Answer:
To solve this problem, we need to divide the total number of students by the number of people that can sit in each row.
44 students ÷ 8 people per row = 5.5 rows
Since we cannot have half a row, we round up to the nearest whole number. Therefore, they will fill up 6 rows in the movie theater.
Here's a simple drawing that explains the solution:
Row 1: 8 students
Row 2: 8 students
Row 3: 8 students
Row 4: 8 students
Row 5: 8 students
Row 6: 4 students
The first five rows are full with 8 students each, and the sixth row has the remaining 4 students. Therefore, a total of 6 rows will be filled with students.
Classifying parallelagram
Answer:
(3,-6)
Step-by-step explanation:
Coordinate for the point R is (3, -6)
What is a quadrilateral?A polygon with four sides and four vertices is called a quadrilateral. Quadrilateral literally means "four sides" because "quad" means four and "lateral" implies sides. Quadrilaterals come in a variety of sizes, forms, and angles, but they all have four sides in common.
If all of the matching sides and angles of two quadrilaterals are equal in size, they are said to be congruent.
Given that the quadrilateral PQRS congruent to the quadrilateral JKLM.
Find out the all sides and angles of given quadrilateral JKLM and quadrilateral PQRS,
according to the graph the points are:
for quadrilateral JKLM,
J (-6, 2)
K (-3, 5)
L (-5, 8)
M (-8, 4)
for quadrilateral PQRS,
P (9, -7)
Q (6, -4)
R ( _, _ )
S (7, -9)
By the formula distance between any two points is:
[tex]d=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2}[/tex]
where, [tex]x_{1}, x_{2} , y_{1}, y_{2}[/tex] are the points of two sides of line.
using that formula we have to find out the points of R is (3, -6)
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80 pts! please correct answer
What is the end behavior of this radical function?
f(x)=4\sqrt{x-6 }
A.
As x approaches positive infinity, f(x) approaches positive infinity.
B.
As x approaches negative infinity, f(x) approaches positive infinity.
C.
As x approaches positive infinity, f(x) approaches negative infinity.
D.
As x approaches negative infinity, f(x) approaches negative infinity.
Answer:
The end behavior of the given radical function f(x) = 4√(x-6) as x approaches positive infinity is option A: As x approaches positive infinity, f(x) approaches positive infinity.
Step-by-step explanation:
This is because as x approaches positive infinity, the value inside the square root (x-6) also approaches positive infinity. As the square root of a positive number is also positive, f(x) approaches positive infinity.
We can also see this by using the concept of limits. As x approaches positive infinity, the limit of f(x) can be evaluated as:
lim f(x) = lim 4√(x-6)
x→∞ x→∞
= 4√(lim(x-6))
x→∞
Since the limit of (x-6) as x approaches positive infinity is positive infinity, we have:
lim f(x) = 4√(∞) = ∞
x→∞
Therefore, as x approaches positive infinity, f(x) approaches positive infinity.
Answer:
Step-by-step explanation:
The end behavior of the given radical function f(x) = 4√(x-6) as x approaches positive infinity is option A: As x approaches positive infinity, f(x) approaches positive infinity.
This is because as x approaches positive infinity, the value inside the square root (x-6) also approaches positive infinity.
As the square root of a positive number is also positive, f(x) approaches positive infinity.
We can also see this by using the concept of limits.
As x approaches positive infinity, the limit of f(x) can be evaluated as:
lim f(x) = lim 4√(x-6)x→∞ x→∞= 4√(lim(x-6))x→∞.
Since the limit of (x-6) as x approaches positive infinity is positive infinity, we have:
lim f(x) = 4√(∞) = ∞x→∞.
Therefore, as x approaches positive infinity, f(x) approaches positive infinity.
Please answer questions 15-18. They are not multiple choice, and you have to look at the line.
