The total number of students calculated with the method called simplification and who are playing volleyball is 206.
How simplification method work?
In mathematics, the simplification method is used for the equation formation for the problem statements. And it also convert the complicated expression into simpler one to make the calculation easy.
According to the question, the given survey data for the playing volleyball is written below and it is solved by the simplification method:
survey of students: 36
play volleyball: 17
As per question, the simplification expression for the given statement which state that, if the survey of 648 students how many students play volleyball?
Therefore, the required simplified expression can be written as:
Required expression: 648÷36= 18
Now, playing volleyball =18×17=206 students play volleyball
Hence, the total number of students calculated with the method called simplification who are playing volleyball is 206.
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Find the value of f (8).
Answer:
4
Step-by-step explanation:
first we go over where 8 is on the x-axis then we move up to the line, and look at the corresponding y value, which is 4
if researchers are 96% confident that they are correct, what is the probability they are wrong
Based on the fact that the researchers are 96% confident that they are correct, then the probability that they are actually wrong is 4%.
How to find probability?If we are to believe the assertions of the researchers that they are 96% certain of them being correct, then the probability that they are wrong can be found by the formula:
= 1 - Percentage certainty
Solving for that probability of being wrong then gives:
= 1 - 96%
= 4%
It is worthy of note that this probability of being wrong is based on their estimates and so there is a chance that the probability of being wrong is 4%.
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Find the equation of the line passing through the points (1.-2) and (-2,7). Write the equation in slope-intercept form. A) y = 3x + 13 B) y = 3x - 5 C) y = -3x -2 D) y = -3x + 1
The equation is of the form y=mx+b, where m = slope and b = y-interset. Therefore, find m and b:
For m
[tex]m=\frac{y2-y1}{x2-x1}=\frac{7-(-2)}{-2-1}=\frac{7+2}{-3}=\frac{9}{-3}=-3[/tex]For b
[tex]\begin{gathered} y=mx+b \\ -2=-3(1)+b \\ -2=-3+b \\ -2+3=-3+b+3 \\ b=1 \end{gathered}[/tex]So, the equation is:
[tex]y=-3x+1[/tex]Answer: D.
Find the equation of a line perpendicular to y=-3x - 4 that contains the point (3, 0). Write the equation in slope-
intercept form.
Answer:
y = 1/3 x + 3
Step-by-step explanation:
1) when finding a perpendicular line, you take the slope and use the reciprocal (you flip it) and change the sign (from negative to positive or positive to negative)
-3 ---> 1/3
2) plug in the slope into a new equation
y=1/3 x + b
3) plug in the points
3= 1/3 (0) + b
b=3
4) rewrite the equation
y=1/3 x + 3
Use the figure to answer the following question.
If AC||DE, which of the following justifies ΔABC ~ ΔDBE?
A. Definition of Similar Triangles
B. SAS Similarity Theorem
C. SSS Similarity Theorem
D. AA Similarity Postulate
The statement that justifies the triangles' similarity is (c) SSS similarity theorem
How to determine the statement that justifies the triangles?The triangles are given as
Triangle ABC and Triangle DBE
From the figure, we can see that the corresponding vertical lines of either triangle are parallel (but not equal)
This means that, the triangles are similar triangles
This is so because the other two sides of the smaller triangle lie completely on the bigger triangle
As a general rule, the corresponding sides of similar triangles are in proportions
So, we can say that the corresponding side lengths of the triangles are similar
The statement that justifies this is the Side-Side-Side similarity theorem
Hence, the true statement is (c) SSS similarity theorem
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Consider the incomplete paragraph proof.
Given: P is a point on the perpendicular bisector, l, of MN.
Prove: PM = PN
Line l is a perpendicular bisector of line segment M N. It intersects line segment M N at point Q. Line l also contains point P.
Because of the unique line postulate, we can draw unique line segment PM. Using the definition of reflection, PM can be reflected over line l. By the definition of reflection, point P is the image of itself and point N is the image of ________. Because reflections preserve length, PM = PN.
Given that P is a point on the perpendicular bisector, l, of MN, we have proved that PM = PN because By the definition of reflection, point P is the image of itself and point N is the image of N.
How to Interpret the Perpendicular Bisector?We are given :
P is a point on the perpendicular bisector, l, of MN.
Now, we want to prove that PM = PN
A Reflection is a transformation in which the figure is the mirror image of the other. Every point is a mirror reflection of itself .
By the definition of reflection, we can deduce that point P is the image of itself , and point N is the image of M .
The line l acts as a Line of symmetry or axis of reflection.
Now, in transformations, we know that reflections preserve length and as a result, PM = PN.
