[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-16}~,~\stackrel{y_1}{11})\qquad (\stackrel{x_2}{16}~,~\stackrel{y_2}{4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~16 - (-16)~~)^2 + (~~4 - 11~~)^2} \implies d=\sqrt{(16 +16)^2 + (4 -11)^2} \\\\\\ d=\sqrt{( 32 )^2 + ( -7 )^2} \implies d=\sqrt{ 1024 + 49 } \implies d=\sqrt{ 1073 }\implies d\approx 32.76[/tex]
in a class of 20 students, there are two students a and b. what will be the probability of selecting these two students randomly?
The probability of selecting two students (a and b) randomly is found as 1/380.
What is referred as the word probability?The study of random experiments is what aids in determining the likelihood of an event.The study of probabilities, which are determined by the ratio of favorable cases to possible cases, is known as probability.The formula for evaluating the Probability is-
Probability = Favourable outcomes / Total outcomes.
As, per the given question.
Total number of students = 20.
The probability for selection of 'a' is 1/20.
Now, the total students left is 19.
Thus, the probability for selection of 'b' is 1/19.
The total probability for selection of both is -
Probability(a and b) = 1/20×1/19
Probability(a and b) = 1/380
Thus, the probability of selecting two students ( a and b) randomly is found as 1/380.
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in a order pair (4,9) witch is the y-coordinate?
In order pair (4,9), 9 is the y- coordinate while 4 is the x-coordinate.
The coordinates are the pair of numbers that describe the position of some point in a plane using the horizontal x-axis and the vertical y-axis as the point of reference. The representation of this coordinate is usually done by (x,y) where x represents the point's reference with respect to the x-axis and y represents the point's reference with respect to the y-axis. There are four quadrants in the graph which are named quadrant 1, quadrant 2, quadrant 3, and quadrant 4. In quadrant 1 both the x and y-axis is positive, in quadrant 2 x-axis is negative and the y-axis is positive, in quadrant 3 both the x and y-axis are negative, and in quadrant 4 x-axis is positive while the y-axis is negative.
I hope this answer helps
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Answer:
9
Step-by-step explanation:
Remember that all points have the form, [tex](x,y)[/tex].
Soo in this problem,
[tex]\begin{cases}\text{4 is the x-coordinate}\\\text{9 is the y coordinate}\end{cases}[/tex]
Thus, The y-coordinate is 9!!
HELPPPPPPPPPPPpp
Robert pays for his family to go to the arcade. He pays an entrance fee for his group and an additional amount per game that his family plays as shown in the graph. Use the graph to answer.
Find the slope and interpret its meaning.
Answer:
3/4,. it's means for every 4 games there's a $3 fee
Step-by-step explanation:
3/4
it's means for every 4 games there's a $3 fee
why do we use the pooled proportion when we calculate the standard error for the difference in proportions when performing a hypothesis test?
we use the pooled proportion when we calculate the standard error for the difference in proportions when performing a hypothesis test whne When the variances of both populations are the same
The standard error for the distinction within the proportions is calculated utilizing the population proportions but in cases where the population proportions are unknown, we utilize the test proportions to calculate the standard error. In the case of hypothesis testing, we are mindful of the population proportions whereas in evaluating the confidence interval for the distinction between the proportions we have no thought of the population proportions. So, the standard error for a hypothesis test of distinction in two proportions is distinctive from the standard error for a certain interval of the difference in two proportion.
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Which of the following sets is equal to {1, 2, 3, ...}?
The set which is equivalent and equal to the given set; {1, 2, 3, ...} is; Z+.
Which set is equivalent to the given set?It follows from the task content that the set which is equivalent to the given set; {1, 2, 3, ...} is to be determined.
Since the numbers in the set are all integers and which happen to be positive integers.
Hence, the best representation of a set which is equivalent to the given set as given in the task content is; Z+.
The set of positive integers is represented as Z+. It implies all the integers greater than 0.
Hence, the set which is equivalent to the given set; {1, 2, 3, ...} is; Z+.
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Heidi thinks the rule for the table below is y = x + 3.
