Answers
The statements that is true is option C FG ⊥ HB and FG ║ DE, that is FG is perpendicular to HB and parallel to DE.
What are perpendicular and parallel lines?Geometry's use of parallel and perpendicular lines is crucial, and their distinctive qualities make it simple to distinguish between them. If two lines are in the same plane, are spaced equally apart, and never cross one another, they are said to be parallel. Perpendicular lines are those that cross at an angle of 90 degrees. Two straight lines are said to be parallel if they are located in the same plane and never cross one another. On the other hand, two lines are said to be perpendicular when they cross each other at a 90° angle.
From the given figure we observe that, the angle between the segments FG and HB is 90 degrees thus,
FG ⊥ HB.
Also, DE ⊥ HB, thus the segments FG ║ DE.
Hence, the statements that is true is option C FG ⊥ HB and FG ║ DE, that is FG is perpendicular to HB and parallel to DE.
Learn more about perpendicular lines here:
https://brainly.com/question/28558890
#SPJ1
Related Questions
solve y = -1/4 x and x + 2y = 4
Answers
Answer:
8
Step-by-step explanation:
Not sure this is correct
substitute y in the second equation
X+2(-1/4x)=4
X-2/4x=4
4/4x-2/4x=2/4x
2/4x=4
4 /2/4
4•4/2
16/2
8
an inner city revitalization zone is a rectangle that is twice as long as it is wide. the width of the region is growing at a rate of 31 m per year at a time when the region is 450 m wide. how fast is the area changing at that point in time?
Answers
The area of the rectangle is increasing at a rate of 27,900,000 meters³ per year when the width of the region is 450 meters.
The inner-city revitalization region is a rectangle that is twice as long as it is wide. At a time when the area is 450 meters wide, the width of the region is increasing at a rate of 31 meters per year. The aim is to find out how quickly the area is changing at this point in time. The area of the rectangle is given by the formula,
Area = length × width
Given that the width of the rectangle is increasing at a rate of 31 meters per year. Let's say the width of the rectangle is w meters, and the rate of change in width is dw/dt meters per year. Then, we can say, dw/dt = 31 meters per year
Width of the rectangle is w meters
Length of the rectangle is twice the width, or 2w meters
Area of the rectangle is given by the formula, A = lw= 2w × w= 2w²
Now, we need to find dA/dt, the rate at which the area of the rectangle is changing with respect to time (t).We can find it using the formula,
dA/dt = dA/dw × dw/dt
dA/dw = 4w (differentiate 2w² with respect to w)
dw/dt = 31 meters per yeard
A/dt = dA/dw × dw/dt= 4w × 31= 124w meters² per year
From the given information, the width of the rectangle is 450 meters wide. So, the width is w = 450 meters.
dA/dt = 124w meters² per year
= 124 × 450 meters² per year
= 27,900,000 meters³ per year
Which is the increasing rate of the rectangle.
To know more about area of the rectangle: https://brainly.com/question/23027949
#SPJ11
Data was collected on the amount of time that a random sample of 8 students spent studying for a test and the grades they earned on the test. a scatter plot and line of fit were created for the data. scatter plot titled students' data, with points plotted at 1 comma 60, 2 comma 60, 2 comma 70, 2 comma 80, 3 comma 80, 3 comma 90, 4 comma 95, and 4 comma 100, and a line of fit drawn passing through the points 0 comma 40 and 2 comma 70. find the y-intercept of the line of fit and explain its meaning in the context of the data.a. 30; for each additional hour a student studies, their grade is predicted to increase by 30% on the testb. 15; for each additional hour a student studies, their grade is predicted to increase by 15% on the test c. 70; a student who studies for 0 hours is predicted to earn 70% on the test d. 40; a student who studies for 0 hours is predicted to earn 40% on the test
Answers
Answer: The y-intercept of the line of fit can be found by looking at the point where the line crosses the y-axis. From the given information, we know that the line passes through the points (0, 40) and (2, 70). To find the equation of the line, we can use the slope-intercept form:
y = mx + b
where m is the slope and b is the y-intercept. We can find the slope of the line by using the two points:
m = (y2 - y1) / (x2 - x1)
m = (70 - 40) / (2 - 0)
m = 30
So the equation of the line is:
y = 30x + b
To find the y-intercept, we can plug in one of the points and solve for b. Let's use the point (0, 40):
40 = 30(0) + b
b = 40
Therefore, the y-intercept of the line of fit is 40. In the context of the data, this means that a student who did not study at all (0 hours) is predicted to earn a grade of 40 on the test. However, it's important to note that this prediction is based on the data collected from the sample of 8 students and the line of fit may not accurately predict the grades of all students who did not study.
