Answer:
Step-by-step explanation:
Let [tex]x_{n}[/tex] represent the nth term in the sequence. Then [tex]x_{n-1}[/tex] represents the previous term
The first term, [tex]x_{1}[/tex] = -7
Each consecutive term is obtained by adding 4 to the previous term.
So the recursive relation is
[tex]\left \{ {{x_{1}= -7} \atop {x_{n}= x_{n-1} + 4}} \right.[/tex]
To which subset of real numbers does the following number belong? Square Root Of 54
A.
whole numbers, natrual numbers, integers
B.
whole numbers, integers, rational numbers
C.
irrational numbers
D.
rational numbers
The number √ 54 is an irrational number.
What is Rational number?A number which can be written in the form of fraction p / q , where q is non zero, are called Rational numbers.
Given that;
The number is,
⇒ √54
Now,
⇒ √ 54 = 7.348469...
Hence, By definition of an irrational number,
It is an Irrational number.
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numbers of students signing up for various math classes for the next school year are
given in the following table:
Grade Geometry Algebra II Pre-Calculus AP Statistics Total
10th 150
5
255
11th 50
20
245
12th 10
65
225
Total 210
90
725
75
100
50
225
25
75
100
200
Part A: What is the probability that a student will take AP Statistics? (2 points)
Part B: What is the probability that a 12th-grader will take either Pre-Calculus or AP
Statistics? (2 points)
Part C: What is the probability that a student will take Algebra II given that he or she
is in the 11th grade? (2 points)
Part D: Consider the events "A student takes Algebra II" and "A student is a 10th-
grader." Are these events independent? Justify your answer. (4 points) (10 points)
Part A 0.124
Part B 0.733
Part C 0.408
How to Calculate probability in AP Statistics?P(A) is the product of the number of outcomes in event A and the overall sample space. The chance of event A occurring, for instance, is 3/6, or 0.5, if we have a sample space of 6 outcomes (such as when rolling a die), and event A consists of 3 of those outcomes (such as when rolling a 1, 2, or 3).
Basic Probability RulesA mathematical representation of a random process, known as a probability model, is used to express the possibility of certain events occurring. A list of all potential outcomes and the likelihood that each outcome will occur make up its two basic parts.
The sample space is a catalogue of every event that could happen in a random operation, such tossing a coin or rolling a die. A sample space for flipping a coin, for instance, might be "heads, tails," but a sample space for rolling a die, for example, might be "1, 2, 3, 4, 5, 6."Probabilities are typically stated as fractions or decimals using this paradigm.For instance, the likelihood of flipping a coin over heads is 0.5 and the likelihood of rolling a six while rolling a die is 1/6.A list of all potential outcomes and the probability for each possibility make up a probability model, which is a representation of some random process. A sample space is the list of all conceivable outcomes.Explanation:Using the table Given :
1.) P(AP Statistics) = 90 / 725 = 0.124
2.) P(12th grade ; Precalculus or AP Statistics) = (100 + 65) / 225 = 165 /225 = 0.733
3.) P(Algebra 11 | 11th grade) = P(Algebara11 n 11th grade) / P(11th grade) = 100 / 245 = 0.408
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6th Math: Fundraising for the Animal Shelter
Noah raised $54, which is 60% of his fundraising goal to support the animal shelter.
Answer: 0.6x=54
$90
Step-by-step explanation: Start by saying the question out loud in a different format:
60% of what is $54?
We know that of means multiplication and is means equals. This helps us create the equation:
60% x what= $54
Then, we need to make 60% a number we can work with by changing it into a decimal: 0.6. We also need to make 'what' something easier to use as well, so we will use x in place of what:
0.6x=54
Then, get x by itself, which is also called isolating the variable. You do this by dividing by 0.6 on both sides, which is known as using inverse operations.
You should get x=90.
This means that $54 is 60% of $90 and $90 is Noah's goal.
11) A plane travels 160 miles on a bearing of 327°. It then changes direction and travels 205 miles on a
bearing of 311°. How far is the plane from its original position?