Is she correct?
X
-2
-1
0
1
2
y
-7
-4
-1
2
5
From the diagram below, choose the correct letter for each of the
following parts of a circle:
a) a major arc
b) a minor sector
c) a major segment
A
B
D
✓ Scroll down
E
From the diagram, A is the major arc
B is the minor sector
C is the major segment.
What do you mean by major arc, minor sector, and a major segment of a circle?
1. Major arc: A significant arc is one that is larger than 180 degrees in measure.
2. Minor sector: A circle's intercepted arc and two of its radii define a region known as a sector. The center angle is the intersection of the two radii. A minor sector is defined as having a center angle of less than 180°.
The major arc is A significant arc is one that is larger than 180 degrees in measure. So, A is the major arc. The minor sector is defined as having a center angle of less than 180°. So, B is the minor sector. And C has the maximum portion of length so C is a major segment.
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Which of the following describes the transionnation of g(x)=3(2) ^-x+2 from the parent iuciction f(x) =2^x?
O reflect across the x-axis, stretch the graph vertically by & factor of 3,shift 2 units up. O reflect across the y-axis, stretch the graph vertically by & factor of 2,shift 3 units up. O reflect across the x-axis, stretch the graph vertically by & factor of 2, shift 3 units up. O reflect across the y-axis, stretch the graph vertically by & factor of 3,shift 2 units up
The transformation of g(x) = 3(2)⁻ˣ+2 from the parent function f(x) = 2ˣ will be carried out by reflecting f(x) across the y-axis, then stretching the graph of f(x) vertically by a factor of 3 and then shifting 2 units up,
What is a transformation function?
A function that transforms one function or graph into another, typically a related function or graph, is called a transformation function.
How to convert the parent function into the transformation function?
The transformation of the parent function is shown in blue. It is a shift down (or vertical translation down) of 1 unit. A reflection on the x-axis is made on a function by multiplying the parent function by a negative. Multiplying by a negative “flips” the graph of the function over the x-axis.
Here, we have
Transformation Function - g(x) = 3(2)⁻ˣ+2
Parent Function - f(x) = 2ˣ
To convert the parent function into the transformation function, we will follow some steps:
Multiply 3 by the function f(x). Due to this the graph of f(x) shift vertically by 3 units. f(x) = 3(2ˣ )Now, replace x with -x. Due to this the graph of f(x) reflects the y-axis. f(x) = 3(2)⁻ˣAdd 2 to the function f(x). Due to this the graph of f(x) shift by two units. f(x) = 3(2)⁻ˣ+2 = g(x)Hence, the transformation of g(x) = 3(2)⁻ˣ+2 from the parent function f(x) = 2ˣ will be carried out by reflecting f(x) across the y-axis, then stretching the graph of f(x) vertically by a factor of 3 and then shifting 2 units up.
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solve for x and y
picture provided
The value of x will be 15 and the value of y will be 4.
What is the similarity?If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
Here in the image, we have a triangle having sub-triangles. The value of x is calculated by considering two right-hand triangles.
x / ( x + 5 ) = 18 / ( 18 + 6 )
x / ( x + 5 ) = 18 / 24
24x = 18x + 90
6x = 90
x = 15
The value of y will be calculated by considering the two left-hand triangles.
12 / ( 12 + y) = 15 / 20
240 = 180 + 15y
15y = 60
y = 60 / 15
y = 4
Therefore, the value of x will be 15 and the value of y will be 4.
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This shows a diagram.
What is the value of x?
Step-by-step explanation:
[tex](3x + 2) + x = 180 \\ 3x + x = 180 - 2 \\ 4x = 178 \\ x = 44.5[/tex]
Answer:
x° = 44.5°
Step-by-step explanation:
x° and (3x + 2)° are supplementary angles, which means they add up to 180°.
Equation: x + 3x + 2 = 180
Step 1: Combine like terms.
[tex]\implies 4x + 2 = 180[/tex]
Step 2: Subtract 2 from both sides.
