a) The probability that the battery lasts more than 4 hours is 0.758 (rounded to 3 decimal places).
b) The 25% value is 240 minutes, and the 75% value is 310 minutes.
c) The value of life in minutes that is exceeded with 95% probability is 357 minutes.
a) To find the probability that the battery lasts more than 4 hours (240 minutes), we first need to convert 240 minutes into a z-score.
z = (X - μ) / σ
z = (240 - 275) / 50
z = -0.7
Now, we'll use a z-table to find the probability that the battery lasts more than 4 hours:
P(Z > -0.7) = 1 - P(Z ≤ -0.7) = 1 - 0.2420 = 0.758
The probability that the battery lasts more than 4 hours is 0.758 (rounded to 3 decimal places).
b) To find the quartiles, we'll use the z-table to find the z-scores corresponding to 25% and 75%:
25%: z = -0.674
75%: z = 0.674
Now, we'll convert the z-scores back into minutes:
Q1 = μ + z * σ = 275 + (-0.674) * 50 = 240 (rounded to the nearest integer)
Q3 = μ + z * σ = 275 + (0.674) * 50 = 310 (rounded to the nearest integer)
The 25% value is 240 minutes, and the 75% value is 310 minutes.
c) To find the value of life in minutes that is exceeded with 95% probability, we first find the z-score corresponding to 95%:
95%: z = 1.645
Now, we'll convert the z-score back into minutes:
X = μ + z * σ = 275 + (1.645) * 50 = 357 (rounded to the nearest integer).
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The circle graph shows how the annual budget for a company is divided by department. If the total annual budget is $12,500,000, what amount is budgeted for Marketing?
In the circle graph, the amount budgeted for marketing is
4,750,000What is circle graphA circle graph is another term for a pie chart, which is a type of data visualization that represents data as a circle, divided into sectors or slices, each representing a proportion or percentage of the total data set.
The size of each sector is proportional to the value it represents, so larger sectors indicate larger values, and smaller sectors indicate smaller values.
In the circle graph, when the total annual budget is $12,500,000. The amount budgeted for marketing is
= 38/100 * 12,500,000
= 4,750,000
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g(x) = (x – )2 + Which are characteristics of the graph of the function f(x) = (x + 1)2 + 2? Check all that apply. The domain is all real numbers. The range is all real numbers greater than or equal to 1. The y-intercept is 3. The graph of the function is 1 unit up and 2 units to the left from the graph of y = x2. The graph has two x-intercepts.
Answer:
The characteristics of the graph of the function f(x) = (x + 1)² + 2 are:
The domain is all real numbers . (option A)
The range is all real numbers greater than or equal to 1 . (option B)
The y-intercept is 3. (option C)
The graph has two x-intercepts. (option E)
Find the value of x and round to the nearest tenth
Answer:
x ≈ 22,6°
Step-by-step explanation:
Use trigonometry:
[tex] \cos(x°) = \frac{12}{13} [/tex]
Use the reverse (SHIFT, cos (12/13)) function on your calculator to find the approximate value of x:
x ≈ 22,6°
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
IQR, because Sunny Town is skewed
IQR, because Desert Landing is symmetric
Range, because Sunny Town is skewed
Range, because Desert Landing is symmetric
Answer:
Range, because it measures the difference between the highest and lowest values in a dataset, providing a clear measure of variability for both sets of data. It is not affected by skewness or symmetry, which makes it a useful measure of variability for comparing the temperature consistency between Desert Landing and Flower Town.
Step-by-step explanation:
Hope this helps!=D
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a researcher believes that 4% of pet dogs in europe are labradors. if the researcher is right, what is the probability that the proportion of labradors in a sample of 851 pet dogs would be greater than 5% ? round your answer to four decimal places.
The probability that the proportion of Labradors in a sample of 851 domestic dogs exceeds 5% is 0.0003.
This is a binomial distribution problem with parameters n = 851 and p = 0.04. We need to calculate the probability of the proportion of Labradors in the sample is greater than 5%.
Let X be the number of labs in the sample.
we need to calculate the mean μ and standard deviation σ of X.
