Answers
M'(11, -8), L'(13, -8), K'(13, -10) and J'(11, -10) are the coordinates of the vertices after a reflection over the line x = 4
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The coordinates of the quadrilateral MLJK are M(7, -8), L(9, -8), K(9, -10)
and J(7,-10)
Now we have to find the coordinates of the vertices after a reflection over the line x = 4
We need to find the coordinates of the vertices after reflecting over the line x = 4, we just need to flip the x-coordinate of each vertex across the line.
M(7, -8)--->M'(7+4, -8)
=M'(11, -8)
L(9, -8)--->L'(9+4, -8)
=L'(13, -8)
K(9, -10)--->K'(9+4, -10)
=K'(13, -10)
J(7,-10)--->J'(7+4, -10)
=J'(11, -10)
Hence, M'(11, -8), L'(13, -8), K'(13, -10) and J'(11, -10) are the coordinates of the vertices after a reflection over the line x = 4
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ9
Related Questions
Joanna has six beads that she wants to assemble into a bracelet. Three of the beads have the same color (like red), and the other three have the same color (ike blue). How many different ways can Joanna assemble her bracelet? (Two bracelets are considered identical if one can be rotated and/or reflected to obtain the other.)
Answers
Joanna can assemble her bracelet in 30 ways.
What is permutation?In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set.
here, we have,
to find the number of ways in which the bracelet can be assembled:
It is given that Joanna has 6 beads and of those 6 beads, 2 are of the same color.
The rest 4 are of different colors.
Six beads can be arranged in a circle in 6!/6 ways.
This means that the six beads can be arranged in 5! ways.
Since this is a bracelet, it can be flipped around.
Therefore, it can be arranged in 5!/2 ways.
5!/2
= 5*4*3*2*1/2
= 60
Now, we know that two beads are of the same color. Therefore, we must divide this by two again.
Therefore, we get:
60/2 = 30
The six beads can be arranged in 30 ways to make the bracelet.
Therefore, we have found that Joanna can assemble her bracelet in 30 ways.
Learn more about permutations here:
brainly.com/question/1216161
#SPJ1
[tex]4x2x^{x} -2x^{x} =4[/tex]
Answers
Therefore , the solution of the given problem of expression comes out to be approximately x ≈ 1.6247.
What is an expression?Addition, multiplication, and division in mathematics are required. When combined, they produce the following: A mathematical operator, some data, and an expression A statement of fact contains values, parameters, and mathematical operations including additions, subtractions, multiplications, and divisions. It is possible to contrast and compare various sentences and words.
Here,
First, we can rewrite the equation as:
4x × 2ˣ = 2ˣ + 4
Dividing both sides by 2ˣ , we get:
4x = 1 + 4/2ˣ
Now, let f(x) = 4x - 1 - 4/2ˣ . We want to find the root of f(x) = 0.
Next, we bisect the interval [1,2] by finding the midpoint:
c = (a + b) / 2 = (1 + 2) / 2 = 1.5
Then, we evaluate f(c):
f(c) = 4c - 1 - 4/2ᶜ = 4(1.5) - 1 - 4/[tex]2^{1.5}[/tex] ≈ -0.6982
Since f(c) is negative, the root must be in the interval [c,b]. We repeat the process by setting a = c and finding the new midpoint:
c = (a + b) / 2 = (1.5 + 2) / 2 = 1.75
Then, we evaluate f(c):
f(c) = 4c - 1 - 4/2ᶜ = 4(1.75) - 1 - 4/[tex]2^{1.75}[/tex] ≈ 0.9026
Since f(c) is positive, the root must be in the interval [a, c]. We repeat the process by setting b = c and finding the new midpoint:
c = (a + b) / 2 = (1.5 + 1.75) / 2 = 1.625
Then, we evaluate f(c):
f(c) = 4c - 1 - 4/2ᶜ = 4(1.625) - 1 - 4/[tex]2^{1.625 }[/tex] ≈ 0.0879
Since f(c) is positive, the root must be in the interval [a, c]. We repeat the process by setting b = c and finding the new midpoint:
c = (a + b) / 2 = (1.5 + 1.625) / 2 = 1.5625
Then, we evaluate f(c):
f(c) = 4c - 1 - 4/2ᶜ = 4(1.5625) - 1 - 4/[tex]2^{1.5625}[/tex] ≈ -0.3081
Since f(c) is negative, the root must be in the interval [c, b]. We repeat the process until we reach a desired level of accuracy.