2051/
2051/2 miles,The plane is travelling in a different direction from its original position, and the distance from the original position can be calculated by using the Law of Cosines.
How far is the plane from its original position?The plane's displacement from its original position can be calculated by finding the magnitude of the vector sum of the two displacements.The first displacement can be calculated using the magnitude of the vector, the bearing, and the formula for the magnitude of a vector in polar coordinates. The magnitude of the vector is equal to the distance traveled (160 miles) multiplied by the cosine of the bearing (327°). Therefore, the magnitude of the first displacement is 149.9 miles.The second displacement can be calculated in the same manner. The magnitude of the vector is equal to the distance traveled (205 miles) multiplied by the cosine of the bearing (311°). Therefore, the magnitude of the second displacement is 176.7 miles.The vector sum of the two displacements can be found by adding their respective x-components and y-components. The x-component of the first displacement is negative 149.9 miles, and the y-component is 131.8 miles. The x-component of the second displacement is negative 176.7 miles, and the y-component is 114.2 miles. The x-component of the vector sum is −326.6 miles, and the y-component is 246 miles.This problem is an example of vector addition. Vector addition is a mathematical process used to calculate the resultant displacement of two or more vector quantities. It is the process of combining two or more vectors to produce a vector that points in the same direction as the total of the individual vectors. In this case, we can use vector addition to find the distance from the plane's original position.
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a smothie recipe calls for 2 1/4 cups of frozen mango. If the recipe serves two. ow many cups of frozen mango is needed to serve one?
1.125 cups of frozen mango is needed to serve one
A smoothie recipe contains 2 1/4 cups of frozen mango
This recipe can serve a total number of two people
The first step is to change the mixed fraction to an improper fraction
2 1/4
9/4
The number of cups of frozen mango needed to serve one person is
9/4 ÷ 2
9/4 × 1/2
= 9/8
= 1.125
Hence the number of cups of frozen mango required to serve one person is 1.125
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Which equation represents a linear function?
A y=1/4x
B y= |x|
C y= x exponent 2
D y= -3x exponent 3
So on solving the provided question, we can say that y= |x| makes a starlight line, this equation is a linear function.
What is linear function ?Two distinct but related concepts are referred to as linear functions in mathematics. A polynomial function of degree 0 or 1 is a linear function in calculus and related subjects if its graph is a straight line. Any function that depicts a straight line on a coordinate plane is said to be linear. For instance, y = 3x - 2 is a linear function since it depicts a straight line on the coordinate plane. f(x) = 3x - 2 can be used to represent the function since f(x) can be linked to y.
equation represents a linear function is that polynomial function of degree 0 or 1 is a linear function in calculus and related subjects if its graph is a straight line.
so, here y= |x| makes a starlight line, this equation is a linear function.
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Find the slope and y-intercept.
Answer: Slope:5/3
Y-intercept: y=1.67x+-4
Step-by-step explanation:
Slope:
Take two points and put it in for m=y2-y1/x2-x1
we can use (0,-4) and (3,1)
m=1--4/3-0
m=5/3
m=1.67
Then we use m in y intercept and use the first point as b
y = mx + b
y=1.67x+b
-4 = 1.67(0) + b
-4 = 0 + b
-4 = b
b = -4
y = 1.67x + -4
Y intercept: y = 1.67x + -4
Slope: 5/3
Good luck
Draw a graph of the signed area represented by the integral and compute it using geometry. (Use symbolic notation and fractions where needed.)
The integral represents a graph of the signed area, and the geometry is calculated. The area is found to be 100 units².
A plane that is created when two perpendicular coordinate axes cross each other is known as a cartesian plane. Everywhere in the Cartesian plane, the functions define the boundaries of regions with regular geometrical patterns. The right triangle and other regular regions are good examples of how the area of a region may be computed using the geometry of the region.