μ = np = 851 * 0.04 = 34.04
standard deviation:
σ = sqrt(np(1-p)) = sqrt(851 * 0.04 * 0.96) = 4.91
Now we can use the normal distribution to approximate the binomial distribution. The 5% value should be normalized.
z = (0.05 * 851 - 34.04) / 4.91 = 3.46
Find the probability that the z-score is greater than 3.46. Using a standard normal distribution table or calculator, we find this probability to be approximately 0.0003.
Therefore, the probability that the proportion of Labradors in a sample of 851 domestic dogs exceeds 5% is 0.0003.
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Bradley cut a square hole out of a block of wood in wood shop. If the block was cube-shaped with side lengths of 8 inches, and the hole had side lengths of 5 inches, how much wood was left after the hole was cut out?
there are 312 cubic inches of wood left after cutting out a square hole with side lengths of 5 inches from a cube-shaped block with side lengths of 8 inches.
How to find the volume ?
To find the volume of the remaining wood, first find the volume of the cube-shaped block. To find the volume of a cube use V = s³ where s is the side of the cube. In this case, s = 8 inches, so V = 8³ = 512 cubic inches.
Then, find the volume of the hole using the side lengths of the hole and the same depth as the cube, which is 8 inches. The hole has side lengths of 5 inches, so its volume is V = 5² * 8 = 200 cubic inches.
To find how much wood is left after cutting out the hole, subtract the volume of the hole from the volume of the cube:
512 - 200 = 312 cubic inches
Therefore, there are 312 cubic inches of wood left after cutting out a square hole with side lengths of 5 inches from a cube-shaped block with side lengths of 8 inches.
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What is the angle ABC to the nearest angle
By using a protractor or visual estimation, we can estimate the measure of angle ABC to the nearest degree.
To answer your question, let's first start with defining what an angle is. An angle is formed by two rays or line segments that share a common endpoint, called the vertex. The measure of an angle is usually given in degrees and is determined by how much the two rays are turned away from each other.
Now, let's look at the specific angle you asked about, angle ABC. Without a diagram or any additional information about the position of point B and C, it is impossible to determine the measure of angle ABC. However, we can make some general assumptions based on the fact that angle measures range from 0 to 360 degrees.
Assuming that angle ABC is a standard angle and not a reflex angle (i.e. it measures less than 180 degrees), we can estimate the measure of angle ABC to the nearest degree by using a protractor or by visual estimation. A protractor is a tool used to measure angles in degrees, and can be found at most office supply stores or online.
If we don't have access to a protractor, we can still estimate the measure of angle ABC by comparing it to other angles we know the measure of. For example, if angle ABC looks to be about halfway between a right angle (90 degrees) and a straight angle (180 degrees), we can estimate that angle ABC measures around 135 degrees.
In summary, without additional information about the specific position of points B and C, we cannot determine the exact measure of angle ABC. However, by using a protractor or visual estimation, we can estimate the measure of angle ABC to the nearest degree.
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page 1 of 2
In Target One Fractions, players choose three numbers to create a whole number and
a fraction that have a product close to 1. Their score is the difference between their
product and 1, and the lowest score wins the round.
1 Erica is playing Target One Fractions. She has these cards: 1, 2, 3, 4, 6.
a Which three cards should she choose to make a whole number and a fraction
that have a product close to 1?
62/3
b Write an expression for the problem Erica will solve.
2/3×4=4
c Solve the problem.
6=2₁b = 6₁ c=30r a=3,5=60-a
d What is Erica's score for this round?
Answer: a) Erica should choose 2, 3, and 6 to make a whole number and a fraction that have a product close to 1.