[tex]\implies 4x + 2 - 2 = 180 - 2[/tex]
[tex]\implies 4x = 178[/tex]
Step 3: Divide both sides by 4.
[tex]\implies \dfrac{4x}{4}=\dfrac{178}{4}[/tex]
[tex]\implies x = 44.5[/tex]
Step 4: Substitute 44.5 as the value of x in (3x + 2) to find its measure.
[tex]\implies 3(44.5)+2[/tex]
[tex]\implies 135.5[/tex]
Therefore, the measure of x° is 44.5°, and the measure of (3x + 2)° is 135.5°. Together, they add up to 180°.
Two cars start at the same point and simultaneously drive in opposite directions.
The speed of the first car is s miles per hour. The speed of the second car is 5
miles per hour less than the speed of the first car.
How far apart are the cars 1.5 hours after they start moving?
Answer:
3s - 7.5 milesStep-by-step explanation:
GivenThe speed of car1 is s,The speed of car2 is 5 less than s,Time is 1.5 hrs.SolutionDistance equation:
Distance = speed * timeIf cars move in opposite directions their speeds add up, then the distance between them after 1.5 hours is:
(s + s - 5)*1.5 = (2s - 5)*1.5 = 3s - 7.5Answer:
After 1.5 hr, they are 3s - 7.5 mi away.
Step-by-step explanation:
Forming the expression,
→ 1.5 × (s + s - 5)
Now the required solution will be,
→ 1.5 × (s + s - 5)
→ 1.5 × (2s - 5)
→ 1.5(2s - 5)
→ 3s - 7.5
Hence, answer is 3s - 7.5 miles.
The total number of participants who went on the seventh-grade field trip to the Pink Palace consisted of all of the seventh-grade students and 19 adult chaperones. Two-thirds of the total participants rode a large bus, and the rest rode a smaller bus. If 104 people rode the larger bus, how many students went on the field trip? Write your answer below as a single integer.
The number of students that went on the field trip is 137.
How many students went on the field trip?Let s represent the number of seventh grade students that went on the field trip.
Total number of participants = number of students + number of teachers
a + 19
Number of participants that rode the larger bus : 2/3 x (a + 19) = 104
In order to determine the value of a, take the following steps:
Multiply both sides of the fraction by 3 / 2
a + 19 = 104 x 3 / 2
a + 19 = 156
Subtract 19 from both sides of the equation:
a = 156 - 19
a = 137
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I fill the 42 l tank in my car and take a 360 km trip. if my car consumes gasoline at a rate of 8 l per 100 km, how much farther can i go before i run out of gasoline?
Using the principle of proportional relationship, you can go 165km farther after the trip of 360km with 42L gasoline in the tank.
Consumption rate =[tex]8L[/tex] for [tex]100 km[/tex]
So, per number of Km per Litre is
[tex]8L = 100km[/tex]
[tex]1 L = x[/tex]
so,
[tex]8x = 100[/tex]
[tex]x=8 \div 100\\[/tex]
[tex]x= 12.5[/tex] kilometer per Litre
Number of kilometers for [tex]42 L[/tex]
[tex]12.5 km = 1 L[/tex]
[tex]y=42L[/tex]
On, Cross multiplying
[tex]y = 12.5\times42[/tex]
[tex]y = 525 km[/tex]
The difference in the distance [tex]= 525 - 360 = 165 km[/tex]
Therefore, the gas can go for a further [tex]165 km[/tex]
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if a password is to have 4 digits, each from 0 to 9, what is the probability that there will be no repeats on the digits?
The probability that there will be no repeats on the digits is 0.504.
What is meaning of probability?
The ratio of favorable outcomes with the total number of outcomes is known as probability of that event.
The number of digits of the password is 4.
The numbers from 0 to 9 is 10.
If the digit can repeat, then we can chose first digit in 10 ways, the second digit in 10, third digit in 10 ways and fourth digit in 10 ways.
The total number of ways is 10 × 10 × 10 × 10 =10000.