The given function is [tex]\int\limits^{10}_{-10} {|x|} \, dx[/tex]. The function of this integrand is defined as f(x)=|x| with -10 ≤ x ≤ 10. Now, the graph is drawn for this function.
From the graph, we can tell the base and height of the two right-angle triangles are 10 units and 10 units. Then, the area is,
[tex]\begin{aligned}A&=2\left(\frac{1}{2}\times b\times h\right)\\&=2\times \frac{1}{2}\times 10 \times 10\\&=\mathrm{100\;{units}^2}\end{aligned}[/tex]
The area can also be calculated by solving the integrals,
[tex]\begin{aligned}\int\limits^{10}_{-10} {|x|} \, dx &=\int\limits^0_{-10} {-x} \, dx +\int\limits^{10}_0 {x} \, dx\\&=\left[\frac{x^2}{2}\right]^{0}_{-10} +\left[\frac{x^2}{2}\right]^{10}_{0}\\&=\frac{1}{2}(100+100)\\&=\mathrm{100\;units^2}\\\end{aligned}[/tex]
The required answer is 100 units².
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Classify the triangle by its sides and angles.
Am I right???
Please help!
according to money magazine, maryland had the highest mean annual household income of any state in at (time website). assume that annual household income in maryland follows a normal distribution with a mean of and standard deviation of .
The probability of getting a household income of $75,000 in Maryland is 0.3989.
The normal distribution formula is given by:
P(x) = 1/√(2πσ^2) * e^[-(x-μ)^2 / (2σ^2)]
Where,
P(x) - Probability of getting a household income of x
μ - Mean annual household income in Maryland
σ - Standard deviation of annual household income in Maryland
Assuming that the mean annual household income in Maryland is $75,000 and the standard deviation is $10,000, the probability of getting a household income of $75,000 can be calculated using the formula given above.
P(75000) = 1/√(2π10000^2) * e^[-(75000-75000)^2 / (2*10000^2)]
= 0.3989 * e^(0)
= 0.3989
Therefore, the probability of getting a household income of $75,000 in Maryland is 0.3989.
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(URGENT) Which pair of functions are inverses of each other?
The requried pair of functions which are inverse of each other is f(x) = 13x - 7 and g(x) = x + 7 / 13.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
(A)
Given function,
f(x) = x / 3 + 10
Its inverse function is given as,
f(x) - 10 = x/3
x = 3(f(x) - 10)
change x = g(x) and f(x) = x
g(x) = 3[x - 10]
Similarly,
Inversfunciton,
B. g(x) = 9/x - 5
C. g(x) = x + 7 / 13
D. g(x) = x³/4
Thus, the requried pair of functions which are inverse of each other is f(x) = 13x - 7 and g(x) = x + 7 / 13.
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HELP 50 PNTS THANK YOZU
The graph shown in 'Option 1' shows the continuous data.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
There are four graph is shown in image.
We know that;
Continuous data changes over time and can have different values at different time intervals. Continuous data is made up of random variables, which may or may not be whole numbers.
And, Continuous data is measured using data analysis methods such as line graphs, skews, and so on.
Hence, By definition of Continuous data; We get;
⇒ The graph shown in 'Option 1' shows the continuous data.
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A spinner with 4 equal sections is spun 20 times. The frequency of spinning each color is recorded in the table below.
Outcome | Frequency
Pink | 6
White | 3
Blue | 7
Orange | 4
What statement best compares the theoretical and experimental probability of landing on pink?
A. The theoretical probability of landing on pink is one fifth, and the experimental probability is 50%.
B. The theoretical probability of landing on pink is one fourth, and the experimental probability is 50%.
C. The theoretical probability of landing on pink is one fifth, and the experimental probability is 30%.
D. The theoretical probability of landing on pink is one fourth, and the experimental probability is 30%.
The theoretical probability of landing on pink is 3/10, and the experimental probability is 30%. Therefore, option D is the correct answer.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Given that, a spinner with 4 equal sections is spun 20 times.
The frequency of spinning each color is recorded in the table below.