Your welcome.
if the actual length is 28.3m and the scale is 1cm to 2m, what is the length on drawing
Answers
The length on drawing with the given scale is 14.15 cm.
How to determine the length on drawingUsing the given scale of 1cm to 2m, we can set up the following proportion to find the length on the drawing:
1 cm : 2 m = x cm : 28.3 m
where x is the length on the drawing that we want to find.
To solve for x, we can cross-multiply and simplify:
1 cm * 28.3 m = 2 m * x cm
Evaluate the products and remove the units
28.3 = 2x
Divide both sides by 2 to solve for x
x = 28.3 / 2
Evaluate
x = 14.15
Therefore, the length on the drawing is 14.15 cm.
Read more about scale factors at
https://brainly.com/question/29229124
#SPJ1
Droughts in a region are categorized as severe and moderate based on the last 60 years of record. The number of severe and moderate droughts are noted as 6 and 16, respectively. The occurrence of each type of droughts is assumed to be statistically independent and follows a distribution, λx e−λ x! where λ is the expected number of droughts over a period. (a) What is the probability that there will be exactly four droughts in the region over the next decade? (Ans 0.193). (b) Assuming that exactly one drought actually occurred in 2 years, what is the probability that it will be a severe drought? (Ans 0.164). (c) Assuming that exactly three droughts actually occurred in 5 years, what is the probability that all will be moderate droughts?
Answers
a) The probability that there will be exactly four droughts in the region over the next decade is approximately 0.193.
b) The probability that it will be a severe drought given that exactly one drought actually occurred in 2 years is approximately 0.164.
c) The probability that all three droughts that actually occurred in 5 years will be moderate is 0.016.
To determine the probability of there being exactly four droughts in the region over the next decade, the expected value of droughts over a decade must first be calculated. λ, the expected number of droughts over a period, can be calculated using the formula:λ = (number of droughts in the last 60 years)/(60 years)λ = (6+16)/(60)λ = 0.367
Therefore, the expected number of droughts in the region over the next decade is 0.367 x 10 = 3.67.Using the Poisson distribution formula, the probability of there being exactly four droughts in the region over the next decade can be calculated as:P(4) = (e^-3.67)(3.67^4)/(4!)P(4) ≈ 0.193
Therefore, the probability that there will be exactly four droughts in the region over the next decade is approximately 0.193.
Assuming that exactly one drought actually occurred in 2 years, the probability that it will be a severe drought can be calculated using Bayes' theorem:P(severe | 1) = P(1 | severe)P(severe) / P(1)First, P(1) must be calculated:P(1) = P(1 | severe)P(severe) + P(1 | moderate)P(moderate)P(1 | severe) = e^-λ(λ^1) / 1! = e^-0.367(0.367^1) / 1! ≈ 0.312P(1 | moderate) = e^-λ(λ^1) / 1! = e^-0.367(0.367^1) / 1! ≈ 0.592P(moderate) = 16 / 60 = 0.267P(severe) = 6 / 60 = 0.1P(1) ≈ 0.312(0.1) + 0.592(0.267) ≈ 0.279Next, P(severe | 1) can be calculated:P(severe | 1) = P(1 | severe)P(severe) / P(1)P(severe | 1) ≈ (0.312)(0.1) / 0.279 ≈ 0.164
Therefore, the probability that it will be a severe drought given that exactly one drought actually occurred in 2 years is approximately 0.164.
Assuming that exactly three droughts actually occurred in 5 years, the probability that all will be moderate droughts can be calculated using the binomial distribution formula:P(3 moderate) = (n choose k)(p^k)(1-p)^(n-k)where n = 3, k = 3, and p = 16 / 60 = 0.267(n choose k) = (n! / k!(n-k)!) = (3! / 3!(3-3)!) = 1P(3 moderate) = (1)(0.267^3)(1-0.267)^(3-3) = 0.016
Therefore, the probability that all three droughts that actually occurred in 5 years will be moderate is 0.016.
Learn more about Probability
brainly.com/question/30034780
#SPJ11
If y =27 when x=9, determine y when x=11
Answers
Answer:
[tex]The \: problem \: probably \\ \: assumes \: direct \: variation \: \\ \\
y \: = \: k \: x \\ \\
IF \: so, \: then \: plug \: in \: the \: \\ values \: and solve \: for \: k \\ \\
27 \: = \: k(8) \\ \\
k \: = \: \frac{27}{8}
\\ \\
y \: = \: ( \frac{27}{8} )x. \\ \\ Now \: let \: x \: = \: 11 \\ \\
y \: = \: ( \frac{27}{8} )11 = \\ \\ \frac{27(11)}{8} \\ \\ = 37.125 = \\ \\ \frac{371}{8y} \\ \\
y \: = \frac{371}{8}
[/tex]
hich of the following is an accurate definition of a type ii error? group of answer choices rejecting a false null hypothesis rejecting a true null hypothesis failing to reject a false null hypothesis failing to reject a true null hypothesis
Answers
The accurate definition of a type II error is failing to reject a true null hypothesis.