The probability are given as follows:
15) P (point is on N.Q.) = 6 / 13
16) P (point is not on Q.R.) = 10 / 13
17) P (point is on N.Q. or RS) = 10/13
18) P = 1/54
15)
To find the probability that the point is on line segment N.Q., we need to divide the length of N.Q. by the total length of the line segment NS. The length of NS is the sum of the lengths of N.Q., Q.R., and RS, which is 12 + 6 + 8 = 26. Therefore, the probability that the point is on line segment N.Q. is:
P(point is on N.Q.) = length of N.Q. / length of NS = 12 / 26 = 6 / 13
16)
To find the probability that the point is not on line segment Q.R., we need to subtract the length of Q.R. from the length of NS and divide by the length of NS. The length of Q.R. is 6, so the length of NS without Q.R is 12 + 8 = 20. Therefore, the probability that the point is not on line segment Q.R. is:
P (point is not on Q.R.) = (length of NS without Q.R.) / length of NS = 20 / 26 = 10 / 13
17)
To find the probability that the point is on line segment N.Q. or RS, we can add the probabilities of the point being on N.Q. and the point being on RS. We already calculated that the probability of the point being on N.Q. is 6/13. To find the probability of the point being on RS, we can use the same method as in part (15). The length of RS is 8, so the probability that the point is on RS is:
P(point is on RS) = length of RS / length of NS = 8 / 26 = 4 / 13
Therefore, the probability that the point is on N.Q. or RS is:
P(point is on N.Q. or RS) = P (point is on N.Q.) + P(point is on RS) = 6/13 + 4/13
= 10/13
18)
The bus stops at the lot every 18 minutes and stays for 2 minutes, so the shuttle is at the lot for a total of 20 minutes out of every 18 * 60 = 1080 minutes. Therefore, the probability that the bus is at the lot when you arrive is:
P (bus is at the lot) = time the shuttle is at the lot / total time = 20 / 1080
= 1/54
Note that this assumes that you arrive at a random time within the 1080 minutes and that the bus is equally likely to be at the lot at any time during its 20-minute stay.
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Rae is saving for a new computer, so she's selling her old antivirus software program for $250. The
software originally cost $985, and she used it for 12 years.
What was the net asset value of Rae's antivirus software two years after her purchase?
O A. $722.50
OB. $755
OC. $825.75
OD. $862.50
OE. $890.75
Answer:
the net asset value of Rae's antivirus software two years after her purchase was $570.84, which is not one of the given options.
Step-by-step explanation:
The software was used for 12 years, and Rae is selling it now. So, it has been used for 12 - 2 = 10 years.
Annual depreciation = (cost - salvage value) / useful life = (985 - 0) / 12 = 82.08
Depreciation for 10 years = 82.08 x 10 = $820.80
Net asset value after 2 years = cost - accumulated depreciation = 985 - 82.08 x 2 = $820.84
However, Rae is selling the software for $250, so her net asset value is $820.84 - $250 = $570.84
Therefore, the net asset value of Rae's antivirus software two years after her purchase was $570.84, which is not one of the given options.
i need help with number 7
Answer:20$ per foot
Step-by-step explanation: just multiply the first cost(400) by the first foot amount(20) 400/20=20
all the faces of the prism meet at right angles. the volume the prism is 490m cube. what is the surface area of the prism?
The required surface area of the prism is 378 square meters.
How to find the area of Prism?To find the surface area of the prism, we need to know the dimensions of the prism. Let's call the length, width, and height of the prism l, w, and h, respectively.
Since the prism has right angles between its faces, we know that it is a right rectangular prism.
The formula for the volume of a right rectangular prism is V = lwh, and we know that the volume of the prism is 490m^3. Therefore,
lwh = 490
We are not given any specific values for l, w, or h, so we need to use another piece of information to solve for one of these variables.
The surface area of a right rectangular prism is given by the formula
SA = 2lw + 2lh + 2wh
If we can find the value of one of these dimensions, we can use it to calculate the surface area of the prism
lwh = 490
Since we know that the prism has right angles between its faces, we can assume that its dimensions are integers. We can start by testing integer values for l and w, and see if we can find an integer value for h that satisfies the equation.
For example, if we let l = 7 and w = 10, we get
7 * 10 * h = 490
Simplifying, we get
70h = 490
Dividing both sides by 70, we get
h = 7
Therefore, the dimensions of the prism are l = 7, w = 10, and h = 7.
To find the surface area, we can substitute these values into the formula for SA:
SA = 2lw + 2lh + 2wh
= 2(7)(10) + 2(7)(7) + 2(10)(7)
= 140 + 98 + 140
= 378
Therefore, the surface area of the prism is 378 square meters.