Continuing the process, we find that the solution is approximately
x ≈ 1.6247.
To know more about expressions visit :-
brainly.com/question/14083225
#SPJ1
. ΔABC is a right triangle, with ∠C being the right angle. m∠A = 51°, b = 8, find a.
Answers
In the given right triangle the length of side a is approximately 9.92 units.
Define the right triangle.A right triangle is a variety of triangles with a 90-degree angle (a right angle). The junction of the triangle's two legs, or the sides that meet at a right angle, creates this angle. The hypotenuse, which is always located opposite the right angle, is the third side of a right triangle.
A key characteristic of right triangles is the Pythagorean theorem, which asserts that the square of the hypotenuse is equal to the sum of the squares of the two legs of a right triangle.
We can use the trigonometric ratios of sine, cosine, and tangent to solve for the missing side of a right triangle. Since we are given the measure of one acute angle and the length of the side opposite that angle, we can use the tangent ratio:
tan A = opposite/adjacent
tan 51° = a/8
Multiplying both sides by 8:
a = 8 tan 51°
Using a calculator, we find that:
a ≈ 9.92
Therefore, the length of side a is approximately 9.92 units.
To know more about the right triangle, visit:
https://brainly.com/question/2217700
#SPJ1
4.3 Simplify without calculator: (-5)(7) + 4 x5 (Show all calculations)
Answers
Answer:
Step-by-step explanation:
-15
A basketball player makes 40% of his shots from the free throw line. Suppose that each of his shots can be considered independent and that he throws 3 shots. Let x = the number of shots that he makes. What is the sample space for x?.
Answers
The probability of throwing 3 shots is 100% and the sample space is set of all possible real number.
Probability is the measure of the likelihood that a given event will occur. In this case, the event is a basketball player making a shot from the free throw line.
Since the player has a 40% success rate, we can calculate the probability of him making x number of shots, where x is the number of shots that he throws.
Since the shots are independent of each other, the sample space for x is the set of all possible numbers of shots that he can make, from 0 to the total number of shots (3 in this case).
Therefore, the sample space for x is {0, 1, 2, 3}, which means that the player has a 0% probability of making 0 shots, a 40% probability of making 1 shot, an 80% probability of making 2 shots, and a 100% probability of making all 3 shots
To know more about probability here.
https://brainly.com/question/11234923
#SPJ4
2. $6500 principal earning 2.8% compounded monthly ... after 2 years
Answers
Answer: To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the amount of money after the given time period
P = the principal (starting amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time period (in years)
In this case, the principal is $6500, the annual interest rate is 2.8% (or 0.028 as a decimal), and the interest is compounded monthly (so n = 12). We want to find the amount after 2 years, so t = 2.
Plugging these values into the formula, we get:
A = 6500(1 + 0.028/12)^(12*2)
A ≈ $7,107.08
Therefore, the amount of money after 2 years is approximately $7,107.08.
Step-by-step explanation:
Exercice 1:
Sur 100 étudiants, on considère les ensembles M de ceux qui étudient les mathématiques, E de ceux qui étudient
l'économie et G de ceux qui étudient la gestion. Sur ces 100 étudiants, 55 étudient les mathématiques, 9 les mathéma-
tiques et la gestion, 7 les mathématiques et l'économie, 8 l'économie et la gestion, 6 les mathématiques et la gestion
mais pas l'économie, 80 les mathématiques ou la gestion et 12 l'économie seulement.
(a) Combien d'étudiants suivent les trois matières ?
(b) Combien sont-ils a étudier les mathématiques ?
(c) Combien sont-ils a étudier la gestion?
(d) Combien sont-ils a étudier l'économie?
(e) Combien n'étudient aucune de ces trois matières ?