Outcome Frequency
Pink 6
White 3
Blue 7
Orange 4
Probability of landing on color pink is 6/20
= 3/10
= 3/10 ×100
= 30%
Therefore, option D is the correct answer.
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The scatter plot shows the average monthly temperature, x , and a family's monthly heating cost, y , for 24 different months.
1. y = -1.15x + 102.8 is the equation of the line of best fit.
2. Using the line of best fit's equation, the estimated price is: $62.55.
What are Equations?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
A statement is not an equation if it has no "equal to" sign.
According to our question-
1. Making use of the two points (20, 80) and (72, 20)
Slope (m) is equal to change in y/change in x, or (80 - 20)/(20 - 72) = 60/-52.
Slope is -1.15 meters.
Change y - b = m to m = -3 and (a, b) = (72, 20). (x - a)
y - 20 = -1.15(x - 72) (x - 72)
y - 20 = -1.15x + 82.8
y = -1.15x + 82.8 + 20
y = -1.15x + 102.8
The best line of fit is the equation y = -1.15x + 102.8.
2. To calculate the monthly heating expense, y, for a month with an average temperature of 35°F (x), enter x = 35 into the formula: y = -1.15x + 102.8.
y = -1.15(35) + 102.8
y = 62.55
The estimated monthly expenditure is $62.55.
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This is a regular polygon.
What are the values of x and y?
Therefore ,in light of this, the solution (n -2) * 180 can be used to solve the following polygon issue, where is the actual number of sides.
A polygon is what?It has straight sides. A polygon's vertices (or corners) are the points at which two of its sides meet. A figure with three or more straight sides is known as a closed, two-dimensional polygon. Any form with angular sides, such as a triangle or a rectangle, is a polygon. Open-sided or curved figures are not considered to be polygons.
Here,
example
The sum of each internal angle in a polygon can be calculated by applying the formula (n-2)*180, where n is the total number of sides in the polygon.
The required polygon has nine sides, hence the sum of external angles in this case is (9-2)*180, or 7, which is equivalent to 1,260 degrees.
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A car travels 60 miles with a constant speed of 57 mph and then another 60 miles with 40 mph. How long
does it take for the car to travel the first 60 miles?
t₁ =
What time is required to travel the second 60 miles?
Units hrs
t₂ =
Units hrs
What is the average speed of the car for the entire trip?
The average speed, v =
Units mph
Answer:
Step-by-step explanation:
t1= 60/57
t2=60/40=1.5
v= (57+40)/2= 48.5
5. 5(x + 10) + x
A. 6x + 15
B.5x + 15
C.6x + 50
D.4x – 50
Answer: C
Step-by-step explanation:
A person's systolic blood pressure, which is measured in millimeters of mercury (mm Hg), depends on a person's age, in years. The equation:
P = 0.006y^2-0.01y+119
gives a person's blood pressure, P, at age y years.
A.) Find the systolic pressure, to the nearest tenth of a millimeter, for a person of age 43 years.
B.) If a person's systolic pressure is 131.78 mm Hg, what is their age (rounded to the nearest whole year)?
Solving the provided question, we cans say that by quadratic equation, the age where a person's systolic pressure is 127.54 mm Hg is 46
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared.
systolic pressure for a person of age 45 years, just plug in y = 45:
systolic pressure is 127.54 mm Hg, plug in P = 127.54
P = 0.004y2 - 0.02y + 120
127.54 = 0.004y2 - 0.02y + 120
0 = 0.004y2 - 0.02y - 7.54
Use the quadratic formula to solve this. The quadratic formula (for ay2 + by + c = 0) is:
y = [-b ± √(b2 - 4ac)]/(2a)
In this case a = 0.004, b = - 0.02 and c = - 7.54 so:
[tex]y = [-b + \sqrt{(b2 - 4ac)]/(2a)}\\y = [-(-0.02) +\sqrt{((0.02)2 - 4(0.004)(-7.54))]/(2(0.004))}\\y = [0.02 + \sqrt{(0.0004 + 0.12064)]/0.008}\\y = [0.02 + \sqrt{0.12104]/0.008}\\y = [0.02+ 0.3479]/0.008\\ y = [0.02 + 0.3479]/0.008 or y = 0.3679/0.008 = 45.989\\ y = [0.02 - 0.3479]/0.008 or y = -0.3279/0.008 = -40.989\\[/tex]
Since -40.988 makes no sense (40.989 years before birth), we throw that answer out.
