The percentage of tardiness among the 102 pupils is 2.94.
Calculation of the percentageAccording to the query,
Course A: Total number of students = 102
Number of tardy students = 3
Percent of students tardy in course A = (number of tardy students/total
number of students) * 100
=(3/102)*100
= 2.941
≈2.94
In case of course B: Total number of students = 85 & tardy student = 5
So, the percent of tardy student = (5/85)*100 = 5.88 %
Therefore, it is concluded that the percentage of student tardiness in course A is 2.94.
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100 points
solve each system by graphing
x=-3
x-y=-2
Answer:
(-3, - 1)--------------------------
Graph each line:
x = - 3, this is a vertical line passing through x = - 3,x - y = - 2 is y = x + 2, which is the line y = x, translated 2 units up.The intersection of the lines is the solution:
(-3, - 1)the length of a rectangle is 6 feet longer than the width. the perimeter is 28 feet. find the dimensions of the regtangle
The length of rectangle :10 feet
The width of rectangle : 4 feet
Given
perimeter of the rectangle :28 feet
let width of the rectangle be :x
and length of the rectangle be : 6+x (as per given condition)
therefore
perimeter = 2(length +width)
28 = 2(6+x+x)
28 = 2(6+2x)
28 = 12+4x
28-12 = 4x
16 = 4x
x = 4
as width of rectangle is : 4
similarly length : 6+x
6+4
:10
The dimensions of the rectangle are : length =10
width = 4
verification :
perimeter =2(l+w)
28 = 2(10+4)
28 = 28
How do you find the center of dilation of two lines?
Finding the center of dilation of two lines involves determining the point that is equidistant from the two lines.
A dilation is a transformation that changes the size of an object, but not its shape, and the center of dilation is the point from which the object is scaled.
The center of dilation of two lines can be found by constructing a line perpendicular to both lines that bisects the angle between them. The point of intersection of this line with the segment connecting the two closest points on the two lines is the center of dilation.
To find the center of dilation, we can use the following steps:
1. Draw the two lines and find the angle between them.
2. Draw a line perpendicular to both lines and bisecting the angle between them.
3. Draw the segment that connects the two closest points on the two lines.
4. The intersection of the line from step 2 with the segment from step 3 is the center of dilation.
It's also possible to use vector and linear algebra to find the center of dilation for two lines. By finding the slope of each line and their intersection point, the center of dilation can be found as the midpoint of the intersection point of the two lines.
In conclusion, finding the center of dilation of two lines requires determining the point that is equidistant from the two lines.
It can be done by drawing a line perpendicular to both lines that bisects the angle between them, or by using vector and linear algebra to find the intersection point of the two lines and finding the midpoint of that point.
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You can work a total of no more than 40 hours each week at your two jobs. Housecleaning pays $4 hour and your sales job pays $8 per hour. You need to earn at least $120 each week to pay your bills. Write and graph a system of inequalities that shows the various numbers of hours you can work at each job.
Using the diagram below, find the measure of angle A.
A
101°
92°
B
68°
C
Answer: the missing angle is going to be 99 because the shape that is being formed it going to be a quaderdiral because that is the next number up.
Step-by-step explanation: add the degress together and then see what number is the closest
Is the triangle with sides 25cm 5 cm and 24 cm a right triangle give reasons for your answers?
No, a triangle with sides 25 cm, 5 cm and 24 cm does not make a right triangle as these lengths does not adhere to the Pythagorean theorem.
A right triangle has one angle that measures exactly 90 degrees. In a triangle, the longest side (the hypotenuse) is opposite the right angle.
The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the hypotenuse.
In this case, the side lengths do not satisfy the Pythagorean theorem, as (24^2 + 5^2 = 601) ≠ (25^2 = 625)
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What is the factor theorem simple?
In mathematics, the factor theorem mostly used when factoring the polynomials totally. factorial theorem is that links factors and zeros of the polynomial.
By to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and ‘a’ is any real number, then, (x-a) is a factor of f(x), if f(a)=0.
including, we can say, if (x-a) is a factor of polynomial f(x), then f(a) = 0. This also proves that the converse of the theorem. Let us see the proof and example.
Factor theorem is mostly used for factoring a polynomial and searching the roots of the polynomial. It is an important case of a polynomial remainder theorem.
