(x⁴) + c(x²) + d(x) + e = a(x⁴) - b(x³) + c(x²) - d(x) + e
Simplifying this equation, we get:
2b(x³) + 2d(x) = 0
Since this equation holds for all values of x, we can set x = 0 to get:
2d(0) = 0
which implies that d = 0. Similarly, setting x = 1, we get:
2b(1³) + 2d(1) = 0
2b = 0
b = 0
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Reggie is rolling a block with the number 1,2,3,4, and 5 on it. Kaitlyn is drawing one desk from a basket of three disks: one blue, one red, and one yellow. use the tree diagram below to answer the question. What is the probability that they end up with a yellow disk
The probability of getting an even number and a yellow disc is 1/6 1/3 = 1/18. This is due to the fact that there is only one method to obtain an even number and a yellow disc.
What is probability?Probabilistic theory is a branch of mathematics that calculates the chance of an event or a claim being true. A risk is a number between 0 and 1, where 1 represents certainty and a probability of about 0 shows how likely an event appears to be to occur. Probability is a mathematical term for the likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1, or as percentages ranging from 0% to 100%. The proportion of occurrences among equally likely choices that result in a certain event in compared to all possible outcomes.
the answers to the questions:
a) The chance of getting a yellow disc is 1/6 + 1/6 = 1/3. This is because there are two methods to acquire a yellow disc: receive an even number and then choose the yellow disc, or get an odd number and then choose the yellow disc.
b) The chance of getting a blue disc is 1/6 + 1/6 = 1/3. This is because there are two methods to receive a blue disc: get an even number and then choose the blue disc, or get an odd number and then choose the blue disc.
c) The chance of getting an odd number with a red disc is (1/6 + 1/6) 1/3 = 1/18. This is because there are two ways to acquire an odd number, and there is only one way to get a red disc for each of those two methods.
d) The chance of getting an even number and a yellow disc is 1/6 1/3 = 1/18. This is due to the fact that there is only one method to obtain an even number and a yellow disc.
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find the ratio of 15 min and 1 hour
Answer:
1 : 4 minutes.
Step-by-step explanation:
Given: 15 minutes / 1 hour.
First convert 1 hour to minutes:
1 hour = 60 minutes
Then write the fraction:
15 : 60
Finally, simplify it:
1 : 4 minutes
What’s -9.1 times 3.75
The population of a slowly growing bacterial colony after t hours is given by p(t)=3t^2+24t+200. Find the growth rate after 2 hours.
The growth rate of a bacterial colony after a 2 hours is given by the derivative of its population function with respect to time is 36 .
The growth rate of a bacterial colony is given by the derivative of its population function.
Thus, we need to find the derivative of the population function p(t) with respect to time t, and then evaluate it at t = 2 to get the growth rate after 2 hours.
p(t) = 3t² + 24t + 200
Taking the derivative of p(t) with respect to t, we get:
p'(t) = 6t + 24
Now, evaluating p'(t) at t = 2, we get:
p'(2) = 6(2) + 24 = 36
Therefore, the growth rate of the bacterial colony after 2 hours is 36.
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Find the missing angle. Round your
answer to the nearest tenth.
tº
11 mi
5 mi
Answer:
24.4 degrees
Step-by-step explanation:
This is a right triangle so you can use trig to solve. If you take the arctan of 5/11 you get 24.4(rounded to the nearest tenth)
An art collector buys a replica of a famous sculpture. The replica has exactly the same shape as the original but it is smaller. The replica is 12 cm tall, and the original sculpture is 28 cm tall. If 162 cm^3 of bronze was needed to make the replica, how much bronze was needed to make the original sculpture?
2052 cm³ volume of bronze was needed to make the original sculpture.
What is volume?Volume is a physical quantity that refers to the amount of space occupied by a three-dimensional object or substance. It is typically measured in cubic units such as cubic meters, cubic centimeters, or cubic feet.
What is Area?Area is a physical quantity that refers to the amount of space within a two-dimensional shape or surface. It is typically measured in square units such as square meters, square centimeters, or square feet.
In the given question,
Since the replica is a scaled-down version of the original sculpture, the ratio of their sizes is the same as the ratio of their volumes.
The ratio of the heights of the original sculpture to the replica is:28 cm / 12 cm = 7/3
Therefore, the ratio of the volumes is:(7/3)³ = 343/27.
This means that the original sculpture is about 12.7 times larger than the replica in terms of volume.
Since 162 cm³ of bronze was needed to make the replica, we can find the amount of bronze needed for the original sculpture by multiplying 162 cm³ by the volume ratio:162 cm³ x 343/27 = 2052 cm³.
Therefore, 2052 cm³ of bronze was needed to make the original sculpture.
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suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. if the population grows to 500 after one year, what will the population be after another three years?
Suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. If the population grows to 500 after one year, the population will be 852.78 after another three years.
What is the logistic model?A logistic model, also known as the Verhulst-Pearl model, is a type of function used to describe population growth that is limited. It’s a form of exponential growth that takes into account the carrying capacity of an environment.