Answers
Answer:
(a) Pour trouver le nombre d'étudiants qui suivent les trois matières, on peut utiliser la formule suivante:
If Michael earns $150 a week from his part-time job, and 20% of his paycheck is
deducted for taxes, his estimated monthly income should be
Answers
His estimated monthly income should be $480.
What is the answer to this problem?
-4(x-5)+6(x+1)+4x-20+3x+12+-1(x-9)+-x-12+8-x+-2x+7(2x+1)=?
Answers
18x+30
Step-by-step explanation:
O think That's the answer...
Which of the following tables shows a valid probability density function? Select all correct answers. Select all that apply: O x P(X = x) 0 0.37 1 0.06 2 0.01 3 0.56 O x P(X = x) 0 3/8 1 3/8 2 1/4O x P(X = x) 0 1/8 1 1/8 2 1/8 3 3/8 4 1/4O x PX =x) 0 0.03 1 0.01. 2 0,61 3 0.31 4 0.21 O x P(X = x) 0 1/10 1 3/10 2 4/5 3 -1/5
Answers
The tables that show a valid probability density function, are tables 1 to 3
How to determine the tablesFrom the question, we have the following parameters that can be used in our computation:
Table of values
For a table to show a valid probability density function, the following must be true
Sum of P(X = x) = 1
Using the above as a guide, we have the following:
Table 1: Sum = 0.37 + 0.06 + 0.01 + 0.56 = 1
Table 2: Sum = 3/8 + 3/8 + 1/4 = 1
Table 3: Sum = 1/8 + 1/8 + 1/8 + 3/8 + 1/4 = 1
Table 4: Sum = 0.03 + 0.01 + 0.61 + 0.31 + 0.21 = 1.17
Table 5: Sum = 1/10 + 3/10 + 4/5 + 1/5 = 1.4
Hence, the tables are tables 1 to 3
Read more about probability density function
https://brainly.com/question/16038947
#SPJ1
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answers
Using the arithmetic operation the value for x in the equation (x – 7)2 = 36 is obtained as 25.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The given equation is (x – 7)2 = 36.
Use the arithmetic operation of multiplication -
2x - 14 = 36
Collect all the like terms -
2x = 36 + 14
Use the arithmetic operation of addition -
2x = 50
Use the arithmetic operation of division -
x = 50/2
x = 25
Therefore, the value is 25.
To learn more about equation from the given link
https://brainly.com/question/28871326
#SPJ1
Please help me
Thank you
Answers
The solution for x in the given equation (x-c)/2 = d is x = 2d + c.
What is the solution for x in the given equation?
Given the equation in the question;
(x-c)/2 = d
x = ?
To solve for x, cross multiply and simplify.
(x-c)/2 = d
x - c = d × 2
x - c = 2d
Add +c to both sides
x - c + c = 2d + c
x = 2d + c
Therefore, the solution for x in the given equation (x-c)/2 = d is x = 2d + c.
Learn more about equations here:
brainly.com/question/14686792
#SPJ1
HELPPPPP
can someone give me the answer for this
Answers
Answer:
x = -1, y = 1
Step-by-step explanation:
2x - 3y = -5
3x + y = -2
2x - 3y = -5
9x + 3y = -6
11x = -11
x = -1
-3 + y = -2
y = 1
x = -1, y = 1
use transformations of f(x)=[tex]x^{2}[/tex] to graph g(x)=[tex]x^{2}[/tex] -3 select all the transformations that are needed to graph the given function
Select all the transformations that are needed to graph the given function using .
A.
Shift the graph to the left.
B.
Stretch the graph vertically by a factor of .
C.
Shift the graph .
D.
Reflect the graph about the y-axis.
E.
Reflect the graph about the x-axis.
F.
Shift the graph to the right.
G.
Stretch the graph horizontally by a factor of .
H.
Shift the graph .
I.
Shrink the graph horizontally by a factor of .
J.
Shrink the graph vertically by a factor of .
Answers
The transformations that are needed to graph the given function is
Shrink the graph vertically by a factor of 3.
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
f(x) = x²
g(x) = x² - 3
We see that,
f(x) → g(x)
There is a vertical shrink by a factor of 3.
Thus,
There is a shrinking vertically of f(x) by a factor of 3.