As examined in the introduction, a polynomial f(x) has a factor (x-a), if and only if, f(a) = 0. It is one of the processes to do the factorization of a polynomial.
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Mancini' Pizzeria ell four type of pizza crut. Lat week, the owner tracked the number old of each type, and thi i what he found. Type of Crut Number Sold
Thin crut 306
Thick crut 212
Stuffed crut 178
Pan tyle 191
Baed on thi information, of the next 3500 pizza he ell, how many hould he expect to be pan tyle? Round your anwer to the nearet whole number. Do not round any intermediate calculation
Now we have a new proportion that out of 3500 pizzas there are a total of 692 thick crust pizzas
Mancini's sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what he found.
Type of Crust Number Sold
Thin crust 306
Thick crust 212
Stuffed crust 178
Pan style 191
Based on this information, of the next 3500 pizzas he sells, how many should he expect to be thick crust? Round your answer to the nearest whole number. Do not round any intermediate calculations.
692 thick crust pizzas
With the data given in the exercise, we must first find the total number of pizzas, then we must find the proportion between the thick crust pizzas and the total number of pizzas, finally we must propose a rule of three to find the new proportion of crust pizzas thick on a total of 3500 pizzas.
Type of Crust Number Sold
Thin crust 306
Thick crust 212
Stuffed crust 178
Pan style 191
total pizzas : 1040
Now we must calculate for 3500 pizzas how much would be the total of thick crust pizzas. For that we must use the relationship found, that is, in 1040 pizzas there are 240 thick crust pizzas
x = 692
Now we have a new proportion that out of 3500 pizzas there are a total of 692 thick crust pizzas
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Find k so that 4x + 3 is a factor of 20x³ + 23 x² - 10x + k.
Answer:
k= 28.875
Step-by-step explanation:
4x+3= 0
4x= -3
X = -3/4
f(X)= 20x³+23x²-10x+k
0= 20(-3/4)³ + 23 (-3/4)² -10(-3/4)+k
20(-27/64)+23(9/16) +30/4+k
-540/64+207/16+7.5+k
-8.4375+12.9375+7.5+k. 0=-28.875+k
k=28.875
What is the 3D distance formula?
The 3D distance formula is represented as √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)
The 3D distance formula, also known as the Euclidean distance formula, is used to calculate the distance between two distinct points in three-dimensional space. The formula is the square root of the sum of the squares of the differences in the x, y, and z coordinates of the two points. Mathematically it can be represented as:
Distance = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)
Where (x1, y1, z1) and (x2, y2, z2) are the coordinates of the two points.
It's used to measure the distance between two points in 3-D space. It's the straight-line distance between two points. This formula can be applied in various fields such as physics, computer graphics, and robotics.
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The table gives the annual global plastic production over time, in years, since 1960.
Fit an exponential model to this data.
The exponential model indicates that plastic production has (1) _____ per year. The model predicts that plastic production 15 years after 1960 was closest to (2) _____ million metric tons. Because the correlation coefficient indicates (3) _____
correlation between the model and the data, this prediction (4) _____.
Answer options:
1-
increased by 4.9 metric tons
decreased by 4.9 metric tons
increased by 4.9%
decreased by 4.9%
2-
40
60
70
3-
moderate
strong
weak
4-
is unreliable
can be accepted with confidence
The exponential model indicates that plastic production has increased by 4.9% per year.
Fit an exponential model to this dataThe exponential model indicates that plastic production has increased by 4.9% per year.The model predicts that plastic production 15 years after 1960 was closest to 70 million metric tons.Because the correlation coefficient indicates strong correlation between the model and the data,this prediction can be accepted with confidence.The exponential model is a powerful tool for predicting future trends in plastic production, and it indicates that plastic production has been increasing at an annual rate of 4.9%.This is an important insight, as it can help us to anticipate the future of the industry.With this information, we can estimate that plastic production 15 years after 1960 was likely to be around 70 million metric tons.The strength of this prediction is supported by the correlation coefficient, which suggests a strong correlation between the model and the data.This suggests that the model is a good predictor of future plastic production, and that the prediction of 70 million metric tons is reliable.To learn more about the annual global plastic production over time refer to:
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Can someone help me with this please?