What is a Type II error?Type II error is known as a statistical term that happens when a null hypothesis is not rejected when it should have been rejected. Type II error can occur in a study when the researcher has failed to detect a real difference between the research subject group and the comparison group. It's often called the "false negative" because it incorrectly concludes that there is no difference when there actually is a difference.
Types of Errors in StatisticsType I Error - It is known as a type I error when a researcher rejects a null hypothesis when it is true. Type I errors are often called "false positives."
Type II Error - Type II error is known as a statistical term that happens when a null hypothesis is not rejected when it should have been rejected. Type II error can occur in a study when the researcher has failed to detect a real difference between the research subject group and the comparison group. It's often called the "false negative" because it incorrectly concludes that there is no difference when there actually is a difference.
To know more about the "null hypothesis": https://brainly.com/question/15980493
#SPJ11
Determine the values of p such that the rank of A=[[1,1,-1,0],[4,4,-3,1],[p,2,2,2],[9,9,p,3]] is 3 .
Answers
The values of p are -3 or 3 such that the rank of A is 3.[1,1,-1,0][4,4,-3,1][p,2,2,2][9,9,p,3] are the values of A.
Given, A = [[1,1,-1,0],[4,4,-3,1],[p,2,2,2],[9,9,p,3]] To find the value of p, such that the rank of A is 3.
Rank of a matrix is defined as the maximum number of linearly independent row vectors or column vectors. It is denoted by R(A).When a matrix is in echelon form, its rank is equal to the number of pivots.The rank of a matrix is equal to the maximum number of linearly independent rows or columns in the matrix.Here, A is a matrix,The rank of A is 3.Thus, we can say that there will be 3 linearly independent rows or columns in the matrix.
The augmented matrix [A|0] should have 1 pivot for each linearly independent rows.Therefore, [A|0] will have 3 pivots.Then, the last row of [A|0] should be a linear combination of the first three rows.To find the value of p,Let the matrix A is in echelon form [1,1,-1,0][0,0,1,1][0,0,0,0][0,0,0,0]Let's analyze the matrix A for rank 3If we swap R2 and R3,R2 <-> R3 [1,1,-1,0][p,2,2,2][4,4,-3,1][9,9,p,3]Then, the matrix in echelon form is [1,1,-1,0][0,0,1,1][0,0,0,0][0,0,0,0]We can see that the third row is not a linear combination of the first two rows. Therefore, the first three rows of A are linearly independent.Then, A has rank 3 if we can get rid of the fourth row using linear combinations of the first three rows.
9R1 + (-9)R2 + (-p)R3 = 0Thus, 9 - 9p - p² = 0p² + 9p - 9 = 0(p + 3)(p - 3) = 0p = -3 or 3So, the values of p are -3 or 3 such that the rank of A is 3.[1,1,-1,0][4,4,-3,1][p,2,2,2][9,9,p,3] are the values of A.
Learn more about Rank of a matrix
brainly.com/question/29857274
#SPJ11
i really need help ple
Answers
Answer:
-6.99 , -4 , -6.9 , -2 , -6.999 , -6 , 1
Step-by-step explanation:
Any number to the right of -7 is greater than -7.
The solid below is dilated by a scale factor of 3 3. Find the volume of the solid created upon dilation.
Answers
Part C
What is the probability that Geraldo, the 25-year-old you're considering for a 30-year policy, lives to be 55 years old?
Remember that Geraldo is a Hispanic male.
B
IU x
, Font Sizes
-A- A
E 1 E 23
V
Characters used: 0/ 15000
Part D
Answers
The probability that client C, the 25-year-old you’re considering for a 30-year policy, lives to be 55 years old is 1.
The potential is implied by the word "probability". This area of mathematics studies how random events occur. The range is the set of values between 0 and 1. Probability has been incorporated into the mathematics to forecast the likelihood of various events. In essence, probability refers to the degree to which something is likely to occur. You can appreciate the possible results of a random experiment using this fundamental probability theory, which is also applied to a probability distribution. Before assessing how likely an event is to occur, we need to know how many possible outcomes there are.
Gerald age = 25 years
Policy considered = 30 years
Age at the end of the policy = 55 years
The probability that Geraldo lives to be 55 years will be:
= P(A + B)
= (25÷55) + (30÷55)
= 55÷55
= 1
learn more about probability,
https://brainly.com/question/30034780
#SPJ4
Please help!!!!!!!!!