If the digit can't repeat, then we can chose first digit in 10 ways, the second digit in 9 (because we can't use first digit) , third digit in 8 ways (because we can't use first digit and second digit) and fourth digit in 7 ways(because we can't use first digit, second digit, and third digit).
The total number of ways is 10 × 9 × 8 × 7 =5040.
The favorable outcomes for this event is 5040.
The total number of outcomes is 10000.
The required probability is 5040/10000 = 0.504.
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Please provide, with your answer, the steps taken.
The value of the given expression is 9/2 when substituting the values of m = -3, n = 2, and p = -1 in the expression.
The value of the given expression is 10/3 when substituting the values of x = 3, y = 2, and z = 4 in the expression.
Given that m = -3, n = 2, and p = -1
The expression is given in the question
⇒ m(p -n)²/ 3p +m
Substitute the values of m = -3, n = 2, and p = -1 in the expression
⇒ -3(-1 -2)²/( 3(-1) +(-3))
⇒ -3(-3)²/(-3-3)
⇒ -3(9)/(-6)
⇒ 27/6
⇒ 9/2
Given that x = 3, y = 2, and z = 4
The expression is given in the question
⇒ (3z + 2x + y)/(4y - 2x + z)
Substitute the values of x = 3, y = 2, and z = 4 in the expression
⇒ (3×4 + 2×3 + 2)/(4×2 - 2×3 + 4)
⇒ (12 + 6 + 2)/(8 - 6 + 4)
⇒ 20/6
⇒ 10/3
Thus, the value of the given expression is 10/3 when substituting the values of x = 3, y = 2, and z = 4 in the expression.
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what is the difference between independent samples and related samples when dealing with two samples
The difference between an independent sample and a dependent sample is that the dependent sample for one set of items is paired measurement while measurements made on two samples are termed an independent sample.
In statistics, while considering two samples and conducting a hypothesis test, one should be aware of which type of test should be conducted based on samples whether they are dependent or independent. If the value of another sample is affected by any one sample then the samples are dependent. If no information can be deduced from the other sample using one sample then the samples are independent.
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a group of 1,000 randomly selected adults is classified into 4 smoking groups: nonsmoker, light smoker, moderate smoker, and heavy smoker. at the end of a ten-year period, the proportion in each group who developed lung cancer was determined. the null hypothesis is that all 4 groups will have the same incidence rate of lung cancer. the p-value is found to be smaller than the level of significance (i.e. smaller than .05). what is the most appropriate conclusion?
The null hypothesis is rejected thus there is a significant difference in the incidence of lung cancer in all four groups.
When the p-value is less than 0.05, the null hypothesis that there is no difference between the means is rejected, and we come to the conclusion that there is a significant difference. The existence of a significant difference cannot be inferred if the p-value is higher than 0.05.
The null hypothesis in the given scenario was that all four groups will have the same incidence rate of lung cancer which is rejected.
An assertion that there is no correlation between two population measures is referred to as a null hypothesis. To prepare the ground for additional experimentation or study that explains the position of interest, researchers reject or refute the null hypothesis.
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Jackson buys 60 books at £3 each.
He sells 35 of these at £8 each and
the remainder at £4 each. What
percentage profit does he make
(give the answer to the nearest
whole number).
Answer:
111%
Step-by-step explanation:
£3 × 60 = £180
(35 × £8) + ( 25 × £4) = £380
£380 ‐ £180 = £200
200/180 × 100% = 111% (nearest whole number)
0.1 times n equal's89.5
the augusta national golf club in augusta, georgia is an 18-hole course that consists of par-3 holes, par-4 holes, and par-5 holes. a golfer who shoots par has a total of 72 strokes for the entire course. there are two more par-4 holes than twice the number of par-5 holes, and the number of par-3 holes is equal to the number of par-5 holes. find the numbers of par-3, par-4, and par-5 holes on the course.