Therefore, we will conclude that point N is the image of M .
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Answer: Point M
Step-by-step explanation:edge 2023
The histogram shows the distribution of hurricanes that have hit a country from 1851 through 2015, where 1 is the weakest level and 5 is the strongest level.
(a) Find the mean, variance, and standard deviation of the probability distribution.
(b) Interpret the results.
Hurricanes
1
2
3
4
5
0.0
0.1
0.2
0.3
0.4
0.5
Category
Probability
0.419
0.276
0.225
0.068
0.012
The mean = 0.2, variance = 0.03226 and Standard deviation = 0.1796
What is standard deviation?A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given:
level x
1 0.419
2 0.276
3 0.225
4 0.068
5 0.012
So, mean = (0.419+ 0.276 + 0.225+ 0.068 + 0.012)/5
mean = 0.2
level x (x- mean) (x- mean)²
1 0.419 0.219 0.0479
2 0.276 0.076 0.0057
3 0.225 0.025 0.000625
4 0.068 -0.268 0 .0718
5 0.012 -0.188 0.0353
So, variance = 0.032265
standard deviation = √(variance)
Standard deviation = √(0.032265)
Standard deviation = 0.1796
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c(x)=(x-5)^3, what is c(3)
Answer:
-8
Step-by-step explanation:
You want the value of c(3) when c(x) = (x -5)^3.
Function valueThe value of a function is found by substituting the argument for the variable and doing the arithmetic.
c(x) = (x -5)^3
c(3) = (3 -5)^3 = (-2)^3
c(3) = -8
2,175/12 what is the answer
Answer: 2,175 divided by 12 will give you 181.25.
Consider a population that begins growing exponentially at a base rate of 4.3% per year and then follows a logistic growth pattern. If the carrying capacity is 62 million, find the actual fractional growth when the population is at 10 million, 30 million, and 50 million.
The actual fraction of growth-
a) population = 10 million; growth rate = 559/155.
b) population = 30 million; growth rate = 344/155
c) population = 50 million; growth rate = 126/155
What is defined as the exponential population growth?In exponential growth, the per capita (per person) growth rate of a population remains constant regardless of population size, causing the population to grow faster and faster as it grows larger.The logistic growth rate of a population decreases as population size approaches a maximum imposition by limited resources available in the environment, recognised as the carrying capacity (K).The base growth rate = 4.3%.
The current carrying capacity = 62 million.
The actual fractional growth for the given values are-
growth rate = r * (1 - population/carrying capacity)
a) population = 10 million,
Put the values;
growth rate = 4.3 × (1 - 10/62)
growth rate = 559/155 is the actual fraction of growth.
b) population = 30 million,
Put the values;
growth rate = 4.3 × (1 - 30/62)
growth rate = 344/155 is the actual fraction of growth.
c) population = 50 million,
Put the values;
growth rate = 4.3 × (1 - 50/62)
growth rate = 126/155 is the actual fraction of growth.
Thus, the actual fraction of growth is estimated.
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Write a polynomial f (x) that satisfies the given conditions.
Polynomial of lowest degree with zeros of -4 (multiplicity 3), 3 (multiplicity 1), and with f (0) =960.
f (x)=
Lowest degree polynomial with f(0) = 960 with zeros of -4 (multiplicity 3), 3(multiplicity 1). The polynomial is f(x)=-5(x+4)³(x-3).
Given that,
Lowest degree polynomial with f(0) = 960 with zeros of -4 (multiplicity 3), 3(multiplicity 1)
We have to find the polynomial of f(x) which satisfy the conditions.
Here,
We have the zeros of the polynomial are -4 (multiplicity 3), 3(multiplicity 1)
Which we can write as -4,-4,-4,3 are the zeros.
Then we can write the polynomial as
f(x)=ω(x+4)³(x-3)
We have to first find the value of ω.
So,
We have f(0)=960
ω(0+4)³(0-3)=960
ω(4)³(-3)=960
64ω(-3)=960
-192ω=960
ω=960/-192
ω=-5
We got the ω as -5.
The polynomial f(x)=-5(x+4)³(x-3)
Therefore, the polynomial is f(x)=-5(x+4)³(x-3).