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Which equation represents the relationship between x, the time in minutes, and y, the shots made?
The relationship that represent between x, the time in minutes and y, the shot made is y = 4x .
How to find proportional relationships?Proportional relationships are relationships between two variables where their ratios are equivalent. A proportional relationship is one in which two quantities vary directly with each other.
Proportional relationships can be represented as follows;
y = kx
where
k = constant of proportionalityHence, the equation that can be used to represent the relationship between x, the time in minutes and y, the shot made is as follows;
Therefore,
y = kx
where
x = time in minutesy = shot madeTherefore,
12 = 3k
k = 12 / 3
k = 4
Therefore,
y = 4x
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To emphasize the slow increase in sales, it would be best for Samantha to use graph B or graph A for her presentation
Answer:
Graph A
Step-by-step explanation:
As can be seen, the trend in graph A is increasing with each month but not seemingly by as much as graph B;
This is because the scale of the y-axis in graph B has smaller increments;
This creates the impression of a slow increase in sales even though the data in both graphs is actually the same.
Answer: graph A.
appear to increase less.
Step-by-step explanation:
Pls help !! Find the equation of a line parallel to that passes y= 4/3x+4 through the point (3,-7).
An equation of a line parallel to that passes y = 4/3x + 4 through the point (3, -7) include the following: A. y + 7 = 4/3(x - 3).
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.Since y = 4x/3 + 4, the slope is equal to 4/3.
At data point (3, -7) and a slope of 4/3, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-7) = 4/3(x - 3)
y + 7 = 4/3(x - 3)
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Please help me on this: 90 BRAINLY POINTS. Yuri bakes lemon bars in a pan shaped like a right rectangular prism. The volume of the pan is 150 cubic inches. The width of the pan is 7 1/2 inches, and its height is 2 inches.
What is the length of the pan?
Enter your answer in the box
Answer:
length of the pan is 10 inches
Step-by-step explanation:
Volume = length x width x height
V = lwh
l = (V) / (wh) = (150 in³) / (7.5 in)(2 in) = 10 in
The following system of linear equations has how many solutions?
3y = x + 6
6y - 2x = 12
The system of linear equations 3y = x + 6 and 6y - 2x = 12 has infinitely many solutions.
What is the number of solutions of the system of equation?Given the system of euqation in the question;
3y = x + 66y - 2x = 12We can solve this system of linear equations using the substitution method:
From the first equation, we can rewrite x in terms of y as:
x = 3y - 6
Substituting this expression for x in the second equation, we get:
6y - 2(3y - 6) = 12
Simplifying this equation, we get:
6y - 6y + 12 = 12
The equation simplifies to 12 = 12.
This means that the two equations are equivalent and represent the same line in the xy-plane.
The system has infinitely many solutions, and all points on the line satisfy both equations.
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On a coordinate plane, a line with positive slope goes through points A and B. Point A is at (0, negative 2) and point B is at (3, 0). Use the graph of the line shown to determine its slope. The slope of line AB is .
According to the given information, the slope of line AB is [tex]\frac{2}{3}[/tex].
What is the slope?
The slope of a line is a measure of how steep the line is. It tells us how much the y-coordinate of the line changes for each unit of change in the x-coordinate.
To visualize a slope, imagine a line on a coordinate plane. If the line is steep, it means that for each unit of increase in the x-coordinate, the y-coordinate changes by a larger amount. Conversely, if the line is less steep, it means that for each unit of increase in the x-coordinate, the y-coordinate changes by a smaller amount.
To find the slope of a line that passes through two given points, we use the slope formula:
[tex]slope = \frac{(change in y) }{(change in x)}[/tex]
In this case, we have points A(0, -2) and B(3, 0).
So the change in y is 0 - (-2) = 2, and the change in x is 3 - 0 = 3.
Therefore, the slope of line AB is:
[tex]slope = \frac{(change in y) }{(change in x)} = \frac{2}{3}[/tex]
Since the slope is positive, we know that the line slants upwards as we move from left to right on the coordinate plane.
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Ben made a sundial in his backyard by placing a stick with height, 6 inch straight into the ground, and marking the hours in the grass.