The age where a person's systolic pressure is 127.54 mm Hg is 46
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Help me I need this NOWWW!!!!!!!
Answer:
25:5:12
wat
Step-by-step explanation:
follow me
pls
Answer: 10, 5, 12, and 3 compear each other.
Step-by-step explanation: only this way, I don't know is there other
Find the equation of a line that passes through (1,8) and is parallel to the graph of y=2x+3. Write the equation in slope-intercept form, if possible.
Therefore , the solution to the given problem of equation comes out to be y = 2x + 4.
Describe the equation.A proclamation of the equivalency of two expressions is an algebraic equation, which is calculated by performing the algebraic of addition, removal, multiplication, division, raising to a power, or extracting a root to a collection of variables. Examples include (y4x2 + 2xy - y)/(x - 1) = 12 and x3 + 1.
Here,
It is important to remember that parallel lines have the same slopes before trying to determine this line's equation.
As a result, we can predict that the new line will have a slope of 2 because the previous line has a slope of 2.
Now that we have that knowledge, we can utilize it to find the equation using point-slope form and the supplied point.
y - y1 = m(x - x1) (x - x1)
y - 8 = 2(x - 2) (x - 2)
y - 8 = 2x - 4
y = 2x + 4
Therefore , the solution to the given problem of equation comes out to be y = 2x + 4.
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help for the love of god
Answer:
W = -8
Step-by-step explanation:
Sorry fir taking so long, the description is pretty long, and difficult to type, but if you need one let me know :D
Ax+By=C
y + 6 = -2 (x + 1) Whats the-answer for the question
The answer for y + 6 = -2 (x + 1) the equation in the general form is y - 2x = -8.
What is equation?
Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
The equation is represented in the general form Ax+By=C.
The given equation is -
y + 6 = -2 (x + 1)
Simplify further -
y + 6 = -2 (x + 1)
y + 6 = -2x -2
y - 2x = -2 - 6
y - 2x = -8
Therefore, the equation is y - 2x = -8.
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plisss can you solve this for me
i got nothin
like what?
The value Q of a material is directly proportional to the square of its weight W. If a material weighing 20 kg is worth 500,find: (a)the value of a material weighing 5 kg (b)the value of a material weighing 50 kg (c)the weight of a material worth 720.
(a) the value of a material weighing 5 kg is 31.25
(b)the value of a material weighing 50 kg is 3125
(c) the weight of a material worth 720 is 24 kg
How to determine the value of the material?
Variation is a relation between a set of values of one variable and a set of values of other variables
If the value Q of a material is directly proportional to the square of its weight W. We can write:
Q α W²
Q = kW² (where k is constant of proportionality)
If a material weighing 20 kg is worth 500, we have:
Q = kW²
500 = k × 20²
500 = 400k
k = 500/400
k = 5/4
k = 1.25
(a)the value of a material weighing 5 kg
Q = kW²
Q = 1.25 × 5² = 31.25
(b)the value of a material weighing 50 kg
Q = kW²
Q = 1.25 × 50² = 3125
(c)the weight of a material worth 720
Q = kW²
720 = 1.25 × W²
W² = 720/1.25
W² = 576
W = √576
W = 24 kg
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12
R
T
37
35
Enter the ratio equivalent to tan(R).
>S
Answer:
[tex]\frac{35}{12}[/tex]
Step-by-step explanation:
The tangent of an acute angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
What is 3 4 in standard form?
81 is the standard form of 3⁴
What is Number system?A number system is defined as a system of writing to express numbers.