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Find P(A/B), in S = {10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80), A = 40 or less in S and B = even in S. Use fraction form for the probability
Answer:
P(A|B) = 1/2
Step-by-step explanation:
Sample space for B = {10, 20, 30, 40, 50, 60, 70, 80}
where B is even
Total number of elements in sample space = 8
P(A|B) = Probability of a number being 40 or less from the sample space of 8
Sample space for A|B = {10, 20, 30, 40}
So out of a possible 8 elements in the sample space for B only 4 elements can be chosen for the sample space of A
So P(A|B) = 4/8 = 1/2
suppose you are35 years old and would like to retire at age65 . Furthermore, you would like to have a retirement fund from which you can draw an income of $150000 per yearforever! How much would you need to deposit each month to do this? Assume a constant APR of8 % and that the compounding and payment periods are the same.
Answer:
$1258.09
Step-by-step explanation:
You want the monthly annuity payment that will let you withdraw $150,000 per year forever from an account earning 8% after 30 years.
Account balanceIn order to withdraw an amount "forever," the withdrawal amount must be equal to the interest earned by the account.
I = Prt
150,000 = P(0.08)(1)
P = 150,000/0.08 = 1,875,000
Annuity paymentThe value of an ordinary annuity is given by the formula ...
A = P(12/r)((1 +r/12)^(12t) -1) . . . . . where P is the monthly payment, and r is the annual interest rate earned over a period of t years.
Using the values we know, we can find P:
1875000 = P(12/0.08)((1 +0.08/12)^(12·30) -1) = 1490.359449P
P ≈ 1258.09
You would need to deposit $1258.09 each month.
__
Additional comment
The formulas used here assume that the deposits and withdrawals occur at the end of the month.
How can you use the Distributive Property to find 11 × 5?
Answer:
You cant use the distributive property because it is when the equation is like this: ax(b+c) so if it was 11x(5+0) you would multiply the 5 by 11 by itself and multiply 0 with 11 then you add them and get 55. I hope that helps :)
Step-by-step explanation:
75+25x=300 situation
Can you please solve this.
Answer:
x^8
Step-by-step explanation:
You want to simplify x^10/x^2.
Rule of exponentsThe applicable rule of exponents is ...
(a^b)/(a^c) = a^(b-c)
ApplicationUsing this rule on the given expression, we find ...
(x^10)/(x^2) = x^(10-2) = x^8
__
Additional comment
An exponent can be considered to be an indicator of repeated multiplication. That is, it tells how many times the base is a factor in the product. Knowing this, you can use the usual rules of division to cancel common factors:
[tex]\dfrac{x^{10}}{x^2}=\dfrac{x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x}{x\cdot x}=x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x=x^8[/tex]
Find an irrational number between 1/12 and 1/10
The irrational numbers lying between 1/12 and 1/10 are -
0.456258824......0.32547965.......0.21448663324........What is meant by the irrational number?Irrational numbers are real numbers that can't be represented by a ratio.Irrational numbers are real numbers that can't be expressed as a fraction, p/q, in which p and q are integers. The numerator q does not equal zero (q ≠ 0). Furthermore, an irrational number's decimal expansion is not terminating and neither repeating.For the given question;
The number are given as 1/12 and 1/10
Write both number in its decimal form.
1/12 = 0.8333333
1/10 = 0.1
Thus, write number which lies between these two.
1/12 = 0.8333333
0.456258824......
0.32547965.......
0.21448663324........
1/10 = 0.1
The dotted parts shows that the number is nether terminating nor repeating.
Thus, the irrational numbers lying between 1/12 and 1/10 are found.
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Simplify the fraction
36
84
as much as possible.
36
84
3
7
5
12
Answer:
3/7
Hope this helps!
Have a good day :).
help with the first one ?
The solution of the equation is x = 5.
How to solve equation?The equation is written as follows:
- 94 = -2 (8x + 7)
The variable to be found as variable x.
A variable is a number represented with a letter in an equation.
Hence,
- 94 = -2 (8x + 7)
open the bracket on the right side of the equation
-94 = - 16x - 14
add 14 to both sides of the equation
-94 = - 16x - 14
-94 + 14 = - 16x - 14 + 14
-80 = - 16x
divide both sides by -16
x = -80 / -16
x = 5
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terrance plants a garden that has 8 rows of flowers, with 28 flowers in each row. how many flowers did terance plant
Answer:
224
Step-by-step explanation:
The answer is 224 since 8 x 28 = 224
Answer: Terrence planted 224 flowers in total
Step-by-step explanation: 8x28
The graph of a linear function is a horizontal line. When x = -3, y = 4. What is the equation for
this linear function? Explain.
For the graph of a linear function x=-3 and y=4 is horizontal line , the equation for this linear function is y = 0(x) +4.
As given in the question,
Graph of a required linear function is a horizontal line.