2 x 3 x 6 = 36, which is close to 1 when expressed as a fraction: 1/36.
b) (2/a) x (3/b) x (6/c) = 1
c) Multiplying both sides by a, b, and c, we get:
6bc = 2ac
3ac = ab
6ab = bc
Multiplying the three equations together, we get:
(6abc)^2 = (2ac) x (3ab) x (6bc)
216a^2 b^2 c^2 = 36a^2 b^2 c^2
a^2 b^2 c^2 = 1/6
Taking the square root of both sides, we get:
abc = 1/sqrt(6)
So, Erica's whole number is 2 x 3 x 6 = 36, and her fraction is 1/sqrt(6). The product of these is:
36 x 1/sqrt(6) = 6sqrt(6)
Her score is the absolute difference between 6sqrt(6) and 1:
|6sqrt(6) - 1| = 13.97 (rounded to two decimal places).
d) Erica's score for this round is 13.97.
Step-by-step explanation:
Chelsea and her two friends split a pizza. They each paid $5. Write a one-step equation for
Answer:
Step-by-step explanation:
$7
Answer:
7$
Step-by-step explanation:
Find the third and first quartile of the data: 0 0 1 6 9 9 10 11 11 12 13 14 15 15 21 22
The first and third quartiles of the given data set are 7.5 and 15.
What is the Median?The median represents the middle number when a dataset is arranged in order. The median is the value that falls in the center when there are an odd number of values. The median is the average of the two center values when there are even more values.
The methods listed below can be used to determine the first and third quartiles of the provided data set:
Step 1: A data collection should be arranged in ascending order:
0 0 1 6 9 9 10 11 11 12 13 14 15 15 21 22
Step 2: Determine the data set's middle.
The median value in the data collection is known as the median. The median is the middle value when the number of values in the data collection is odd. The median is the average of the two middle values when the number of values in the data collection is even.
The data set in this instance contains 16 values, which is an even amount. In order to calculate the average, we select the two middle values:
Median = (11 + 12) / 2 = 11.5
Step 3: Calculate the first quartile (Q1).
In the bottom half of the data set, Q1 represents the median. The median of the bottom half of the data set must first be determined in order to determine Q1.
The lower half of the data set: 0 0 1 6 9 9 10 11
It is an even number since the bottom half of the data set contains 8 values. Consequently, we calculate the average of the two center values:
Median of lower half = (6 + 9) / 2 = 7.5
Therefore, Q1 = 7.5
Step 4: Calculate the third quartile (Q3).
The middle point of the data set's top half is Q3. The median of the top half of the data set must first be determined before we can determine Q3.
The upper half of the data set: 12 13 14 15 15 21 22
Seven values, an odd number, are present in the data set's top half. The median, then, is the midpoint of the range:
The median value for the top half is 15.
Therefore, Q3 = 15
Hence, the first and third quartiles of the given data set are 7.5 and 15, respectively.
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factor the expression using the gcf, 144+216
please help will give brainliest
The correct explicit rule is f(n) = 50 + 30n
What is Explicit Rule?An explicit rule is a mathematical formula that directly gives the n-th term of a sequence or the value of a function for a given input, without the need to find other terms first. It can be expressed using variables, constants, and operations such as addition, subtraction, multiplication, and division.
To determine who is correct, we need to first understand the meaning of the variables in the explicit rules.
Let n be the number of days the car is rented for.
Let f(n) be the cost of renting the car for n days.
The deposit is a one-time charge and is not dependent on the number of days rented. Therefore, the constant term in the explicit rule should be 50.
Now, for each day rented, the cost is $30. This means that the cost for n days should be 30n.
So the correct explicit rule is:
f(n) = 50 + 30n
Therefore, Kevin is correct with the explicit rule f(n) = 50 + 30(n-1). This is because we subtract 1 from n since the deposit is charged only once at the beginning and is not included in the daily rate.
Suzanne's explicit rule, f(n) = 80 + 30(n-1), adds an extra $30 to the cost of renting the car, which is not correct.
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find the value of x that makes [tex]\frac{8^{3x} }{8^{2x+1} } =8^{9}[/tex] true.
The value of variable "x", which makes the equation " 8³ˣ/2²ˣ⁺¹ = 8⁹" true is 10.
We first simplify the left-hand side of the equation using the rules of exponents: which states that if the base of the numerator and denominator is same, then the power can be subtracted,
So, We have : 8³ˣ/2²ˣ⁺¹ = 8³ˣ - ⁽²ˣ⁺¹⁾ = 8ˣ⁻¹ ,
⇒ 8ˣ⁻¹ = 8⁹,
To solve for x, we can use the fact that if two exponential expressions with the same base are equal, then their exponents must be equal as well.