Therefore , the solution of the given problem of trigonometry comes out to be the length of the shadow at a 60° angle from the light is 2 to 3 inches.
What is trigonometry?It is thought that the interaction of the triangle different fields led to the development of astrophysics. With the aid of precise mathematical techniques, many metric issues can be resolved or the consequences of about there calculation can be established. The analysis of six fundamental trigonometric formulas is known as angle of trigonometry..
Here,
The length of the stick's shadow can be calculated using trigonometry when the sun is at a 30° or 60° angle with the earth.
Assume that the silhouette measures "x" inches in length.
The shadow and stick form a right triangle when the sun forms a 30° angle with the ground. The stick is 6 inches tall, and it is angled 30 degrees away from the shade. Therefore, we can use the tangent function to determine the shadow's length:
=> tan(30°) = 6/x
=> x = 6/tan(30°)
=> 6/(1/√3)
=> 6√3
As a result, the shadow's length at a 30° angle from the light is 6 34 inches.
Consequently, we can use the tangent function once more to determine the length of shadow:
=> tan(60°) = 6/x
=> x = 6/tan(60°) = 6/√3 = 2√3
As a result, the length of the shadow at a 60° angle from the light is 2 to 3 inches.
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The complete question is " Ben made a sundial in his backyard by placing a stick with height 6 in. straight into the ground, and marking the hours in the grass. To test it, he checks the time each day when the sun makes an angle of 30° or 60° with the ground. Select all the possible lengths of the shadow when Ben checks the sundial.
A. 12 in.
B. 23√ in.
C. 8 in.
D. 63√ in.
E. 22√ in."
9. The blueprint for a new house includes a triangular shaped room in the attic. The triangular room appears on the blueprint as shown.
If the blueprint was made using a scale factor of 12
centimeter = 1 meter, what is the actual perimeter of the triangular room?
A. 2.5M
B. 4.5M
C. 9M
D. 18M
By answering the presented question, we may conclude that As a result, equation the real circumference of the triangle space is around 30 metres.
What is equation?A math equation is a technique that links two assertions and denotes equivalence using the equals sign (=). In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For example, in the equation 3x + 5 = 14, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on either side of a letter. The logo and the programme are usually interchangeable. As an example, 2x - 4 equals 2.
Because the blueprint is designed on a scale of 12 centimetres Equals 1 metre, each 1 centimetre on the blueprint represents 0.0833 metres (1/12 of a metre).
Assume the triangle chamber on the blueprint has a perimeter of 30 cm. We may apply the following calculation to determine the real perimeter in metres:
Blueprint perimeter x Scale factor x 0.0833 = Real perimeter
Real circumference = 30 x 12 x 0.0833
Actual circumference = 29.988 metres
As a result, the real circumference of the triangle space is around 30 metres.
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can some please help me
do the odds
please show work
By conversion formulas, the measures of angles in degrees are, respectively:
θ' = 145°θ' = 255°θ' = 160°θ' = 275°θ' = 50°θ' = 265°θ' = 40°θ' = 47°θ' = 1°θ' = 68°θ' = 46°θ' = 462°θ' = - 327°θ' = 114°θ' = 699°θ' = 17°θ' = 655°θ' = 764°θ' = - 142°θ' = 582°θ' = 895°θ' = 825°θ' = - 233°θ' = 50°θ' = 299°θ' = 807°θ' = 534°θ' = 188°θ' = 910°θ' = - 428°How to convert angles in radians to degrees
In this problem we find thirty cases of angles in radians that must be converted in degrees, this can be done by following conversion formula:
θ' = (180 / π) × θ
Where:
θ - Angle, in radians.θ' - Angle, in degrees.Now we proceed to determine the angles, measured in degrees:
Case 1:
θ' = (29π / 36) × (180 / π)
θ' = 145°
Case 2:
θ' = (17π / 12) × (180 / π)
θ' = 255°
Case 3:
θ' = (8π / 9) × (180 / π)
θ' = 160°
Case 4:
θ' = (55π / 36) × (180 / π)
θ' = 275°
Case 5:
θ' = (5π / 18) × (180 / π)
θ' = 50°
Case 6:
θ' = (53π / 36) × (180 / π)
θ' = 265°
Case 7:
θ' = (2π / 9) × (180 / π)
θ' = 40°
Case 8:
θ' = (47π / 180) × (180 / π)
θ' = 47°
Case 9:
θ' = (π / 180) × (180 / π)
θ' = 1°
Case 10:
θ' = (17π / 45) × (180 / π)
θ' = 68°
Case 11:
θ' = (23π / 90) × (180 / π)
θ' = 46°
Case 12:
θ' = (77π / 30) × (180 / π)
θ' = 462°
Case 13:
θ' = (- 109π / 60) × (180 / π)
θ' = - 327°
Case 14:
θ' = (19π / 30) × (180 / π)
θ' = 114°
Case 15:
θ' = (- 233π / 60) × (180 / π)
θ' = 699°
Case 16:
θ' = (17π / 180) × (180 / π)
θ' = 17°
Case 17:
θ' = (131π / 36) × (180 / π)
θ' = 655°
Case 18:
θ' = (191π / 45) × (180 / π)
θ' = 764°
Case 19:
θ' = (- 71π / 90) × (180 / π)
θ' = - 142°
Case 20:
θ' = (97π / 30) × (180 / π)
θ' = 582°
Case 21:
θ' = (- 179π / 36) × (180 / π)
θ' = 895°
Case 22:
θ' = (55π / 12) × (180 / π)
θ' = 825°
Case 23:
θ' = (- 233π / 180) × (180 / π)
θ' = - 233°
Case 24:
θ' = (- 5π / 18) × (180 / π)
θ' = 50°
Case 25:
θ' = (299π / 180) × (180 / π)
θ' = 299°
Case 26:
θ' = (- 269π / 60) × (180 / π)
θ' = 807°
Case 27:
θ' = (- 89π / 30) × (180 / π)
θ' = 534°
Case 28:
θ' = (47π / 45) × (180 / π)
θ' = 188°
Case 29:
θ' = (91π / 18) × (180 / π)
θ' = 910°
Case 30:
θ' = (- 107π / 45) × (180 / π)
θ' = - 428°
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The radius of a cylindrical construction pipe is 2.5 ft. If the pipe is 20 ft long, what is its volume…..
10. In the diagram shown, AC is congruent to DC and ZA and ZD are both right angles. SS | RS 1. GIVEA ACANC ELL X-3 en 1. AC DC LA CALD are rt L's 2 LBCB Reflex Hue propert 344DBC LAB ALE HL Fungh D Prov
Answer:
4Step-by-step explanation:
pls help fast!! Find the equation of a line perpendicular to 4x+3y=−24 that passes through the point (−8,3).
Answer:
y - 3 = [tex]\frac{3}{4}[/tex] (x + 8)
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
4x + 3y = - 24 ( subtract 4x from both sides )
3y = - 4x - 24 ( divide through by 3 )
y = - [tex]\frac{4}{3}[/tex] x - 8 ← in slope- intercept form
with slope m = - [tex]\frac{4}{3}[/tex]
given a line with slope m then the equation of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{4}{3} }[/tex] = [tex]\frac{3}{4}[/tex]
-------------------------------------------
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = [tex]\frac{3}{4}[/tex] and (a, b ) = (- 8, 3 ) , then
y - 3 = [tex]\frac{3}{4}[/tex] (x - (- 8) ) , that is
y - 3 = [tex]\frac{3}{4}[/tex] (x + 8) ← equation of perpendicular line
A student received a standardized score of -.63 on a class assignment. Which statement best describes the student’s score in relation to the rest of the class?
A pendulum is a weight attached to a fixed rod, as shown in the figures. Suppose that during an experiment, a pendulum moves back and forth in a periodic manner. At the beginning of the experiment , when the time is t = 0 seconds , the pendulum is at a point halfway between its maximum and minimum distances from the wall, 2.5 m away from the wall (Figure 1) and moving toward the wall. The pendulum first reaches its minimum distance from the wall , 1 m from the wall , when t = 1 second (Figure 2). When t = 4 seconds, the pendulum is back to a point halfway between its maximum and minimum distances from the wall. The pendulum continues to move back and forth so that the distance between the pendulum and the wall over time can be modeled by a sinusoida ! function .