Answers
The length of arc of the sector is 52.2 cm and the area of the sector is 260.8 cm²
What is length of an arc?Arc length is defined as the distance between the two points placed on the circumference of the circle and measured along the circumference. Arc length is the curved distance along the circumference of the circle.
area of an arc = tetha/360 × πr²
l = 299/360 × 3.14 × 10²
l = 93886/360
l = 260.8 cm² ( 1 dp)
The length of arc of the sector
=( tetha)/360 × 2πr
= 299/360 × 2 × 3.14 × 10
= 18777.2/360
= 52.2 cm
therefore the area of the sector is 260.8cm² and the length of the arc is 52.2 cm
learn more about length of an arc from
https://brainly.com/question/2005046
#SPJ1
Graph the inequality in the coordinate plane. x < -7
Answers
For the given inequality x < -7 we draw a straight line at the point -7. The inequality is not strict, hence the line is dotted.
What is inequality?A mathematical statement called an inequality compares two numbers or expressions, typically by employing a symbol. Inequalities show that two quantities are not equal and that one is more than or less than the other.
Number lines can be used to visualise inequality conditions. Depending on whether the endpoint is part of the solution set or not, numbers that meet the inequality are shaded in or denoted by an open or closed circle. A number line would, for instance, show the inequality x > 2 with an open circle at 2 and shading to the right to show all values higher than 2.
In many areas of mathematics as well as in other disciplines like economics and social sciences, inequality is used.
For the given inequality x < -7 we draw a straight line at the point -7.
The inequality is not strict, hence the line is dotted.
Learn more about inequality here:
https://brainly.com/question/30231190
#SPJ1
The list of ordered pairs below represents a function.
{(10,−2),(−9,6),(5,−8),(2,−4)}
Find the range of the function.
Answers
10,-2
Step-by-step explanation: 10-2, -9,6, 5-8, 2,-4
Domain: 10,-9, 5, 2,
Range -8, 6,-4, -2
Analyze the diagram below and complete the instructions that follow.Find m
Answers
The measure of angle A is equal to 41.11 rounded to two decimal place, using trigonometric ratio for the cosine of the angle A. The correct option is B.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
cos A = 55/73 {adjacent/hypotenuse}
A= cos⁻¹(55/73) {cross multiplication}
A = 41.1121
Therefore, the measure of angle A is equal to 41.11 rounded to two decimal place, using trigonometric ratio for the cosine of the angle A
Know more about trigonometric ratios here: https://brainly.com/question/11967894
#SPJ1
Michelle needs to rent storage space for some of her belongings. She paid a one-time original storage fee of $50.00, and now pays $15.00 each month,
. Which answer choice shows an expression that represents the total amount Michelle has paid after a certain number of months,
?
Answers
The total amount Michelle has paid after "m" months is:
50 + 15m
So the correct answer is:
50 + 15m
Show that x^5-5x^3+5x2+-1=0 has 3 equal roots and find that root
Answers
First, we can find the derivative of the polynomial:
f(x) = x^5 - 5x^3 + 5x^2 - 1
f'(x) = 5x^4 - 15x^2 + 10x
Next, we can set f(x) equal to zero and solve for x:
x^5 - 5x^3 + 5x^2 - 1 = 0
We can then substitute this value of x into the derivative f'(x):
f'(x) = 5x^4 - 15x^2 + 10x
f'(x) = 5(x^4 - 3x^2 + 2)
f'(x) = 5(x^2 - 1)(x^2 - 2)
We can see that the derivative has two roots, x = -1 and x = 1, each with multiplicity 2. This implies that the original polynomial has three equal roots, since each of these roots will be a repeated root of multiplicity 2.
To find the roots, we can use synthetic division to divide the polynomial by (x - 1)^2:
1 | 1 0 -5 5 -1
| 1 -1 4 -1
| 1 1 -6 9 -2
1 | 1 1 -6 9 -2
| 1 -5 1
| 1 2 -11 10
So, (x - 1)^2 is a factor of the polynomial, and we can factor the remaining quadratic as:
(x - 1)^2(x^2 + 2x - 10) = 0
Solving for the roots of the quadratic factor, we get:
x^2 + 2x - 10 = 0
(x + 1 + sqrt(11))(x + 1 - sqrt(11)) = 0
Therefore, the roots of the original polynomial are:
x = 1 (with multiplicity 2)
x = -1 + sqrt(11)
x = -1 - sqrt(11)
So, the three equal roots of the polynomial are 1, 1, and -1 ± sqrt(11).
A large rectangular swimming pool is 10,000 feet long, 100 feet wide, and 10 feet deep. The pool is filled to the top with water.
