Answer:
4.5 billion years
Step-by-step explanation:
Answer: We can use the formula for radioactive decay:
N = N0 * (1/2)^(t/T)
where N is the current amount of the radioactive substance, N0 is the original amount, t is the time that has passed, T is the half-life.
Let's assume that the original amount of the substance in the rock was 8 units. If the current amount is 1 unit, then:
1 = 8 * (1/2)^(t/1.5 billion)
Taking the natural logarithm of both sides, we get:
ln(1) = ln(8) - (t/1.5 billion)*ln(2)
Simplifying:
0 = ln(8) - (t/1.5 billion)*ln(2)
t/1.5 billion = ln(8)/ln(2)
t = 1.5 billion * (ln(8)/ln(2))
t ≈ 3.91 billion years
Therefore, the moon rock is about 3.91 billion years old.
Step-by-step explanation:
A campground allows a maximum of 6 campers in a camp site. How many camp sites does a group of 237 campers need?
a group of 237 campers would require 40 campsites (since we cannot have half of a campsite).
How to solve the question?
To determine the number of camp sites required for a group of 237 campers, we can divide the total number of campers by the maximum number of campers allowed per site.
237 campers ÷ 6 campers per site = 39.5
Since we cannot have a fraction of a campsite, we need to round up to the nearest whole number. This is because we need to ensure that there is enough space for all of the campers, and rounding up will ensure that we have enough sites to accommodate them.
Therefore, a group of 237 campers would require 40 campsites (since we cannot have half of a campsite).
It is important to note that while this calculation is a good starting point, it is always a good idea to check with the campground to ensure that they can accommodate a group of this size. Additionally, the campground may have specific policies or procedures in place for reserving campsites for large groups.
To know more about divison visit :-
https://brainly.com/question/25289437
#SPJ1
find the quotient of 504 ÷ 12.
Step-by-step explanation:
Refer the attachment!!~
Answer:
Step-by-step explanation:
Refers to the attachment given belowA byte is how many bits?
a. 8
b. 80
c. 800
d. Depends on the computer
Answer:
A byte is 8 bits.
Camile realizes she is charged more based on the volume of the box and not the weight which box would fit her requirements and be the best choice to save her on shipping cost? Explain your reasning
To save on shipping costs, Camile should choose a box that is lightweight and has a small volume.
Why should Camile choose a box that is lightweight and has a small volume?This is because she has realized that she is charged based on the volume of the box and not the weight.
Therefore, a smaller volume box would cost her less than a larger volume box of the same weight.
For example, if Camile needs to ship a 5-pound item, she should choose a smaller box with a volume that is just enough to fit the item, rather than a larger box with more empty space. This is because the larger box would have a greater volume, and therefore, incur a higher shipping cost even though it weighs the same as the smaller box.
In summary, when selecting a box to save on shipping costs, it is important to consider both weight and volume. Camile should choose a box that is lightweight and has a smaller volume to reduce her shipping costs.
Learn more about volume from
https://brainly.com/question/14460183
#SPJ1
Rihanna worked for 3 hours 35 minutes
on Monday. She worked for 2 hours
50 minutes on Wednesday. She wants
to work enough hours on Friday so she
works a total of 8 hours. How much
longer does she need to work?
Answer:
1 hour and 35 minutes
Step-by-step explanation:
3 hours and 35 minutes + 2 hours and 50 minutes = 6 hours and 25 minutes.
8 hours - 6 hours and 25 minutes = 1 hour and 35 minutes
someone js help me answer this question:
3 + 2 if = 7
the solution to the equation "3 + 2 if = 7" when solving for "if" is "if = 2".It's possible intended question was to solve variable "if" in the equation "3 + 2 if = 7". In that case, we use algebra to solve for "if" as follows:
what is variable ?
In mathematics, a variable is a symbol or letter that represents a quantity that can vary or change in value. Variables are used to express relationships between different quantities and to solve equations.
In the given question,
It seems like the question is incomplete or there may be a typo. The equation provided "3 + 2 if = 7" is not solvable as it is.