Which estimation technique will yield a solution that is farthest from the actual product of (-14.89)(1.35)?
front-end estimation
rounding to the nearest tenth
rounding to the nearest whole number
compatible numbers
It’s not C
Two similar triangles have a scale factor of 2/3. The area of the larger triangle is 27 what is the area of the smaller triangle
The area of the smaller triangle is 12 square units
How to determine the area of the smaller triangleIf the scale factor between two similar triangles is 2/3
It means that every length of the smaller triangle is 2/3 the length of the corresponding side of the larger triangle.
So, the ratio of their areas is the square of the scale factor
This is represented as
(area of smaller triangle) / (area of larger triangle) = (2/3)^2 = 4/9
We are given that the area of the larger triangle is 27
So, we have
Area of smaller triangle/27 = 4/9
Multiplying both sides by 27, we get:
Area of smaller triangle = (4/9) * 27
Evaluate
Area of smaller triangle = 12
Hence, the area of the smaller triangle is 12.
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Find an equation for the graph.
The equation for the trigonometric graph is y = 2sin4x
What is a trigonometric graph?A trigonometric graph is the graph of a trigonometric function.
Since we desire to find the equation of the graph, we then want to use the equation for the general sine graph.
y = AsinBx where
A = amplitude and B = 2π/T where T = period.Now, A = (maximum - minimum)/2
From the graph,
maximum = 2 and minimum = -2So, we now substitute the variables into the equation, thus
A = (maximum - minimum)/2
= [2 - (-2)]/2
= (2 + 2)/2
= 4/2
= 2
Also B = 2π/T
Now from the graph, T = π/2
So, we substitute for B in the equation for B, thus
B = 2π/T
= 2π/(π/2)
= 2π × 2/π
= 4
We then substitute A and B into y, thus
y = AsinBx
= 2sin4x
So, y = 2sin4x
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Question 11 (1 point)
Mary Ellen is making a table cloth for a client's dining room. She selected some pale-
yellow linen from a craft store and has it laid out on her work table to cut into the
correct shape. What tool is Mary Ellen MOST LIKELY going to use to cut the linen?
Scissors
Shears
A measuring tape
A Color Scheme Guide
Answer:
Mary Ellen is MOST LIKELY going to use shears to cut the linen.
(8x+17), (12x-39) find m
The measure of the angle M is 129 degrees
How to determine the valueIt is important to note that the properties of a parallelogram are;
Opposite sides are equalOpposite angles are congruentSame-Side interior angles (consecutive angles) are supplementary, that is, 180 degreesEach diagonal of a parallelogram divides it into two congruent trianglesThe diagonals of a parallelogram bisect each otherThen, we have that;
m< M = m < K
substitute the values
12x - 39 = 8x + 17
collect the like terms, we have;
12x - 8x = 17 + 39
Add the collected like terms, we get;
4x = 56
divide both sides by the coefficient of 4, we get;
4x/4 = 56/4
Divide the values
14
Then, m < M = 12(14) -39 = 129 degrees
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The complete question:
In the parallelogram, Find mZN: K (8x + 17)9 (12x - 39)8 01;0 - Lx'An M Ax+8x +17 + iax -3 = 360 3ax-33 = H0 +3 42 20 22X 7 x=17.30
100 POINTS PLUS BRAINLIEST!!!!
screenshot with problem attached below
answers must be serious
non-serious answers / incorrect answers will be deleted
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Answer:
see step by
Step-by-step explanation:
a) the polynomial must be fifth degree, so it must have a [tex]x^5[/tex] term, also need to have 2 additional terms (Lets add any, lets say [tex]x^2+8[/tex] (notice this is totally random, just need to be under 5th degree)
So a polynomial can be
[tex]x^5+x^2+8[/tex]
notice is in standard form since degrees drops from left to right.
Also notice there's an infinite amount of possible answers
b) p-q is the same as -q+p
For example, lets say
[tex]p=x+1[/tex]
[tex]q=3x^2-5[/tex]
[tex]p-q=x+1-(3x^2-5)=x+1-3x^2+5=-3x^2+x+6[/tex]
also
[tex]-q+p=-(3x^2-5)+x+1=-3x^2+5+x+1=-3x^2+x+6[/tex]
notice is the same expression.