No. of par-3 holes be represented by = 5
No. of par-4 holes be represented by = 8
No. of par-5 holes are represented by = 5
Total number of courses in the club= 18 (given in the question)
Total shot taken by golfer=72 (given in the question)
Let par-3 holes be represented by t
Let par-4 holes be represented by f
Let par-5 holes be represented by v
forming equations:
f+2=2v
t=v
f + v + t = 18
f+2=2v
f=2v-2 -(i)
t=v -(ii)
f + t + v=18
putting values from (i) and (ii)
(2v-2) + v + v=18
2v-2+2v=18
4v=18+2
4v=20
v=20/4
v=5
Number of par-5 holes=5
from (i)
f=2v-2
putting value
f=2(5)-2
f=10-2
f=8
Number of par-4 holes=8
from (i)
t=v-
putting value
t=5
t=5
Number of par-3 holes=5
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Complete the equation so that it has no solution.
9(x – 4) – 5x =__x-30
For the given equation 9(x-4) -5x = __x -30 has no solution when it is written as 9(x - 4) -5x = 4x -30.
As given in the question,
Given equation is equal to :
9 ( x - 4) - 5x = _ x - 30
Simplify Left hand side of the given equation we get,
9 ( x - 4) -5x
= 9x - 36 - 5x
Collect the like terms we have,
9x - 5x - 36
= 4x - 36
Now compare left hand side and right hand side to get no solution of the equation,
4x -36 = _x -30
Blank should be filled by 4
Therefore, for the given equation 9(x-4) -5x = __x -30 has no solution when it is written as 9(x - 4) -5x = 4x -30.
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A study of interior designers' opinions with respect to the most desirable primary color for executive offices showed that: What is the probability that a designer does not prefer red? 1.00 0.77 0.73 0.23
The probability that a designer does not prefer red is 0.77.
Define the meaning of the term probability?Probability is synonymous with possibility. It is a mathematical branch that deals with both the occurrence of something like a random event. The value varies from 0 to one. Probability has just been introduced in mathematics to predict the likelihood of occurrences occurring.Probability (event) = favorable outcome / total outcome
Total primary color designers = 400.
The number of opinions for red = 92
The probability for designer prefer red = 92 /100
The probability for designer prefer red = 0.23
Then, the probability that a designer does not prefer red = 1 - 0.23
The probability that a designer does not prefer red = 0.77
Thus, the probability that a designer does not prefer red color = 0.77.
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The correct question along with table is attached-
-
Find the equation of a line parallel to x - 4y = 36 that passes through the point
(-4,-5).
The equation of a line parallel to x - 4y = 36 is x - 4y = 16.
If the two lines are parallel then their slope must be equal. Two parallels lines have different intercepts but same slope. The slope intercept form of a line is y = mx + c. Where m is the slope and c is the intercept.
Now, writing the given equation in slope-intercept form,
x - 4y = 36
4y = x - 36
[tex]y=\frac{1}{4}x-9[/tex]
By comparing it with slope-intercept form, we get
[tex]m=\frac{1}{4}[/tex]
c = -9
Now, Finding the equation of line passing through (-4,-5) with slope as [tex]\frac{1}{4}[/tex],
[tex]m=\frac{y-y_1}{x-x_1} \\\\\frac{1}{4}=\frac{y-(-5)}{x-(-4)}\\\\ \frac{1}{4}=\frac{y+5}{x+4}\\x+4=4y+20\\x-4y=16[/tex]
The equation of parallel line is x - 4y = 16.
Hence, the equation of a line parallel to x - 4y = 36 is x - 4y = 16.
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Given that x is a nonnegative number, a student conjectured that x+4
Which value of x is a counterexample to the student's conjecture?
Responses
A. x=−1/4
(x equals negative one fourth)
B. x=−4
C. x = 1
D. x = 4
The value of x that is a counterexample to the student's conjecture is (a) x = -1/4
How to determine the value of x?From the question, we have the following statement that can be used in our computation:
x = Non-negative number
Student's conjecture:
x + 4 < x²
Using the options, we have:
(a) x = -1/4
x + 4 < x²
-1/4 + 4 < (-1/4)²
3.75 < 1/16 -- false
(b) x = -4
x + 4 < x²
-4 + 4 < (-4)²
0 < 16 -- true
(c) x = 1
x + 4 < x²
1 + 4 < (1)²
5 < 1 -- false
This cannot be used because x is non-negative
(c) x = 4
x + 4 < x²
4 + 4 < (4)²
8 < 16 -- true
The false statements are the counterexamples
Hence, the value of x is (a) x = -1/4
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Complete question
Given that x is a nonnegative number, a student conjectured that x + 4 < x². Which value of x is a counterexample to the student's conjecture?