It's possible that the intended question was to solve for the variable "if" in the equation "3 + 2 if = 7". In that case, we can use algebra to solve for "if" as follows:
First, we can isolate the variable term by subtracting 3 from both sides of the equation:
3 + 2 if - 3 = 7 - 3
Simplifying the left-hand side:
2 if = 4
Finally, we can solve for "if" by dividing both sides by 2:
if = 2
Therefore, the solution to the equation "3 + 2 if = 7" when solving for "if" is "if = 2".
To know more about variable, visit:
https://brainly.com/question/17344045
#SPJ1
Someone js help me answer this question:
. simplify 3 + 2 if = 7 ?
Special right triangles
The measure of angle FCD is 130 degrees.
What is an angle?
In planar geometry, an angle is a shape made up of two rays or lines that share an endpoint. The Latin word "angulus" (which means "corner") is where the word "angle" first arose.
The pair of alternative internal angles that are congruent must first be found. The angles formed on the opposing sides of the transversal EF are known as alternate internal angles since AB and CD are parallel lines. We possess
Angle AGE and angle FCD are alternate interior angles.
Angle AGE measures 130 degrees.
Therefore, we can conclude that angle FCD also measures 130 degrees. So, the measure of angle FCD is 130 degrees.
To know more about angle visit,
brainly.com/question/28451077
#SPJ1
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.
The appropriate measure of center for the data on the tickets sold is C. The median is the best measure of center, and it equals 19.
Why is the median best ?In a box plot, the median is represented by the horizontal line that divides the box into two equal parts. The median is the middle value of the dataset when it is ordered from smallest to largest.
The median is the best measure of center for a box plot. The median is represented by the line inside the box, which in this case is at 19 on the number line.
Find out more on median at https://brainly.com/question/14277132
#SPJ1
Answer:
ccccccccccccccccccccccccc
Step-by-step explanation:
The elephants at the Hancock Zoo are fed 4 9/10 barrels of corn each day. The buffalo are fed 1/6 as much corn as the elephants. How many barrels of corn are the buffalo fed each day?
Write your answer as a fraction or as a whole or mixed number.
PLEASE PLEASE PLEASE HELP
Answer: 49/60 of corn
Step-by-step explanation:
How I got this answer was I basically paid attention to the wording. 1/6 as much meaning x 1/6. So, I converted 4 9/10 to a fraction and got 49/10. Then, I multiplied 49/10 by 1/6 and got 49/60. The fraction can't be simplified any lower, so it is supposed to be left as is. Hope this helped!
The Columbus Zoo conducts a study to determine whether a household’s income can be used to predict the amount of money the household will give to the zoo’s annual fund drive. The response (i.e. the effect) variable in this study is
a. the Columbus Zoo.
b. a household’s income.
c. the amount of money a household gives to the zoo’s annual fund drive.
d. all households in Columbus.
The response (i.e. the effect) variable in this study is option (c) the amount of money a household gives to the zoo's annual fund drive
The response (i.e. the effect) variable in this study is the amount of money a household gives to the zoo's annual fund drive. This is the variable that the study is attempting to predict based on the household's income. The Columbus Zoo is the entity conducting the study, and a household's income is the predictor (i.e. the independent) variable.
The study is focused on the relationship between a household's income and the amount of money it gives to the zoo's annual fund drive, so the response variable is the amount of money given to the fund drive. The study is not attempting to make predictions about all households in Columbus, so option d is not the correct answer.
Therefore, the correct option is (c) the amount of money a household gives to the zoo’s annual fund drive.
Learn more about response here
brainly.com/question/13285680
#SPJ4
Consider ▰WXYZ. If WV=18, what is XZ?