The given expression is 3⁴
We need to write in the form of the standard form
3⁴ is nothing but three is multiplied four times
3×3×3×3
Thee times of three for two times
81
Hence, 81 is the standard form of 3⁴
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the function get list of powers takes in a list x and integer k and returns a list l whose elements are themselves lists. the ith element of l contains the powers of x[i] from 0 to k. for example, running get list of powers with inputs x
The function will use the formula x^i, where x is the element in x and i is the power.
Let x = [2, 3] and k = 3.
The function get list of powers will calculate the powers of each element in x, from 0 to k.
For the given example, the list of powers will be l = [[1, 2, 4, 8], [1, 3, 9, 27]].
The first element in l is the powers of 2 from 0 to 3, which are 1, 2, 4, and 8. The second element in l is the powers of 3 from 0 to 3, which are 1, 3, 9, and 27.
To calculate these powers, the function will use the formula x^i, where x is the element in x and i is the power.
For example, to calculate 8 (2^3), the function will use the formula 2^3.
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Complete the table.
Distance
(ft)
0
EN R
2
37
2
2π
Height
(ft)
a
b
с
d
e
The complete distance in feet on the table are a=6, b=7, c=8, d=7, and e=6.
What is revolution?In mathematics, a revolution is a full rotation, or a full 360-degree turn. The item starts and ends in the same location during a 360-degree revolution.
The circumference of the wheel is equal to the length of a full revolution, or 2*pi*radius. The whole rotation of the wheel is 360 degrees.
The eight of the point is 6 feet, and the wheel's radius is 1 feet.
The point will be in its initial position, which is 6 feet high.
The height will thus be a = 6 + 0 = 6 ft.
The point will reach half the whole height of the wheel, or 2 feet, when the distance travelled is pi/2.
Height of b = 6 + 1 = 7 feet will result.
The point will be at the top of the wheel, which is 2 feet higher than the lower point of the wheel, when the distance travelled equals pi.
The height will thus be c = 6 + 2 = 8 ft.
The point will be half the whole height of the wheel, or 2 feet, when the distance travelled is 3 pi/2.
The height will thus be d = 6 + 1 = 7 ft.
The point will be in its initial position, which is 6 feet high, when the distance travelled is 2 pi.
The height will thus be e = 6 + 0 = 6 ft.
Hence, the complete distance in feet on the table are a=6, b=7, c=8, d=7, and e=6.
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Graph the trapezoid A(6,5), B(8,-2), C(-4,-2), D(-2,5)
The trapezoid is a form of quadrilateral that has at least one parallel sides. The trapezoid here is given by the mentioned coordinates.
What is a point?A point is a dot on a sheet of paper or in a plane. There are no lengths, widths, or heights in a point. It establishes a plane's position or location.
What are coordinates?It is possible to find any point in a 2D plane or 3D space using coordinates, which are ordered pairs of points. You may have observed the use of grids in mathematics.
Select a point on the graph according to the given coordinates. Connect all the points on the graph using a line segment. The shape formed by joining all the points together is knows as a trapezoid.
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Aaron works at a garden center where he plants
flowers. It takes him 3 1/2 hours to plant 21 flowers.
How many plants can he plant in 1 hour?
The number of flowers that can be planted in 1 hour is 6 flowers.
What is cross-multiplication?To solve equations or determine the value of a variable, cross multiplication is employed in mathematical operations. In this procedure, the numerator of one side is multiplied by the denominator of the other side.
Given that the time required to plant trees is:
3. 5 hours = 21 flowers
Convert 3.5 hours into minutes.
3 hours 60 = 180 minutes,
Additional half hour can be represented as: 1/2 hours 60 = 30 minutes.
Total hours is 180 + 30 = 210 minutes.
So it takes, 210 minutes to plant 21 flowers.
The time taken to plant flowers in 60 minutes is:
[tex]x = \frac{(21)(60)}{210} \\\\x=6[/tex]
Hence, the number of plants that can be planted in 1 hour is 6 flowers.
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