Learn more about translation here:
https://brainly.com/question/12463306
#SPJ1
A clothing business finds there is a linear relationship between the number of shirts, x, it can sell and price, p, it can charge per shirt
In particular, historical data shows that 12000 shirts can be sold at a price of $29, while 18000 shirts can be sold at a price of $5
Express the data as ordered pairs:
Determine the average rate of change (slope) between the data values:
Round the value of your slope to three decimal places
Create a linear equation (p(x) = mx + b or p(x) = m(x-x1) +y1 for the price p they can charge for x shirts.
p(x) =
Use your equation to predict the price they can charge for 7500 shirts:
Answers
Based on given question, average rate of change or slope is-0.004 and
the predicted price for 7500 shirts is $47.
Analysis of Linear Relationship between Number of Shirts Sold and PriceThe ordered pairs for the historical data are:
(12000, 29) and (18000, 5)
To find the slope (average rate of change) between these two data points, we can use the formula:
slope = (change in y) / (change in x)
slope = (5 - 29) / (18000 - 12000)
slope = -24 / 6000
slope = -0.004
Rounding to three decimal places, the slope is -0.004.
To find the linear equation, we can use the point-slope form of a line:
y - y1 = m(x - x1)
Using the point (12000, 29) and the slope we just calculated, we get:
p - 29 = -0.004(x - 12000)
Simplifying and solving for p, we get:
p(x) = -0.004x + 77
Therefore, the equation for the price p they can charge for x shirts is p(x) = -0.004x + 77.
To predict the price they can charge for 7500 shirts, we can substitute x = 7500 into the equation:
p(7500) = -0.004(7500) + 77
p(7500) = 47
Therefore, the predicted price for 7500 shirts is $47.
To know more about finding price of items, visit:https://brainly.com/question/8993278
#SPJ1
For many years the only way to test if a person had tuberculosis (TB) required a laboratory procedure that could take up to several weeks to produce a definite result. There are now DNA-based tests to detect TB that can be done in a couple of hours.
We have the following data on a DNA test for TB
· If a person does not have TB then the DNA test always is negative.
· If a person does have TB, then the DNA test will be positive 94% of the time.
Assume that we will use the test in Africa where the rate of incidence of TB is 450 per 100,000.
Has TB
Does not have TB
Row Totals
Test result: negative
Test result: positive
P
Column Totals
Q
100,000
What is the value of P?
· 100,000
· 99,550
· 450
· 423
For many years the only way to test if a person had tuberculosis (TB) required a laboratory procedure that could take up to several weeks to produce a definite result. There are now DNA-based tests to detect TB that can be done in a couple of hours. We have the following data on a DNA test for TB • If a person does not have TB then the DNA test always is negative. • If a person does have TB, then the DNA test will be positive 94% of the time. Assume that we will use the test in Africa where the rate of incidence of TB is 450 per 100,000. Has TB Does not have TB Row Totals Test result: negative Test result: positive P Column Totals Q 100,000 What is the value of P? • 100,000 • 99,550 • 450 • 423
Answers
The number of positive results for all persons with TB will be D. 423
How to calculate the value of PProbability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true
Rate of incidence of TB is 450 per 100,000
Column Totals of "Has TB" = (450 / 100,000) * Grand Total = (450 / 100,000) * 100,000 = 450
If a person does have TB, then the DNA test will be positive 94% of the time.
Therefore, P = Number of positive results for all persons with TB:
= 0.94 * 450
= 423
Learn more about probability on:
https://brainly.com/question/24756209
#SPJ1
What is the answer to this problem?
3x+6+x-2+8(x-3)+-4-4+x+1+-2(x+2)+6+7x+-8x=?
Answers
Answer:
Step-by-step explanation:
Let's simplify the given expression by combining like terms:
3x + 6 + x - 2 + 8(x - 3) - 4 - 4 + x + 1 - 2(x + 2) + 6 + 7x - 8x
First, let's simplify the expression inside the parentheses:
8(x - 3) = 8x - 24
Now we can combine like terms:
3x + x + x + 7x - 8x + 6 - 2 - 4 - 4 + 1 + 6 - 2( x + 2) + 8x - 24
Simplifying further:
6x - 2 - 4 - 4 + 8x - 2(x + 2) - 17
6x + 8x - 2x - 2(2) - 25
12x - 4 - 25
12x - 29
Therefore, the answer to the given expression is 12x - 29.