WX must be positive because it measures the width of a trapezoid's side. WX thus equals 16.
what is trapezium ?A parallelogram with at least two pair of parallel sides is known as a trapezium in geometry (or a parallelogram in American English). The legs of a trapezium are the non-parallel sides, whereas the parallel sides are referred to as the bases. The legs of a zygomatic arch might be equal in length (isosceles) or varied in length (non-isosceles). By averaging the widths of the two bases and multiplying by the height, a trapezium's area can be determined (the perpendicular distance between the two bases). that is Area equals (a + b)*h / 2. where h is the trapezium's height and a and b are the lengths of the base's two parallel sides (the bases).
given
MN can be used in place of XV2 in the equation, and the result is simplified to:
XV² = (1/4) (WX + 18)² + h²
Now, we can add the following expression for XV2 to the equation for WX2:
WX² = 18² + XV²
WX² = 18² + (1/4) (WX + 18)² + h²
Adding and subtracting:
3WX² - 218WX - 18² = 4h²
We can now resolve WX:
WX is equal to (218 sqrt((218)2 - 43(-182))). / (2*3)
WX = 16 or -27
WX must be positive because it measures the width of a trapezoid's side. WX thus equals 16.
To know more about trapezium visit:
https://brainly.com/question/8208556
#SPJ1
Select and use the most direct method to solve 2x(x + 1.5) = -1.
The solutions to the equation 2x(x + 1.5) = -1 are x = -1/2 and x = -1.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
We can use the distributive property to simplify the left-hand side of the equation:
2x(x + 1.5) = -1
2x^2 + 3x = -1
Now we can move all the terms to one side of the equation:
2x² + 3x + 1 = 0
This is a quadratic equation in standard form, where a = 2, b = 3, and c = 1. We can use the quadratic formula to solve for x:
x = (-b ± √(b² - 4ac)) / 2a
Plugging in the values for a, b, and c, we get:
x = (-3 ± √(3² - 4(2)(1))) / 2(2)
Simplifying this expression, we get:
x = (-3 ± √(1)) / 4
x = (-3 ± 1) / 4
x = -1/2 or x = -1
Therefore,
The solutions to the equation 2x(x + 1.5) = -1 are x = -1/2 and x = -1.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ1
PLEASE HELP WITH EXPLANATION AND ANSWER ASAP
The graph of the solution would be a number line with an open circle at 48 and an arrow extending to the right, indicating all values greater than 48 are solutions to the inequality. The solution would be (48, ∞).
What justifies inequality?The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.
Part A:
We can solve the inequality as follows:
1/4x - 3 - 5 > 4
1/4x - 8 > 4
1/4x > 12
x > 48
Therefore, the solution to the inequality is x > 48.
Part B:
Since the inequality is stringent, the graph of the solution would be a number line with an open circle at 48 and an arrow pointing to the right, signifying that all numbers greater than 48 are solutions to the inequality. The answer would be (48, ) in interval notation.
To know more about inequality visit:-
https://brainly.com/question/30228778
#SPJ1
Kalani has a savings account and a checking account. For one year she deposited x dollars into her checking account every week and y dollars into her savings account every month. Each checking account deposit was half the amount of each savings account deposit, and the total of all deposits for the year was $15,200. Which system of equations can be used to determine the values of x and y?
Kalani deposited $200 into her checking account every week and $400 into her savings account every month.
What is system of equation?A group of equations that must be solved simultaneously is referred to as a system of equations. Typically, a system of equations involves multiple variables, and the goal is to find the values of those variables that satisfy all of the equations in the system.
According to question:Let's start by using the given information to write equations for the total amount deposited in each account over the course of the year.
For the checking account, Kalani deposited x dollars every week for 52 weeks, so the total amount deposited for the year is:
52x
For the savings account, Kalani deposited y dollars every month for 12 months, so the total amount deposited for the year is:
12y
We are also told that each checking account deposit was half the amount of each savings account deposit, so we can write:
x = (1/2)y
Finally, we are given that the total of all deposits for the year was $15,200, so we can write:
52x + 12y = 15200
A system of two equations with two variables is now available:
x = (1/2)y
52x + 12y = 15200
We can solve this system to determine the values of x and y. The result of putting the first equation into the second equation is:
52(1/2)y + 12y = 15200
Simplifying:
26y + 12y = 15200
38y = 15200
y = 400
Substituting y = 400 into the first equation, we get:
x = (1/2)y = (1/2)(400) = 200
Therefore, Kalani deposited $200 into her checking account every week and $400 into her savings account every month.