Responses
A. x=−1/4
B. x=−4
C. x = 1
D. x = 4
Write equivalent fractions for 11/12 and 5/6 using least common denominator.
Type the fractions using a slash ( / ) to separate the numerator and denominator.
11/12 =
5/6 =
a survey showed that a family of four spends an average of $215.60 per day while on vacation. suppose a sample of 64 families of four vacationing at niagara falls resulted in a sample mean of $252.45 per day and a sample standard deviation of $74.50. a. develop a 95% confidence interval estimate of the mean amount spent per day by a family of four visiting niagara falls. 9 pts. b. based on the confidence interval from part (a), does it appear that the population mean amount spent per day by families visiting niagara falls differs from the mean reported by the survey? explain. 1 pt.
The confidence interval is (233.8436; 271.0564).
What is a confidence interval?
The likelihood that a population parameter will fall between a set of values for a specific percentage of the time is referred to as the confidence interval. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.
What is the margin of error?
In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings.
We have,
Sample mean = 252.45
Sample standard deviation = 74.50
n = 64
α = 0.05
By applying the margin of error formula, we get
Margin of Error = tα/2 * s/√n
df = n - 1 = 64 - 1 = 63
t(α/2, df = 63) = 1.998
Margin of Error = 1.998 * 74.50/√64
Margin of Error = 18.6064
The confidence interval = 252.45 ± 18.6064
= (233.8436; 271.0564)
Hence, the confidence interval is (233.8436; 271.0564).
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Determine which set of side measurements could be used to form a right triangle.
square root of 19 comma square root of 35 comma 54
square root of 15 comma 6 comma square root of 51
5, 8, 30
5, 6, 7
Answer:
Square root 19 comma, 5,8,30
Answer:5,8,30
Step-by-step explanation: i took a test
How would you write the work to get the answer to the problem your neighbor pays you $20 every two hours you work you work for eight hours on saturday how much does your neighbor owe you
The neighbour us an amount of $160 for the work that we did for him.
As per the agreement the never will pay 20 dollars were every hour that we work.
We worked for a total of 8 hours on Saturday.
So, according to the unitary method,
Total amount of money owned by the neighbour = number of hours for which we work x the amount received for working per hour.
Total amount of money owned by the neighbour = 8 × 20
Total amount of money owned by the neighbour = 160 dollars.
The total amount of money owned by the neighbour to us is 160 dollars.
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A biology class examined some flowers in a local meadow. They saw 60 flowers, of which 70% were perennials. How many perennial flowers did the students see?
The number of perennials flower from 60 flowers seen by the students with of which 70% were perennials flowers is 42.
What is perennial flower?Perennials Flowers are plants that live more than two years.
To calculate the amount of perennial flowers seen by the students, we use the techniques of percentage.
Using the formula,
P = N(q)/100............. Equation 1Where:
P = Number of perennial flowers seen by the studentsN = Total number of flowers seenq = Percentage of perennials flowers from the total number of flowers seen.From the question,
Given:
N = 60 flowersq = 70%Substitute these values into equation 1
P = (60×70)/100P = 42.Hence, the number of perennials flower is 42.
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How will you solve problems involving equations of circles and coordinates?
NEED ASAP
An equation is a mathematical statement showing the equality of two
opposite variables
How to determine the equation of the circle using coordinates?
The equation of a circle is determined by the function r²=(x-x1)² +(y-y1)²
where :
(x1,y1,) marks the centre of the circlex,y marks the points on the circumference of the circumference of the circler marks the radius of the circlethen, the last thing is to write the equation of the circle and input the values of the coordinates to arrive at your answer,
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