Answer:
hope this helps!!
Step-by-step explanation:
Identify the solution to the system of linear equations.
y = -3x + 2
y = x - 6
A. (2, -4)
B. (4, -2)
C. (0, 2)
D. (1, -1)
Answers
The system of linear equations is solved by finding x = 2 and y = -4, making the solution (2, -4).
To find the solution to the system of linear equations,
find the values of x and y that satisfy both equations simultaneously.
The equations are,
y = -3x + 2
y = x - 6
To find the solution, set the right-hand sides of both equations equal to each other:
-3x + 2 = x - 6
Now, let's solve for x:
-3x - x = -6 - 2
-4x = -8
x = -8 / -4
x = 2
Now that the value of x, we can find y by substituting x back into one of the equations.
Let's use the second equation:
y = 2 - 6
y = -4
Therefore, the solution to the system of linear equations is equal to option A. (2, -4).
Learn more about system of linear equations here
brainly.com/question/20379472
#SPJ2
Solve for x.
5/25=9/(x+4)
Answers
Answer: x = 41
For x in the equation
5/25=9/(x+4)
5(x+4) =9(25)
5x + 20 = 225
5x = 205
x = 41
Therefore, the value of x for the equation 5/25=9/(x+4) is x = 41
To know solution of Solve for x. 5/25=9/(x+4) visit:
brainly.com/question/30804962
brainly.com/question/15476080
100 POINTS HELP BRAINLIEST A company buys equipment for $625 to help increase sales. What is the shareholder's equity if $450 was put on credit?
A. $450
B. $1075
C. $625
D. $175
Answers
Answer:
Step-by-step explanation:
175
5x2 + 2x − 3) − (2x2 − 3x + 7) expressed as a trinomial
Answers
Answer:
13x-16
Step-by-step explanation:
I am assuming that you mean 5*(2 + 2x − 3) − (2*2 − 3x + 7).
That equals 10x-5+3x-11=13x-16
What is the length of CG??
Answers
The length of CG is approximately 5.4 units.
Describe Triangles?A triangle is a closed geometric figure that is formed by connecting three straight line segments called sides. These sides meet at three points called vertices. Triangles are one of the simplest and most fundamental shapes in geometry and can be found in many natural and man-made objects.
Triangles can be classified into different types based on their sides and angles.
By sides:
Equilateral triangle: all three sides are equal in length.
Isosceles triangle: two sides are equal in length.
Scalene triangle: all three sides are different in length.
By angles:
Acute triangle: all three angles are acute (less than 90 degrees).
Right triangle: one angle is a right angle (exactly 90 degrees).
Obtuse triangle: one angle is an obtuse angle (greater than 90 degrees).
Triangles have many properties and are used in various fields such as architecture, engineering, physics, and mathematics. They are also commonly used in trigonometry to solve problems involving angles and distances.
We can use the property of similar triangles to solve this problem.
First, let's label the intersection point of FG and BC as point H. Also, let's label the length of CG as x.
Since FG is parallel to AC, we can use the property of similar triangles to find that triangles ABF and HBG are similar.
Therefore, we can set up the proportion:
AB/FB = HG/GB
Plugging in the given values, we get:
10/63 = (x + 57)/57
Solving for x, we get:
x = 5.4
Therefore, the length of CG is approximately 5.4 units.
To know more about intersection visit:
https://brainly.com/question/13373561
#SPJ1
The measures of the exterior angles of a hexagon are x°, 4x°, 5x°, 7x°, 9x°, and 10x°. Find the measure of the largest exterior angle.
Answers
The measure of the largest exterior angle of the polygon in discuss is; 100°.
What is the measure of the largest exterior angle of the polygon?It follows from the task content that the measure of the largest exterior angle of the polygon be determined.
Since the sum of all exterior angles of a polygon is equal to 360°;
x° + 4x° + 5x° + 7x° + 9x° + 10x° = 360°
36x° = 360°
x = 10
Therefore, it follows that the measure of the largest exterior angle is; 10x° = 10(10)° = 100°.