To know more about system of equation visit:
https://brainly.com/question/12895249
#SPJ1
A ball is thrown straight up into the air by three different people, Alberto, Ben and Carrie. Below are different representations of their throws. Alberto’s throw can be described by the equation height=−16(time)^2+32(time)+4 Ben's throw can be described by the following table:
For given data, Carrie threw the ball highest = 35ft and ball stayed in the air longest = 3s for Carrie as well.
How does projectile motion work?Any object that is fired into the air and travels in that direction is referred to as a projectile. Gravitation, however, is another force that an object experiences after the first force that pushes it.
Three distinct individuals, Alberto, Ben, and Carrie, each toss a ball straight up into the air.
Following equation may be used to explain Alberto's throw.
[tex]H = -16t^2 + 32t + 4[/tex]
Now , to find the maximum height, we solve for first derivative w.r.t.t,
[tex]-32t + 32 = 0[/tex]
[tex]32t=32\\t = 1s[/tex]
Using t=1, we can find maximum height as
[tex]H =-16(1)^2 + 32(1) + 4\\\\H=(-16)+32+4[/tex]
[tex]H= 20[/tex] ft
Thus, when Alberto threw ball, maximum height attained= 20 ft and total time duration ball was in air = 1s.
From the given table( refer to attached image),
Fom given table,
we can drive the function for maximum height as,
[tex]H=at^2+bt+c[/tex]
now, putting values of t, to get values of H,
from table, for t=0,H=6
6=[tex]a(0)+b(0)+c[/tex]
[tex]c=6[/tex]
[tex]H=at^2+bt+6[/tex]
for t=1,H=14
[tex]14=a(1)^2+b.1+6\\\\8=a+b............(1)[/tex]
similarly,for t=2,H=14
[tex]14=a(2)^2+b.2+6\\\\8=4a+2b........(2)[/tex]
solving equation 1 and 2,
a=(-4) and b=12
∴[tex]H=-4t^2+12t+6[/tex]
we know, [tex]t=\frac{-b}{2a}\\\\t=\frac{-12}{-8}=3/2=1.5s[/tex]
When Ben threw ball, the maximum height ball attained was 14 ft and total time duration for which ball was in air was 1.5 seconds.
From the given graph(refer to attached image),When Carrie threw the ball Maximum Height attained = 35ft and Time duration ball was afloat is 3s
Thus,When Carrie threw the ball attained Maximum Height 35ft and ball stayed in the air longest.
Learn More about projectile motion here
brainly.com/question/11049671
#SPJ1
Complete Question: A ball is thrown straight up into the air by three different people, Alberto, Ben and Carrie. Below are different representations of their throws. Alberto’s throw can be described by the equation height=−16(time)^2+32(time)+4 Ben's throw can be described by the following table(refer to attached image).Who threw the ball highest and for whom the ball was in air for the longest?
1 1/2 x 1 1/2 what is the answer for that equation?
Answer:
9/4.
Step-by-step explanation:
Hope this helps! =D
Find the area of the shape
The measure of angle ABD (which is the same as angle CBD) is 45 degrees.
Is a parallelogram in the figure of a CBD? Why?The quadrilateral's opposing sides are equal. Triangles ABC and ABCD have equal angles on either side of their equal sides. In the quadrilateral ACBD, the opposing angles are also equal. A parallelogram is formed by ACBD.
We can use the fact that the total of the angles of a triangle is always 180 degrees to determine the measure of angle CBD. As a result, we have:
Angle ABD + Angle CBD + Angle BCD = 180 degrees
Substituting the given angle measures, we get:
Angle ABD + Angle CBD + 90 degrees = 180 degrees
Simplifying, we get:
Angle ABD + Angle CBD = 90 degrees
But we know that Angle ABD = Angle CBD, so we can substitute:
2 x Angle ABD = 90 degrees
Dividing both sides by 2, we get:
Angle ABD = 45 degrees
So, the measure of angle ABD (which is the same as angle CBD) is 45 degrees.
To know more about angle visit:-
https://brainly.com/question/16448127
#SPJ1
The selling price for peanut butter is $3. 79 and the cost is $2. 84
Answer: Profit = .95 or 95 cents
Step-by-step explanation:
What is the question here?