By using the triangle inequality theorem, the possible side lengths for the third side is equal to: D. 4 < c < 42.
What is the triangle inequality theorem?In Euclidean geometry, the Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than or equal (≥) to the third side of the triangle.
Mathematically, the Triangle Inequality Theorem is represented by this mathematical expression:
b - c < a < b + c
Where:
a, b, and c represent the side lengths of this triangle.
By applying the Triangle Inequality Theorem, the possible side lengths of the triangle's third side is given by:
b - c < a < b + c
23 - 19 < a < 23 + 19
4 < a < 42.
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The nearest whole number.
12) Huong enlarged the size of a painting to a
width of 12 cm. What is the new height if
it was originally 4 cm wide and 3 cm tall?
The nearest whole number to which the new height of the image is enlarged is 9cm.
What is scaling?By scaling, we can create a drawing of an object that corresponds to the object's true size. In geometry, scaling refers to either growing or reducing figures in order to preserve their fundamental shape. Similar figures are what we call scaled figures.
Given that the original size was in the ratio 4: 3.
When the image is enlarged the enlarged image will be in the similar ratio to the original size.
Hence, the ratio in which the enlarged image will be increased is 4x : 3x.
The new width is given as 12,
The value of 4x = 12
x = 3
Then the new height of the image is:
3 (3) = 9cm.
Hence, the new height of the image is 9cm.
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What is final value theorem Mcq?
The steady state value of the system is determined using the final value theorem.
The main characteristics of the Laplace transform are the initial and final value theorems. Pierre Simon Marquis De Laplace, a French mathematician and scientist, presented these theorems. Limiting theorems refer to both the initial and final value theorems.
The final value theorem asserts that one can compute a system's ultimate value using. The function's Laplace transform is
[tex]\lim_{t\rightarrow\infty}f(t) = \lim_{s\rightarrow0}sF(s)[/tex]
(1) Final value theorem prerequisites are the functions f(t) and f(t)' should be Laplace transformable.
(2) sF(s), where F(s) is the Laplace transform of f(t), has no pole on the j-w axis and right half plane.
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What are the types of substitute?
Answer:
"Substitution comes in three flavors: nominal, verbal or clausal, depending on the item being substituted.
Step-by-step explanation:
Hope it helps!
Given h(2) -I + 4, solve for a when h(2) = 4.
At h(2) = 4 the value of 'I' will be equal to 0.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the function is h(2) = I + 4. The value of I at h(2) = 4 will be calculated as,
h(2) = I + 4.
4 = I + 4
I = 4 - 4
I = 0
Hence, the required value of 'I" at h(2) = 2 will be 0.
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What is the formula for finding the area of a sector of a triangle?
The formula for a sector's area is: 1. A = (sector angle / 360 ) * (pi *r2)
2. A = (sector angle / (2*pi)) * (pi * r2) 3. A = (fraction of the circle) * (pi * r2)
The ratio used to find the area of the sector is that of how to know what fraction of the circle is the sector.
Ratio = (θ/360°)
θ is the angle subtended at the center of the circle by the arc, measured in degrees.
For this question,
θ = 60°
Ratio = (θ/360°) = (60°/360°) = (1/6)
Area of a circle is given as
Area of a circle = πr²
where
π = pi
r = radius of the circle = 8
Area of the circle = πr²
Area of the circle = π (8²) = 64π square units
Area of the sector is given as
Area of the sector = (Ratio) × (Area of the circle)
Ratio = (1/6)
Area of the circle = 64π square units
Area of the sector = (Ratio) × (Area of the circle)
Area of the sector = (1/6) × (64π) = (64π/6) = (32π/3) square units
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Which function has the lowest minimum value, and what are its coordinates?
A. Function 1 has the lowest minimum value, and its coordinates are (−1, −3).
B. Function 1 has the lowest minimum value, and its coordinates are (0, 1).
C. Function 2 has the lowest minimum value, and its coordinates are (−1, 0).
D. Function 2 has the lowest minimum value, and its coordinates are (0, 2).
Answer:
A. Function 1 has the lowest minimum value, and its coordinates are (−1, −3).
Step-by-step explanation:
To find the minimum value for f(x), set its first derivative to 0 and solve for x.