1. What is the area of the surface of the water in the pool? ______ square feet
2. How much water does the pool hold? _______ cubic feet
Answers
1. The surface area of the pool is given as follows: 2,202,000 square feet.
2. The amount of water that the pool holds is of: 10,000,000 cubic feet.
What is the surface area of a rectangular prism?The surface area of a rectangular prism of height h, width w and length l is given by:
S = 2(hw + lw + lh).
This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.
The dimensions for this problem are given as follows:
l = 10000, w = 100, h = 10.
Hence the surface area is given as follows:
S = 2 x (10000 x 100 + 10000 x 10 + 100 x 10)
S = 2,202,000 square feet.
What is the volume?The volume of a rectangular prism is given by the multiplication of it's dimensions, hence:
V = 10000 x 100 x 10
V = 10,000,000 cubic feet.
More can be learned about the surface area of a rectangular prism at https://brainly.com/question/1310421
#SPJ1
Use the drawing tools to form the correct answer on the graph.
Plot function h on the graph.
Answers
The graph of the piecewise function is shown in the image attached below.
How to plot a piecewise function
In this problem we need to graph a piecewise function formed by two linear equations, a horizontal line and an oblique line. According to Euclidean geometry, a line can be formed from two distinct points set on Cartesian plane. The procedure is summarized below:
Plot the points (-5, - 4) and (- 4, - 4) of function f(x) = - 4.Generate the line of function f(x) for x < - 3.Plot the points (0, 5) and (5, 10) of function g(x) = x + 5.Generate the line of function f(x) for x ≥ - 3.Lastly, the piecewise function is shown in the image attached below.
To learn more on piecewise functions: https://brainly.com/question/28225662
#SPJ1
Use the Pythagorean Theorem to find the missing side of this right triangle. Estimate with a calculator (to one decimal place) if the answer doesn't simplify to a whole number.
Answers
Answer:
13.2
Step-by-step explanation:
using Pythagorean theorem, create the equation for the unknown side, x.
x^2+9^2=16^2
subtract 9^2
x^2=16^2-9^2
Use difference of squares.
x^2=(16-9)*(16+9)
Solve
x^2=7*25
x^2=175
Take the square root of both sides
x=sqrt175
x=13.2
Malaya has 5different shapes of blocks: rectangle, rhombus, square, trapezoid, and triangle. She has 10 of each shape. She selects a block at random.
Answers
Using probability, we can find that the probability of getting a triangle shape block when selected at random is 1/5.
Define probability?The chance of an event can be calculated using the probability formula by only dividing the favourable number of possibilities by the total number of potential outcomes.
The likelihood of an event occurring can be anything between 0 and 1, as the favourable number of outcomes can never exceed the total number of outcomes. Therefore, the percentage of successful results cannot be zero.
In the question,
Malaya has 5 different shapes of blocks.
Malaya has 10 blocks of each shape.
So, the total no. of blocks = 5 × 10 = 50.
Now, Malaya has 10 blocks of triangular shape.
probability of getting a triangular shape is:
P = 10/50
= 1/5
Therefore, the probability of getting a triangle shape block when selected at random is 1/5.
To know more about probability, visit:
https://brainly.com/question/30034780
#SPJ1
The complete question is:
Malaya has 5different shapes of blocks: rectangle, rhombus, square, trapezoid, and triangle. She has 10 of each shape. She selects a block at random. What is the probability of getting a triangle shape block when selected at random?
Given JL=12.7 and KM=25.1, find the area of rhombus JKI. M. Round your answer to the nearest tenth if necessary.
Answers
According to the formula, the area of rhombus JKI M is approximately 315.3 square centimeters.
What is area of rhombus formula?
The formula for the area of a rhombus is half the product of its diagonals. That is,
Area of rhombus = (diagonal 1 x diagonal 2)/2
where diagonal 1 and diagonal 2 are the lengths of the two diagonals of the rhombus.
Let D be the intersection of diagonals JK and IM.
Since JK and IM are perpendicular bisectors of each other, D is the midpoint of both diagonals. Let AD = x and BD = y. Then, we have:
[tex]$$\begin{aligned} x + y &= \frac{1}{2} JM = \frac{1}{2}(KL + KM) = \frac{1}{2}(2 \cdot 12.7 + 25.1) = 25.25 \ y - x &= \frac{1}{2} KL = \frac{1}{2} \cdot 12.7 = 6.35 \end{aligned}$$[/tex]
Solving for x and y, we get:
x = [tex]\frac{25.25 - 6.35}{2}[/tex]= 9.95cm
y = [tex]\frac{25.25 + 6.35}{2}[/tex] = 15.8cm
Therefore, the diagonals of rhombus JKI M have lengths 2x = 19.9 cm and 2y = 31.6 cm, respectively. The area of the rhombus is half the product of the diagonals, so we have:
[tex]$$\begin{aligned} A &= \frac{1}{2} \cdot 19.9 \cdot 31.6 \ &= 315.32 , \text{cm}^2 \end{aligned}$$[/tex]
Rounding to the nearest tenth, we get:
[tex]$$A \approx 315.3 , \text{cm}^2$$[/tex]
Therefore, the area of rhombus JKI M is approximately 315.3 square centimeters.