A theme park's rides are rated as mild, moderate and
max. They have restrictions requiring that passengers
have heights of at least 42 inches, 48 inches, and 54
inches, respectively. Suppose the population of children
attending the park has a mean height of 53 inches with
a standard deviation of 4 inches.
If a child is chosen randomly, what is the probability
that: (Round all answers to nearest thousandths)
a) the child can go on all rides?
b) the child can participate in only mild and moderate
rides?
c) the child can only go on mild rides?
d) the child is excluded from all rides?
Answer:
the probability that a child is excluded from all rides is 0.5000 (rounded to three decimal places).
Step-by-step explanation:
We can use the standard normal distribution to solve this problem. We first need to standardize the height requirements using the population mean and standard deviation.
a) To find the probability that a child can go on all rides, we need to find the probability of getting a height of at least 54 inches.
z-score = (54 - 53) / 4 = 0.25
Using a standard normal table or calculator, we find that the probability of getting a z-score of 0.25 or greater is 0.4013.
Therefore, the probability that a child can go on all rides is 0.4013 (rounded to three decimal places).
b) To find the probability that a child can participate in only mild and moderate rides, we need to find the probability of getting a height between 42 inches and 48 inches.
First, we find the z-scores for each height requirement:
z-score for 42 inches = (42 - 53) / 4 = -2.75
z-score for 48 inches = (48 - 53) / 4 = -1.25
Using a standard normal table or calculator, we find that the probability of getting a z-score between -2.75 and -1.25 is 0.2375.
Therefore, the probability that a child can participate in only mild and moderate rides is 0.2375 (rounded to three decimal places).
c) To find the probability that a child can only go on mild rides, we need to find the probability of getting a height of less than 42 inches.
z-score = (42 - 53) / 4 = -2.75
Using a standard normal table or calculator, we find that the probability of getting a z-score of -2.75 or less is 0.0030.
Therefore, the probability that a child can only go on mild rides is 0.0030 (rounded to three decimal places).
d) To find the probability that a child is excluded from all rides, we need to find the probability of getting a height less than 42 inches or greater than 54 inches.
First, we find the z-scores for each height requirement:
z-score for 42 inches = (42 - 53) / 4 = -2.75
z-score for 54 inches = (54 - 53) / 4 = 0.25
Using a standard normal table or calculator, we find that the probability of getting a z-score of less than -2.75 or greater than 0.25 is 0.0987 + 0.4013 = 0.5000.
Therefore, the probability that a child is excluded from all rides is 0.5000 (rounded to three decimal places).
Ayudaaaaa no sé cuando vaya a venir a revisar estoooolo
Si 25$ representa el 15% de una cuenta cuanto hay en total en la cuenta?
Si 25 dólares representan el 15% de una cuenta, podemos usar una regla de tres simple para determinar cuánto hay en total en la cuenta:
15% -----> $25
100% ----> ($25 x 100)/15
100% ----> $166.67
Por lo tanto, hay $166.67 en total en la cuenta.
Consider the graph of 5x² + 8x + 4y² - 4y = 70.
If the graph of 5x² + 8x + 4y - 4y = 70 is stretched horizontally by a factor of 3, the equation of the stretched graph will be
If the graph of 5x² + 8x + 4y² - 4y = 70 is stretched vertically by a factor of 7, the
equation of the stretched graph will be
To stretch the graph horizontally by a factor of 3, we need to multiply the x-coefficient by 1/3. Similarly, to stretch the graph vertically by a factor of 7, we need to multiply the y-coefficient by 1/7. Therefore:
Horizontally stretched graph: 5(1/3x)² + 8(1/3x) + 4y² - 4y = 70
Simplifying:
(5/9)x² + (8/3)x + 4y² - 4y = 70
Vertically stretched graph: 5x² + 8x + 4(1/7y)² - 4(1/7)y = 70
Simplifying:
5x² + 8x + (4/49)y² - (4/7)y = 70
A man borrowed $ 3700 from a bank for 6 months. A friend was cosigner of the
man's personal note. The bank collected 7 1/2% simple interest on the date of maturity.
a) How much did the
man pay for the use of the money?
b) Determine the amount
he repaid to the bank on the due date of the note.