If it is profit then the answer is 3.79-2.84
pls hlp thx sososos much
The measure of the angle MSP, m∠MSP, obtained using the relationship between linear pair angles is 80°
What are linear pair angles?Linear pair angles are angles that have a sum of 180°. Linear pair angles come together to form a straight line.
The specified measure of the angle NSM is m∠NSM = 100°
The angles ∠NSM and ∠MSP are linear pair angles therefore;
m∠NSM + m∠MSP = 180°
Plugging in the known value of the angle NSM, we get;
100° + m∠MSP = 180°
Therefore; m∠MSP = 180° - 100° = 80°
The measure of the angle MSP, m∠MSP is 80°
Learn more on linear pair angles here: https://brainly.com/question/28964305
#SPJ1
LAST QUESTION how many pounds
The weight of the tallest dog which is of height 20 inches on this scatter-plot showing dog heights and their weights is 30 pounds.
What is a scatter-plot?The graphs, scatter plots, or scatter charts show the relationship between two variables in a data set that has been analysed. Both a two-dimensional plane and the Cartesian-system are used to represent the data points. Observing and illuminating correlations between two numerical variables is the main purpose of scatter plots. When the data are viewed as a whole, the dots in a scatter plot show patterns in addition to the values of the individual data points. The Y-axis is used to plot the dependent variable, while the X-axis is used to represent the independent variable or attribute. Using a scatter plot, you may see what happens to one variable when another variable is altered. To determine whether the two variables are connected, a scatter plot is utilised.
The scatter plot shows the dog weights & their heights surveyed.
Data represented on X-axis(independent variable) : heights of dogs
Data represented on Y-axis(dependent variable) : weights of dogs
Lowest weight of dog=5 pounds(approx)
Greatest weight of the dog surveyed=41 pounds(approx)
Lowest height of surveyed dog=5 inches.
Greatest height of surveyed dog=20 inches.
∴The weight of tallest dog with 20 inches if height=30 pounds
To know more about scatter-plot , visit:
https://brainly.com/question/29231735
#SPJ1
Please help me I've been stumped on this problem
a. Angle 1 and angle 2 are equal because they are alternate to each other
b. since angle 1 and angle 2 are equal, arc AC and BD will be equal too
c. Parallel lines will intercept congruent arcs.
What is angle formed by parallel lines?When any two parallel lines are cut by a transversal, there are various pairs of angles that are formed.
These angles are corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles.
Therefore , angle 1 and 2are alternate to each other, this means that they are equal.
Since the two angles are equal , the corresponding arc formed by the two angles are also equal.
This means parallel lines will intercept congruent arcs
learn more about angles formed by parallel lines from
https://brainly.com/question/28929828
#SPJ1
What is the measure of Arc A U? 44° 50° 64° 92°
The measure of Arc AU is 50⁰. Hence, the correct option is B.
An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc.
arc QU = 88 and <QUA = 111
QDA = 2 <QUA
= 2 X 111
= 222⁰
Now, QUA = 360- 222 = 138
arc AU = QUA - arc QU
= 138- 58
= 50⁰
Hence, the measure of AU is 50⁰.
To know more about arc here
https://brainly.com/question/15815364
#SPJ4
-- The given question is incomplete, the complete question is attached below. --
Answer:
50⁰
Step-by-step explanation:
The measure of Arc AU is 50⁰. Hence, the correct option is B.
An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc.
Edge 2023
you need to answer every question and you get 25pts and brainliest
Using probability, we can find the following:
a. In the figure.
b. The probability that the first set is green is = 0.8
c. Probability that the second set is green is = 0.06
d. The probability that both the sets are green is = 0.48
e. The probability that at least one set is green is = 0.86
Define probability?The likelihood that an event will occur is described by probability. There are many circumstances in real life where we may need to foresee how something will turn out. We might be able to predict the outcome of an event or we might not. At this point, we say, "There is a chance that the event will happen or not."
Here in the question,
b.
The probability that the first set is green is:
P = 1 - 0.2
= 0.8
c.
Now the first set is given as not green.
Probability that the second set is green is:
p = 0.2 × 0.3
= 0.06
d.
Now probability that both the sets are green is:
P = 0.8 × 0.6
= 0.48
e.