To learn more about the area of rhombus visit:
brainly.com/question/16205763
#SPJ1
if a = -1/2 is a root of the quadratic equation 8x²-bx-3 . find the value of b, the other root, and (1/a - 1/b)²
Answers
Answer:
If a = -1/2 is a root of the quadratic equation 8x² - bx - 3, then we know that when x = -1/2, the equation is equal to 0. We can use this information to solve for b.
Substituting x = -1/2 into the equation, we get:
8(-1/2)² - b(-1/2) - 3 = 0
Simplifying and solving for b, we get:
2 - (b/2) - 3 = 0
b/2 = -1
b = -2
Therefore, b = -2 is the value we are looking for.
To find the other root, we can use the fact that the product of the roots of a quadratic equation is equal to the constant term divided by the leading coefficient. In this case, the constant term is -3 and the leading coefficient is 8. Therefore, the product of the roots is:
(-1/2) times the other root = -3/8
Solving for the other root, we get:
(-1/2) times the other root = -3/8
other root = (-3/8) / (-1/2)
other root = (3/8) * 2
other root = 3/4
Therefore, the other root is 3/4.
Finally, to find (1/a - 1/b)², we can substitute a = -1/2 and b = -2 into the expression:
(1/a - 1/b)² = (1/(-1/2) - 1/(-2))²
= (-2 - 1/2)²
= (-5/2)²
= 25/4
Therefore, (1/a - 1/b)² is equal to 25/4.
Answer:
[tex]b=2[/tex]
[tex]\textsf{Other root} = \dfrac{3}{4}[/tex]
[tex]\left(\dfrac{1}{a}-\dfrac{1}{b}\right)^2=\dfrac{25}{4}[/tex]
Step-by-step explanation:
Roots are also called x-intercepts or zeros. They are the x-values of the points at which the function crosses the x-axis, so the values of x when f(x) = 0.
If x = α is a root of a polynomial f(x), then f(α) = 0.
Therefore, given that a = -1/2 is a root of the quadratic equation 8x² - bx - 3, substitute x = -1/2 into the equation and set it to zero:
[tex]\implies 8\left(-\dfrac{1}{2}\right)^2-b\left(-\dfrac{1}{2}\right)-3=0[/tex]
Solve for b:
[tex]\implies 8\left(\dfrac{1}{4}\right)+\dfrac{1}{2}b-3=0[/tex]
[tex]\implies \dfrac{8}{4}+\dfrac{1}{2}b-3=0[/tex]
[tex]\implies 2+\dfrac{1}{2}b-3=0[/tex]
[tex]\implies \dfrac{1}{2}b-1=0[/tex]
[tex]\implies \dfrac{1}{2}b=1[/tex]
[tex]\implies b=2[/tex]
Therefore, the quadratic equation is:
[tex]\boxed{8x^2-2x-3}[/tex]
The product of the roots of a quadratic equation is equal to the constant term divided by the leading coefficient.
The constant term of the quadratic equation is -3 and the leading coefficient is 8. Let the other root be "r". Therefore:
[tex]\implies a \cdot r=\dfrac{-3}{8}[/tex]
Substitute the known value of a = -1/2 and solve for r:
[tex]\implies -\dfrac{1}{2} \cdot r=\dfrac{-3}{8}[/tex]
[tex]\implies r=\dfrac{3}{4}[/tex]
Therefore, the other root of the quadratic equation is 3/4.
To find the value of (1/a - 1/b)², substitute the given value of a and the found value of b into the equation and solve:
[tex]\implies \left(\dfrac{1}{a}-\dfrac{1}{b}\right)^2[/tex]
[tex]\implies \left(\dfrac{1}{-\frac{1}{2}}-\dfrac{1}{2}\right)^2[/tex]
[tex]\implies \left(-2-\dfrac{1}{2}\right)^2[/tex]
[tex]\implies \left(-\dfrac{5}{2}\right)^2[/tex]
[tex]\implies \dfrac{25}{4}[/tex]
An SRS of 1000 voters finds that 57% believe that competence is more important than character in voting for President of the United States.
(A) Determine a 95% confidence interval estimate for the percentage of all voters who believe competence is more important than character.
(B) Based on the interval you found in part (a), is it reasonable to assume that a majority of voters believe that competence is more important than character. Explain why or why not.