First derivative of f(x) is
f'(x) = 8x + 8 + 0 = 8x + 8
Setting this equal to 0 gives
8x + 8 = 0
8x = -8
x = -1
Plugging in this value for x in 4x² + 8x + 1 gives
f(x) = 4(-1)² + 8(-1) = 4 · 1 - 8 + 1
= 4 - 8 + 1
-4 + 1
= -3
So minimum for f(x) occurs at (-1, -3)
For g(x) the minimum is 0 and is at x = -1
So f(x) has minimum of -3 at x = -1
g(x) has minimum of 0 and occurs at x = -1
Answer:
A. Function 1 has the lowest minimum value, and its coordinates are (−1, −3).
lcm(x-3)^2(x+4);(x-3)(x+4)^2
Answer:
[tex](x - {3})^{2} x(x + {4})^{2} [/tex]
A ratio of 4 to 7 maybe written as the following, except 4:7 8:14 7/4 8/14 12:21
Answer:
except 7/4
Step-by-step explanation:
The ratio of 4 to 7 is the same as the fraction 4/7
7/4 is not equal to 4/7 and therefore they cannot be written in the same way.
Triangle PQR was transformed to create the congruent triangle STU. Which describes how triangle PQR could have been transformed.
The term "congruent" refers to having exactly the same shape and size. Even if we flip, turn, or rotate the shapes, the shape and size should remain the same.
What exactly is SSS SAS RHS AAS?SSS (Side-Side-Side) (Side-Side-Side) SAS (Side-Angle-Side) (Side-Angle-Side) ASA (Angle-Side-Angle) (Angle-Side-Angle) AAS (Angle-Angle-Side) (Angle-Angle-Side) RHS (Right angle-Hypotenuse-Side) (Right angle-Hypotenuse-Side)
What is the distinction between SSS SAS and ASA postulates?The first two postulates, Side-Angle-Side (SAS) and Side-Side-Side (SSS), emphasise the side aspects, whereas the following lesson discusses two additional postulates that emphasise the angles. The Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS) postulates are what they are.
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if each quadrilateral below is a trapezoid, find the missing measures
If each of the quadrilateral is a trapezoid, then the measure of ∠Q = 89 and ∠S = 153.
What is a trapezoid?A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.
Given that in a trapezoid, the angle T is 91 and the angle R is 27.
For a trapezoid the measure of angle are as follows:
∠T + ∠Q = 180
∠R + ∠S = 180
Substituting the measures of ∠T and ∠R in the above equations we have:
91 + ∠Q = 180
∠Q = 89
27 + ∠S = 180
∠S = 153
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9,365,000 rounded to the nearest million place
Mrs. Peterson had lunch at Lunchee's. She paid $12.99 for her meal. She left a tip of 2.60. What percent did she leave?
answer = _____%
The percentage of the tip that she leaves will be 20.02%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Mrs. Peterson had lunch at Lunchee's. She paid $12.99 for her meal. She left a tip of 2.60.
Then the percentage is given as,
P = [2.6 / 12.99] x 100
P = 0.2002 x 100
P = 20.02%
The percentage of the tip that she leaves will be 20.02%.
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Jarrod helped his teachers pack textbooks into boxes for the summer. He packed 6 boxes of science textbooks with 14 books per box. He also packed math textbooks with 12 books per box. If x represents the total number of boxes he packed, which of the following equations can be used to find the total number of books that Jarrod packed into boxes?
The total number of books that Jarrod packed into boxes can be represented by 84 + x*12.
The total number of books that Jarrod packed into boxes can be found by multiplying the number of boxes he packed with the number of books per box.
In this case, Jarrod packed 6 boxes of science textbooks with 14 books per box, so the number of books in the science boxes is 614 = 84. He also packed math textbooks with 12 books per box, so the number of books in the math boxes can be represented by x*12, where x represents the total number of boxes he packed.
So the total number of books that Jarrod packed into boxes can be represented by 84 + x*12.
Therefore, the equation that can be used to find the total number of books that Jarrod packed into boxes is: 84 + x*12 = Total number of books.
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Please help me find the value and the kind of angel this is?
Answer: the only line crossed is called a transversal line. x +3 would be vertically opposite to the other angle,and 2x-61 would also be vertically opposite. if you look at alternate and corresponding angles you would find the exact answer. this angle does not have a kind i guess.
hope it helps you!!!