When both the sets are not green, probability is:
0.2 × 0.7
= 0.14
So, probability that at least one set is green is:
P = 1- 0.14
= 0.86
To know more about probability, visit:
https://brainly.com/question/16484393
#SPJ1
Jack and Carlie each deposit $17,250 into accounts that earn 6% interest for 6.5 years. Jack's account earns annual simple interest and Carlie's account earns annual compound interest. Who will earn more interest after 6.5 years, and how much more interest will they earn?
Read the following excerpt from Pointed Roofs by Dorothy Richardson. Then, respond to the question that follows. In a well-written paragraph of 5–7 sentences, explain how the author uses stream of consciousness and one other narrative technique to enhance her writing. Be sure to include specific textual evidence to support the narrative techniques you discuss in your response
In "Pointed Roofs," Dorothy Richardson makes use of conversation and stream of consciousness to improve her writing. Using stream of consciousness, in the given expert.
An excerpt is indeed a quotation from that other resource that the author introduces with fresh language in a sentence. This phrase is taken from Thomas Jefferson's 1801 inaugural speech: As he warned his audience, "I may often go wrong by defect of judgement," Jefferson admitted the fallibility of human nature. "I shall frequently err through lack of judgement" is the excerpt.
In "Pointed Roofs," Dorothy Richardson makes use of conversation and stream of consciousness to improve her writing. Using stream of consciousness, the author lets readers peek inside the protagonist, Miriam, to understand her feelings and thoughts as they happen. For instance, readers can feel Miriam's mild dizziness
To know more about excerpt, here:
https://brainly.com/question/29708851
#SPJ1
PLEASE HELP WITH NUMBER 2! <3 :)))
1. Range of Surveyed Students: 1,650 to 1,800 students.
2. Range of Students in Orange County: 39,364 to 42,972 students
How did we calculate range of a survey?To determine the range of surveyed students that agreed with the statement, we need to calculate the minimum and maximum percentages based on the margin of error. Given that 86% of students agreed with the statement and the margin of error is ±3.7%, we can find the range as follows:
Minimum percentage: 86% - 3.7% = 82.3%
Maximum percentage: 86% + 3.7% = 89.7%
Now, we'll apply these percentages to the total number of surveyed students (2,006):
Minimum number of students: 0.823 x 2,006 ≈ 1,650 students
Maximum number of students: 0.897 x 2,006 ≈ 1,800 students
Range of Surveyed Students: 1,650 to 1,800 students
b. To determine the range of grade 10-12 students in OCPS who would likely agree with the statement, we'll apply the same minimum and maximum percentages found earlier (82.3% and 89.7%) to the total number of grade 10-12 students in Orange County Public Schools (47,851):
Minimum number of students: 0.823 * 47,851 = 39,364 students
Maximum number of students: 0.897 * 47,851 = 42,972 students
Range of Students in Orange County: 39,364 to 42,972 students
The above answer is based on the information below provided in the picture;
A research survey of 2,006 public and private school students in the United States (grades 10-12) between April 12 and June 12, 2016 asked students if they agreed with the statement, "If I make a mistake, I try to figure out where I went wrong." The survey found that 86% students agreed with the statement. The margin of error for the survey is +3.7%.
a. Determine the range of surveyed students that agreed with the statement.
Range of Surveyed Students .......................................................
b. In 2022, there were 47,851 students in grades 10-12 in Orange County Public Schools (OCPS). Determine the range of grade 10-12 students in OCPS who would likely agree with the statement, "If I make a mistake, I try to figure out where I went wrong."
Range of Students in Orange County ..................................
Find more exercises on calculating range in surveys;
https://brainly.com/question/2775000
#SPj1
Graph of polygon ABCDE with vertices at negative 3 comma 3, negative 3 comma 6, 1 comma 6, 1 comma 3, negative 1 comma 1. A second polygon A prime B prime C prime D prime E prime with vertices at negative 5 comma 3, negative 5 comma 6, negative 9 comma 6, negative 9 comma 3, negative 7 comma 1.