Population growth that is limited and slows down as the population approaches its carrying capacity is modeled using the logistic model. It is given by this equation:
[tex]P(t) = K / (1 + Ae^{-rt})[/tex]
where P(t) is the population at time t, K is the carrying capacity, A is the constant of proportionality, and r is the growth rate.
Suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. If the population grows to 500 after one year, substitute this information into the logistic model: [tex]P(1) = 500[/tex], [tex]K = 2000[/tex], and [tex]P(0) = 200[/tex].
[tex]500 = 2000 / (1 + Ae^{-r(1)})[/tex]
Now, solve for A by dividing both sides by 2000 / (1 + A):
[tex]1 + A = 4A = 3[/tex]
Substitute the value of A back into the logistic model equation:
[tex]P(t) = 2000 / (1 + 3e^{-rt})[/tex]
Solve for r by using the data provided in the problem for the first year (t = 1) and second year (t = 4):
[tex]P(1) = 500 = 2000 / (1 + 3e^{-r(1)})[/tex]
[tex]P(4) = ? = 2000 / (1 + 3e^{-r(4)})[/tex]
Solve the first equation for r:
[tex]500 = 2000 / (1 + 3e^{-r})\\1 + 3e^{-r} = 4e^{-r}\\1 + 3e^r = 4e[/tex]
Solve for e using the quadratic formula to get:
e = 0.4274 and e = 1.1713
Let e = 0.4274:
[tex]1 + 3e^{-r} = 4e^{-r}\\1 + 3(0.4274)^{-r} = 4(0.4274)^{r}\\1 + 0.5746^r = 1.7166^r[/tex]
Take the natural logarithm of both sides:
[tex]ln(1 + 0.5746^r) = ln(1.7166^r) - lnr\\ln(1 + 0.5746^r) = rln(1.7166) - lnr[/tex]
Use a graphing calculator to solve for r:
[tex]ln(1 + 0.5746^r) = rln(1.7166) - lnr[/tex]; -0.1568 < r < 0.7534
Solve for r using the second year’s data:
[tex]2000 / (1 + 3e^{-r(4)}) = P(4)\\2000 / (1 + 3(0.4274)^{-r(4)}) = P(4)\\P(4) = 852.78[/tex]
Thus, the population will be 852.78 after another three years.
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When a researcher draws conclusions about a population based on the results of a test on a sample, he or she is most likely using which of the following? a) inductive statistics b) deductive statistics c) descriptive statistics d) inferential statistics
When a researcher draws conclusions about a population based on the results of a test on a sample, he or she is most likely using inferential statistics. Therefore Option A is correct.
Inferential statistics: It involves using sample data to make inferences or draw conclusions about a population. In this case, the researcher is using the results from the sample to make inferences about the population from which the sample was drawn.
Deductive statistics, inductive statistics, and descriptive statistics are other branches of statistics that are used for different purposes.
Deductive statistics:Deductive statistics involves starting with a general principle or theory and testing it with data, Inductive statistics:Inductive statistics involves starting with data and using it to develop a theory or principle. Descriptive statistics: Descriptive statistics involves summarizing and describing data using measures such as mean, median, and standard deviation.Therefore the researcher draws a conclusion to use inferential statistics about a population based on test of sample.Option A is correct.
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Halla los números desconocidos de estas operaciones
A)872+. +173=2000
B)9180:. =102
C). -99=706
Con los mismos números y las mismas operaciones podemos obtener diferentes resultados,coloca los paréntesis de manera que se obtengan los resultados indicados. A)3+5x7-2=40
B)3+5×7-2=54
C)3+5×7-2=28
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In equation A the missing number is 955, In equation B the missing number is 90 and In equation C the missing number is 805.
A) To find the missing number in the equation 872 + ? + 173 = 2000, we need to subtract 872 and 173 from 2000, which gives us:
2000 - 872 - 173 = 955
Therefore, the missing number is 955.
B) To find the missing number in the equation 9180 ÷ ? = 102, we need to divide 9180 by 102, which gives us:
9180 ÷ 102 = 90
Therefore, the missing number is 90.
C) To find the missing number in the equation ? - 99 = 706, we need to add 99 to 706, which gives us:
706 + 99 = 805
Therefore, the missing number is 805.
To obtain the indicated results with the same numbers and operations, we need to use parentheses to change the order of operations.
A) 3 + (5x7) - 2 = 40
B) (3 + 5) × 7 - 2 = 54
C) 3 + (5 × (7-2)) = 28
Equations are used extensively in various fields of science, engineering, economics, and finance, to name a few. It is formed by placing an equal sign between the two expressions. Equations are used to solve problems and find unknown values.
An equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The variables in an equation represent unknown values that need to be found, while the constants are known values that are already given. Solving an equation involves manipulating the expressions on both sides of the equal sign using mathematical operations to isolate the variable on one side and constants on the other. The final solution obtained is the value of the variable that satisfies the equation..
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Complete Question: -
Find unknown numbers of these operations
A ) 872 +. + 173 = 2000
B ) 9180:. = 102
C ). -99 = 706
With the same numbers and the same operations we can obtain different results, place the parentheses so that the indicated results are obtained.
A ) 3 + 5 x 7-2 = 40
B ) 3 + 5 × 7-2 = 54
C ) 3 + 5 × 7-2 = 28
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