(C) Explain what is meant by 95% confidence in this situation
Answers
(A) A 95% confidence interval estimate for the percentage of all voters who believe competence is more important than character is (0.538, 0.602).
(B) This is due to the interval's lower bound's value of 0.538, which is higher than 0.5.
(C) In this instance, 95% confidence indicates that if the sampling procedure were repeated numerous times and a 95% confidence interval estimate was calculated for each sample
(A) Using the method below, we can calculate an estimate with a 95% confidence interval for the proportion of voters who think competence is more significant than character:
CI equals p z*(sqrt(p*(1-p)/n)/p)).
where: p = the percentage of voters who say character is more essential than competence = 0.57; n = the sample size; 1000; and z = the z-score for a 95% confidence level; 1.96.
By entering the numbers, we obtain:
CI = 0.57 1.96*(sqrt(0.57*(1-0.57)/1000)), which equals 0.57 0.032. (0.538, 0.602)
the 95% confidence interval estimate for the proportion of respondents overall who think competence is more significant than character is (0.538, 0.602).
(B) Based on the range discovered in part, it is reasonable to infer that the majority of voters value competence over character (a). This is due to the interval's lower bound's value of 0.538, which is higher than 0.5. Therefore, we can state with 95% certainty that the actual proportion of voters who think competence is more crucial than character is at least 53.8%, which is a majority.
(C) In this instance, 95% confidence indicates that if the sampling procedure were repeated numerous times and a 95% confidence interval estimate was calculated for each sample, then roughly 95% of those intervals would contain the actual proportion of voters who believe competence is more significant than character. That is to say, we have a 95% confidence interval (0.538, 0.602) that contains the actual proportion of voters who think competence is more significant than character.
Learn more about percentage here:
https://brainly.com/question/29306119
#SPJ4
The distance between the points (10,4) and (1,-8)
Round decimals to the nearest tenth
Answers
the distance between the points (10, 4) and (1, -8) is 15 units. We round this to the nearest tenth by looking at the first decimal place after the decimal point, which is 5. Since 5 is greater than or equal to 5, we round up the tenths place, giving us a final answer of 15.0 units.
To find the distance between two points in a coordinate plane, we can use the distance formula. The distance formula is derived from the Pythagorean theorem and is given by:
d = √[(x2 - x1)² + (y2 - y1)²]
Where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between them.
In this case, the coordinates of the two points are (10, 4) and (1, -8). Substituting these values into the distance formula, we get:
d = √[(1 - 10)² + (-8 - 4)²]
= √[(-9)² + (-12)²]
= √(81 + 144)
= √225
= 15
Therefore, the distance between the points (10, 4) and (1, -8) is 15 units. We round this to the nearest tenth by looking at the first decimal place after the decimal point, which is 5. Since 5 is greater than or equal to 5, we round up the tenths place, giving us a final answer of 15.0 units.
In summary, to find the distance between two points in a coordinate plane, we can use the distance formula. In this case, we found that the distance between the points (10, 4) and (1, -8) is 15 units, rounded to the nearest tenth as 15.0 units.
To know more about Pythagorean theorem click here:
brainly.com/question/28361847
#SPJ4
Let θ be an angle in standard position, with its terminal side in quadrant IV such that tanθ = -7/9. Find the exact values of sinθ and cosθ.
Answers
The value of sin θ is -[tex]\frac{7\sqrt{130} }{130 }[/tex] and cos θ is [tex]\frac{9\sqrt{130} }{130 }[/tex] . The solution has been obtained by using trigonometry.
What is trigonometry?
The study of right-angled triangles, including their sides, angles, and connections, is referred to as trigonometry.
We are given that tan θ is -7/9. The minus sign is there because it lies in the fourth quadrant.
This means that the perpendicular is 7 and the base is 9.
Let the hypotenuse be x.
Now, by using Pythagoras theorem, we get
⇒ [tex]7^{2}[/tex] + [tex]9^{2}[/tex] = [tex]x^{2}[/tex]
⇒ 49 + 81 = [tex]x^{2}[/tex]
⇒ [tex]x^{2}[/tex] = 130
⇒ x = √130
By trigonometry,
⇒ Sin θ = -[tex]\frac{7}{\sqrt{130} }[/tex]
⇒ Sin θ = -[tex]\frac{7\sqrt{130} }{130 }[/tex]
Similarly,
⇒ Cos θ = [tex]\frac{9}{\sqrt{130} }[/tex]
⇒ Cos θ = [tex]\frac{9\sqrt{130} }{130 }[/tex]
Hence, the values for sin θ and cos θ have been obtained.