Read more on exterior angles of a polygon;
https://brainly.com/question/29166902
#SPJ1
A triangle has two sides of length 7 and 10. What is the largest possible whole-number length for the third side?
Answers
Answer:
The largest possible whole-number length for the third side of a triangle with two sides of length 7 and 10 is 13. This is due to the fact that the two given lengths must be added together, and then subtracted from the third side in order to create a valid triangle. Therefore, the third side must be at least 13 in order to create a triangle.
Solve for x: 48:36::4:x
Answers
Answer:
x=3
Step-by-step explanation:
the answer is 3 because 3*12=36 and 4*12=48
Suppose ABC is a right triangle with sides a, b, and c and right angle at C. Use the Pythagorean theorem to find the unknown side length. Then find the values of the six trigonometric functions for angle B. Rationalize the denominators when applicable.
a=8, b=15
Answers
The six trigonometric functions' values for angle B in this right triangle are as follows: Tan(B) = 8/15 CSC(B) = 17/8 Sin(B) = 8/17 Cos(B) = 15/17 Tan(B) = 8/15 (rationalized denominator)
cot(B) = 15/8 sec(B) = 17/15.
The length of the unknown side, which in this case is the hypotenuse c, can be determined using the Pythagorean theorem:[tex]c2 equals a2 + b2; c2 equals 82 + 152; c2 equals 64 + 225^2 = 289 \sc = √289 \sc = 17[/tex]
Thus, the hypotenuse's length is 17.
We must first get the measure of angle B before we can determine the values of the six trigonometric functions for that angle. Since angle C is a right angle and the total of the angles in a triangle is 180 degrees, we can calculate angle B's measure as follows:
angle B is equal to 90 times angle A, or 90 times angle B.
For now, since we lack sufficient data to estimate the size of angle A, angle B will be specified in terms of an unknowable angle. We are still able to calculate the six trigonometric functions for angle B using the ratios of the triangle's side lengths.
B = opposite/hypotenuse = a/c = 8/17;
B = adjacent/hypotenuse = b/c = 15/17;
B = opposite/adjacent = a/b = 8/15;
B = hypotenuse/opposite = c/a = 17/8;
B = cos(B) = (rationalized denominator)
Hypotenuse/nearby = c/b = 17/15; adjacent/opposite = b/a = 15/8; sec(B) = c/b = 17/15; cot(B) = b/a = 15/8.
For angle B in this right triangle, the values of the six trigonometric functions are as follows:
sin(B) = 8/17
cos(B) = 15/17
tan(B) = 8/15
csc(B) = 17/8 (rationalized denominator)
sec(B) = 17/15
cot(B) = 15/8
To know more about Trigonometric Functions visit:
brainly.com/question/15706158
#SPJ1
Adam is planning
a rectangular patio that will have an area of
16x2 1 20x square feet. The length of the patio
will be x 1 5 feet. Write an expression to
represent the width of the patio.
Answers
Answer:
The width of the patio is 15 feet
Step-by-step explanation:
We can start by using the formula for the area of a rectangle:
Area = length x width
In this case, we know that the area of the patio is given by:
16x^2 + 20x square feet
And we also know that the length of the patio is x + 5 feet. So we can substitute these values into the formula to get:
16x^2 + 20x = (x + 5) x width
Simplifying the right-hand side by multiplying x + 5 by width, we get:
16x^2 + 20x = width x^2 + 5x
To solve for the width, we can move all the terms with width to the left-hand side and all the other terms to the right-hand side:
width x^2 - 16x^2 + 20x - 5x = 0
Simplifying the left-hand side by combining like terms, we get:
width x^2 - 16x^2 + 15x = 0
Factoring out x, we get:
x (width x - 16x + 15) = 0
Now we can solve for the width by setting each factor equal to zero and solving for x:
x = 0 or width x - 16x + 15 = 0
Since the length and width of the patio must be positive values, we can disregard the solution x = 0. So we are left with:
width x - 16x + 15 = 0
We can factor this quadratic equation by finding two numbers whose product is 15 and whose sum is -16. These numbers are -1 and -15, so we can write:
(width x - 1)(x - 15) = 0
Setting each factor equal to zero and solving for x, we get:
width x - 1 = 0 or x - 15 = 0
width x = 1 or x = 15
Since the length of the patio is x + 5, which is 20 feet, we know that x = 15 is the correct solution. So we can substitute x = 15 into the expression for the width:
width x = 1, x = 15, so we choose x = 15
width x - 16x + 15 = (15) x - (16)(15) + 15 = 15 feet
Therefore, the width of the patio is 15 feet.