Step-by-step explanation:
What are the 3 types of 3 dimensional coordinate system?
The 3 types of 3-dimensional coordinate systems are the x-axis, the y-axis, and the z-axis.
The Cartesian coordinates of a point in three dimensions are a triplet of numbers (x,y,z). The three numbers, or coordinates, specify the signed distance from the origin along the x,y, and z-axes, respectively.
The three axes intersect at the point called the origin. The x-axis is the horizontal line along which the wall to your left and the floor intersect.
The y-axis is the horizontal line along which the wall to your right and the floor intersect. The z-axis is the vertical line along which the walls intersect.
To locate the point (a, b, c), we can start at the origin O and move units along the x-axis, then b units parallel to the y-axis, and then c units parallel to the z-axis.
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Write an equation in slope form of the line that passes through the given point and is parallel to the graph of the given equation
(-6,-8);y=-4x+2
An equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation is y = -4x - 32.
What is the point-slope form?Mathematically, the point-slope form of a line is given by this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.From the given linear equation y = -4x + 2, the slope is given by:
y = -4x + 2
m₁ = -4
In Geometry, two (2) lines are parallel under the following conditions:
m₁ = m₂ (m represents the slope.)
At point (-6, -8), an equation of this line can be calculated in slope-intercept form as follows:
y - y₁ = m(x - x₁)
y - (-8) = -4(x - (-6))
y + 8 = -4(x + 6)
y + 8 = -4x - 24
y = -4x - 24 - 8
y = -4x - 32
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Find the polynomial function in standard form that has the zeros listed. 2 (multiplicity 2), 3+i (multiplicity 1)
A. f(x) = x4 - 10x³ + 36x² - 56x +32
B. f(x) = x4 – 10x³ + 38x² - 64x + 40
C. f(x) = x³8x² +22x - 20
D. f(x) = x4 – 10x³ + 37x² − 60x + 36
The polynomial function in standard form that has the zeros - 2 (multiplicity 2), and 3+i (multiplicity 1) is option b: f(x) = x^4-10x^3+38x^2-64x+40.
What is a polynomial function?
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.
The zeros of the polynomial function are -
2 (multiplicity 2), and 3+i (multiplicity 1)
If the zero is 2, the factor is (x-2).
A multiplicity of 2 implies there are 2 factors -
(x-2) or (x-2)(x-2) = (x-2)^2
= (x^2-4x+4)
For the complex zero (3+i), there will also be a zero at the complex conjugate (3-i).
The factors are -
= [x-(3+i)] and [x-(3-i)] or
= (x-3-i)(x-3+i)
= x^2-3x+ix-3x+9-3i-ix-+3i-i^2
= x^2-6x+9-i
= x^2-6x+9-(-1)
= x^2-6x+10
Multiply all factors to find the polynomial in standard form -
f(x) = (x^2-4x+4)(x^2-6x+10)
= x^4-6x^3+10x^2-4x^3+24x^2-40x+4x^2-24x+40
= x^4-10x^3+38x^2-64x+40
Therefore, the polynomial function in standard form is x^4-10x^3+38x^2-64x+40.
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Write the coordinates of the vertices after a dilation with a scale factor of 1/3, centered at the origin.
The coordinates of the vertices after a dilation with a scale factor of 1/3 centered at the origin is E'(0, -2), F'(3, -2), G'(3, 1) and H'(0, 1).
What is Dilation?Dilation is a type of transformation where the figure is enlarged or made smaller such that it preserves the shape but not size.
Every dilated image are similar figures to the original figure.
Given that center of the dilation is origin.
Any coordinate (x, y) when dilated to a scale factor k is (kx, ky).
The coordinates of the quadrilateral are E(0, -6), F(9, -6), G(9, 3) and H(0, 3).
Dilation is with a scale factor of 1/3.
So all the coordinates become (1/3x, 1/3y).
E(0, -6) becomes E'(0, -2)
F(9, -6) becomes F'(3, -2)
G(9, 3) becomes G'(3, 1)
H(0, 3) becomes H'(0, 1)
Hence the coordinates are E'(0, -2), F'(3, -2), G'(3, 1) and H'(0, 1).
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