50 POINTS ASAP Determine the line of reflection.
Reflection across x = −4
Reflection across y = 1
Reflection across the x-axis
Reflection across the y-axis
Answer:
The correct line of reflection that maps the polygon ABCDE to its image polygon A' B' C' D' E' is:
C. Reflection across the x-axis
Explanation:
The given vertices of the original polygon ABCDE are:
A(-3, 3)
B(-3, 6)
C(1, 6)
D(1, 3)
E(-1, 1)
The given vertices of the image polygon A' B' C' D' E' are:
A'(-5, 3)
B'(-5, 6)
C'(-9, 6)
D'(-9, 3)
E'(-7, 1)
Comparing the coordinates of the original polygon ABCDE and its image polygon A' B' C' D' E', we can see that the y-coordinates are negated, while the x-coordinates remain the same. This indicates that the reflection is happening along the x-axis, as it is the line that reverses the y-coordinates while keeping the x-coordinates unchanged.
Therefore, the correct line of reflection is the x-axis, as shown by option C. Reflection across the x-axis.
Double-check this answer i wrote.
Find the exact value of tan P in simplest radical form. √85 2 N √89
Answer:
We can start by using the tangent formula:
tan(P) = sin(P) / cos(P)
We are not given the values of sin(P) and cos(P) directly, but we can use the Pythagorean identity to relate them:
sin^2(P) + cos^2(P) = 1
We can rearrange this expression to solve for sin(P) in terms of cos(P):
sin^2(P) = 1 - cos^2(P)
sin(P) = ±√(1 - cos^2(P))
Now we can substitute this expression into the tangent formula:
tan(P) = ±√(1 - cos^2(P)) / cos(P)
Substituting the given values and simplifying:
tan(P) = ±√(1 - (2/√85)^2) / (1/√89)
tan(P) = ±√(1 - 4/85) * √89
tan(P) = ±√(81/85) * √89 / 1
We want to express tan P in simplest radical form, so we can simplify the square root by factoring out the greatest perfect square factor of the numerator:
tan(P) = ±(√9/√85) * (√89/1)
tan(P) = ±(3/√85) * (√89/1)
Therefore, the exact value of tan P in simplest radical form is ±(3/√85) * (√89/1).
Consider the expression (x2 − 4)(x + 3).
Select all values of x for which (x2 − 4)(x + 3) = 0.
M. −4
P. −3
R. −2
S. 2
T. 3
V. 4
To find the values of x for which (x2 − 4)(x + 3) = 0, we can use the zero product property which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we can set each factor equal to zero and solve for x:
(x2 − 4) = 0 or (x + 3) = 0
Solving for x in the first equation, we get:
x2 = 4 x = ±2
Solving for x in the second equation, we get:
x = −3
Therefore, the values of x for which (x2 − 4)(x + 3) = 0 are −2, 2, and −3. The answer choices that correspond to these values are R. −2, S. 2, and P. −3.
In a sample of 20 items, you found six defective. In constructing a confidence interval for the proportion of defectives, you should use: the plus four method. the large-sample interval. neither of these two methods.
To construct a confidence interval for the proportion of defectives, we should use the plus four method.
Since the sample size is 20, which is not very large, the large-sample interval is not appropriate. Instep, we ought to utilize a strategy that's suitable for little test sizes.
The plus four method is one such method that is commonly used when the sample size is small. Therefore, to construct a confidence interval for the proportion of defectives, we should use the plus four method.
The plus four strategies may be a strategy for building a certainty interim for an extent when the test estimate is little.
To utilize this strategy, we to begin with include four fanciful perceptions to our test, two of which are flawed and two of which are not imperfect.
This increments the test estimate to 24, which permits us to utilize the typical guess to the binomial dispersion to build the certainty interim.
The equation for the certainty interim utilizing the also four strategies is:
p ± zα/2 √((p + 2) (1 - p + 2) / n + 4)
where:
p is the test extent (number of defectives/test estimate)
zα/2 is the basic esteem from the standard typical dissemination at the level of importance α/2
n is the test estimate (counting the included four nonexistent perceptions)
Therefore, to construct a confidence interval for the proportion of defectives, we should use the plus four method.
learn more about the plus four method
brainly.com/question/31504643
#SPJ4