A music industry researcher wants to estimate, with a 95% confidence level, the proportion of young urban people (ages 21 to 35 years) who go to at least 3 concerts a year. Previous studies show that 42% of those people (21 to 35 year olds) interviewed go to at least 3 concerts a year. The researcher wants to be accurate within 1% of the true proportion. Find the minimum sample size necessary.
Answers
To find the minimum sample size necessary to estimate the proportion of young urban people who go to at least 3 concerts a year with a 95% confidence level and an accuracy of within 1%, we can use the formula:
n = (z^2 * p * q) / E^2
where:
n is the minimum sample size
z is the z-score for the confidence level (in this case, 1.96 for a 95% confidence level)
p is the estimated proportion from previous studies (42% or 0.42)
q is 1 - p (the complement of p)
E is the maximum error or accuracy (1% or 0.01)
Plugging in the values, we get:
n = (1.96^2 * 0.42 * 0.58) / 0.01^2
n = 1.96^2 * 0.42 * 0.58 * 10000
n = 1092.33
Rounding up to the nearest whole number, the minimum sample size necessary is 1093.
Therefore, the researcher needs a minimum sample size of 1093 young urban people (ages 21 to 35 years) to estimate the proportion of those who go to at least 3 concerts a year with a 95% confidence level and an accuracy of within 1%.
If f(x)=3x^2+1 and g(x)=1-x, what is the value of (f-g)(2)?
Answers
Answer:
14
Step-by-step explanation:
To find the value of (f-g)(2), we first need to compute the function (f-g), which is defined as the difference between f(x) and g(x), and then evaluate it at x=2.
So, (f-g)(x) = f(x) - g(x)
Substituting the given functions, we get:
(f-g)(x) = (3x^2 + 1) - (1-x)
(f-g)(x) = 3x^2 + x
Now, to find (f-g)(2), we substitute x=2 into the expression we just obtained:
(f-g)(2) = 3(2)^2 + 2
(f-g)(2) = 3(4) + 2
(f-g)(2) = 12 + 2
(f-g)(2) = 14
Therefore, the value of (f-g)(2) is [14.]
Can someone please answer these questions for me i cant figure them out!! (brainliest promised)
What is the fractional equivalent of the repeating decimal n = 0.1515... ?
Answer the questions to find out.
1. How many repeating digits does the number represented by n have? (2 points)
2. You need to multiply n by a power of 10 to help you find the fraction. Decide on the power of 10 to multiply by, and tell how you identified that number. (2 points)
3. Write an equation where the left side is your power of 10 times n and the right side is the result of multiplying 0.1515... by that power. (2 points)
4. Write the original equation, n = 0.1515... underneath your equation from question 3. Then subtract the equations. Show your work. (2 points)
5. Write n as a fraction in simplest form. Show your work. (2 points)
Answers
The fractional equivalent of the repeating decimal is 15/99
What does division of fractions mean?
A fraction is divided into additional equal pieces when it is divided into fractions. For instance, if you had three-fourths of a pizza remaining and divided each slice into two pieces, you would have received six slices, which would be equivalent to six-eighths of the entire pizza.
n = 0.1515...-------(1)
multiply n by 100 =10²
The reason we multiply x by 100 is because 0.1515... has 2 repeating digits and 100 has two zeros.
100n=15.15......--------(2)
Subtract (1) from (2)
100n=15.15...
n = 0.1515....
___________
99n=15
=> n=15/99
The fractional equivalent of the repeating decimal is 15/99
To learn more about the division of fractions from the given link
https://brainly.com/question/1622425
#SPJ1