Learn more about trigonometry from the given link
https://brainly.com/question/13729598
#SPJ1
high voltage, inc., a light bulb manufacturer, wants to know if there's a difference in mean life span between its product and that of a competitor. they collect paired data and calculate the difference in each pair to create one set of numbers that represents the differences within each pair. what notation should high voltage use to construct its null and alternative hypotheses?
Answers
High Voltage, Inc. should use the following notation to construct its null and alternative hypotheses: Null Hypothesis: H0: μ1 - μ2 = 0; Alternative Hypothesis: H1: μ1 - μ2 ≠ 0; where μ1 represents the mean life span of High Voltage's product and μ2 represents the mean life span of the competitor's product.
The notation High Voltage should use to construct its null and alternative hypotheses is:
(i) Null Hypothesis: H0: μ1−μ2=0
where μ1 represents the mean life span of High Voltage's product and μ2 represents the mean life span of the competitor's product.
(ii) Alternative Hypothesis: Ha: μ1−μ2≠0
Where,μ1 and μ2 are the mean lifespan of the light bulbs of High Voltage and its competitor, respectively.
In this problem, paired samples t-test should be used to test the hypotheses.
Paired sample t-test: It is a statistical procedure used to compare two population means with two samples of dependent observations, where the dependent variable is the same or the same subject measured under different conditions. It is used when the observations are paired, i.e., each pair of observations consists of two measurements made on a single subject or item.
Know more about Null Hypothesis here:
https://brainly.com/question/4436370
#SPJ11
Pls help due tomorrow
Answers
circles have 360 degrees so multiple each one by 6
25x 6 = 150
12 x 6= 72
8 x 6= 48
15x 6 = 90
You notice that a stairwell railing is a parallelogram. In parallelogram RALS: ALsegment A L = 26.5 feet RIsegment R I = 5.3 feet ARsegment A R = 6.2 feet What is the area of parallelogram RALS? Use the given information to complete the worksheet.
HELPP I MEED IT
Answers
Answer:
To find the area of a parallelogram, we need to multiply the base by the height. In this case, we need to find the height of the parallelogram.
We can see that segment AL and segment RI are both perpendicular to segment AR. Therefore, we can use either of them to find the height.
Let's use segment AL as our height. To find the length of segment LS, we can use the Pythagorean theorem:
LS² = AR² - RI²
LS² = 6.2² - 5.3²
LS² = 16.21
LS = √16.21
LS ≈ 4.02 feet
Now we can find the area of the parallelogram:
Area = base x height
Area = AL x LS
Area = 26.5 x 4.02
Area ≈ 106.23 square feet
Therefore, the area of parallelogram RALS is approximately 106.23 square feet.
Step-by-step explanation:
Can sum1 help please
You can use the desmos graphing calculator
Answers
According to the given information, Mack should make 4 necklaces and 8 wristbands to maximize his profit.
What are linear programming problems?
LPP stands for Linear Programming Problems. Linear programming is a mathematical optimization technique used to maximize or minimize a linear objective function subject to a set of linear constraints. An LPP involves identifying a set of decision variables, an objective function that depends linearly on these variables, and a set of constraints that specify linear relationships between the variables. The objective is to find the values of the decision variables that optimize the objective function while satisfying all the constraints.
To solve this problem, we need to use a system of linear inequalities to represent all the constraints. Let's start by defining the variables:
x = number of necklaces
y = number of wristbands
Now we can write the constraints:
Time constraint: Mack has 360 minutes to make the necklaces and wristbands.
40x + 25y ≤ 360
Production constraint: Mack wants to make no more than 12 items.
x + y ≤ 12
Non-negative constraint: Mack cannot make a negative number of necklaces or wristbands.
x ≥ 0, y ≥ 0
To maximize Mack's profit, we need to define the objective function as the total profit:
P = 3x + 2y
Now we can graph these constraints and find the feasible region:
40x + 25y ≤ 360
x + y ≤ 12
x ≥ 0, y ≥ 0
As shown in attachment 1.
The feasible region is the shaded polygon bounded by the lines: x=0, y=0, x + y ≤ 12, and 40x+25y=360.
To find the optimal solution, we need to evaluate the objective function at each corner point of the feasible region:
Corner point A: (0,0)
P = 3(0) + 2(0) = $0
Corner point B: (0,12)
P = 3(0) + 2(12) = $24
Corner point C: (4,8)
P = 3(4) + 2(8) = $28
Corner point D: (9,0)
P = 3(9) + 2(0) = $27
The maximum profit is $28, which occurs when Mack makes 4necklaces and 8 wristbands. Therefore, Mack should make 4 necklaces and 8 wristbands to maximize his profit.
To know more about linear programming problems visit:
brainly.com/question/14309521
#SPJ1