Given :
When x=-3 y=4
Two coordinates of the required linear function are :
(x₁ ,y₁) = (-3, 4)
(x₂, y₂) = ( 0,4)
Equation of the linear function :
(y -y₁) /(x-x₁) = (y₂ -y₁) / (x₂- x₁)
⇒( y-4)/(x+3) =(4-4)/(0+3)
⇒ (y-4)/(x+3) = 0/3
⇒ y = 0(x) +4
Therefore, for the graph of a linear function x=-3 and y=4 is horizontal line , the equation for this linear function is y = 0(x) +4.
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Please help I’ll mark you as brainliest if correct!!
Time can be used to quantify, contrast, or even rank the length of events or the gaps between them. To complete the cooking at 2:00 PM, George needs to start his cooking at 12:30 PM.
What is meant by Time?Time can be defined in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present and into the future. The duration of events or the gaps between them can be calculated, compared, or even ordered utilizing time.
Given time needed for each meals are;
Turkey = 70 min
Pumpkin pie = 17 min
Rolls = 30 sec
coffee = 45 sec
Total time = 87 min 75 sec
= 1 hour 27min 75 sec
So in order to complete the cooking at 2:00 PM, George needs to start his cooking at 12:30 PM.
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Which figure is a line?
Answer:
Bottom left
Step-by-step explanation:
The figure that looks like <-------------------------> is a line
Top left *------------------------* is a segment
Bottom right is a ray *---------------->
Top right is a * point or dot
I hope this helps!
Find the mode or modes (if any).5, 9, 96, 3, 2, 8, 79, 1, 4, 16
Given:
5, 9, 96, 3, 2, 8, 79, 1, 4, 16
To determine the mode based on the given data set, we note first that mode is the number in a data set that occurs most frequently. Since each value occurs only once, there is no mode of this data set.
Therefore, the answer is: no mode or none.
please help me solve this
Answer:
bottom right
Step-by-step explanation:
bottom right
Please help me with this!!!
Answer:
Is this correct??
if yes reply
Mary runs 4 laps around the track inb8 minutes. Paul runs 12 laps in 18 minutes. Who ran faster
Answer:
Step-by-step explanation:
thanks
Parul ran the fastest.
For Mary,
4/8 = x/1
4/8 or 1/2 laps per minute.
x= 0.5
For Paul,
12/18 = y/1
12/18 or 2/3 laps per minute.
y=0.666
Hence, Parul ran faster.
The SI unit of speed is m/s, and speed is defined as the ratio of distance to time.
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What are the zeros of the polynomial function f(x) = x3 + 9x2 + 20x? (5 points)
0, −5, −4
0, −5, 4
0, 5, −4
0, 5, 4
The zeros of the function f(x) = x³ + 9x² + 20x is :
0, 5 ,4
Explanation :Steps to solve quadratic equation:
Put all of the terms on one side of the equal sign and zero on the other.Factor.Set each factor to a value of zero.Each of these equations must be solved.Because they are the values of x for which f(x) = 0, the solutions of the quadratic equation ax² + bx + c = 0 correspond to the roots of the function f(x) = ax² + bx + c.Check your answer by plugging it into the original equation.
Given function,
f(x) = x³ + 9x² +20x
take x common from f(x),
=> x(x² + x - 20) = 0
=> x(x² + 5x + 4x + 20) = 0
=> x( x + 5 ) + 4 ( x +5 ) = 0
=> (x + 5) ( x + 4 ) = 0
=> x -5 = 0 or x -4 = 0
=> x = 5 and x = 4 .
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write an equation of the line in point-slope form that passes through the given points in the table. Then write the equation in slope-intercept form.
an equation of the line in point-slope form is
An equation of the line in point-slope form is y = 6x + 50.
Define point slope form.y = y₁ = m(x -x₁) is the equation of a straight line, where m is the slope and (x₁, y₁) are the coordinates at a given point on the line (see slope-intercept form). When you know the slope and another point on the line, the point-slope form of a linear equation is most helpful for locating a point on a line. When two other points are known, it can also be used to locate a point on a line.
Given,
y₂ = 200
y₁ = 230
x₂ = 30
x₁ = 25
Slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Slope = [tex]\frac{230-200}{30-25}[/tex]
Slope = [tex]\frac{30}{5}[/tex]
Slope = 6
Equation:
y - y₁ = m(x - x₁)
y - 200 = 6(x - 25)
y - 200 = 6x - 150
y = 6x + 50
An equation of the line in point-slope form is y = 6x + 50.
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The mark scored in a test by ten pupils are as follows: 15, 14, 15, 13, 16, 16, 17, 13, 16, 17. Find the modal mark?
The modal mark is 16.because as we can see there are two 15, two 13,one 14, two 17 and three 16.