We equate,
⇒ x - 1 = 9,
⇒ x = 10,
Therefore, the value of x that makes the equation true is x = 10.
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What is the system of equation for this equation ?
Y=-2,4x-3y=18
Answer:
x = -30
y = 18
Step-by-step explanation:
-2,4x - 3y is equal to both 18 and y
Since there are two equal signs, we have a double equation (we can write each equation seperately and put them in a system):
{y = -2,4x - 3y,
{-2,4x - 3y = 18;
.
We move 3y to the left, so we change the sign to the opposite:
{4y = -2,4x, / : 4 (put y and 3y together)
{-2,4x - 3y = 18;
.
y = -0,6x,
-2,4x - 3y = 18;
Replace y in the 2nd equation with its value from the 1st equation:
-2,4x - 3 × (-0,6x) = 18
-2,4x + 1,8x = 18
-0,6x = 18 / : (-0,6)
x = -30
y = -0,6 × (-30) = 18
HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
- - 4 turns into + 4
then 3/4 + 7/12 + 4 find common denominator to add or subtract fractions
9/12 + 7/12 + 48/12 = ( 9+7+48 ) / 12 = 64/12 = 5 1/3
factorize quadratic expressions x-+x+6
After answering the presented question, we can conclude that Therefore, the factorization of the quadratic expression is: x =2 , x= -3
What is quadratic equation?A quadratic equation is x[tex]ax2+bx+c=0,[/tex]which is a single variable quadratic polynomial. a 0. Because this polynomial is of second order, the Basic Theorem of Algebra implies that it has at least one solution. Simple or complex solutions are possible. A quadratic equation is a quadratic equation. This means it has at least one word that must be squared. One of the most common solutions for quadratic equations is [tex]"ax2 + bx + c = 0.[/tex]" where a, b, and c are numerical coefficients or constants. where the variable "X" is unnamed.
In a quadratic equation
[tex]ax2+bx+c=0, to solve one splits the middle term in two parts so that their sum is b and product is ac.Hence, in x2+x−6=0 one needs to split 1×(−6)=−6 in two parts whose sum is 1. It is apparent that these are 3 and −2, hence x2+x−6=0 can be written asx2+3x−2x−6=0 orx(x+3)−2(x+3)=0 or(x−2)(x+3)=0i.e. either x−2=0 i.e. x=2or x+3=0 i.e. x=−3[/tex]
Therefore, the factorization of the quadratic expression is:
x = 2, x=-3
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question is - How do you factor and solve
[tex]x2+x−6=0?[/tex]
twice a number is fourteen
The number such that twice a number is fourteen is 7
Calculating the numberIf we let the number be "x", we can write the given information as an equation:
2x = 14
To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides by 2:
2x/2 = 14/2
x = 7
Therefore, the number is 7.
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Is the volume of the sphere 2/3 the volume of cylinder now ?
Yes, that’s correct! A sphere's volume is equivalent to a cylinder's volume by a factor of two-thirds whose height and diameter match the sphere's diameter
What is formula volume of sphere?The formula below can be used to calculate a sphere's volume:
V = 4/3πr³
what distinguishes a sphere from a cylinder?The points on the three-dimensional surface of a sphere are all equally far from the object's centre.
A cylinder is a three-dimensional shape made up of two parallel bases joined together by curves.
What distinguishes a sphere from a ball?A sphere is viewed by mathematicians as a two-dimensional closed surface encased in three-dimensional space that is Euclidean. They distinguish between spheres and balls, which are three-dimensional manifolds with boundaries that encompass the volume encompassed by the sphere.
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Math Journal Choose one of the following percents: 25%, 40%, or 60%. Use a
model and words to explain what that percent means. Write at least two fractions
that represent your percent.
End of Lesson Checklist
Two fractions that also represent 60% are 6/10 and 12/20, which can be simplified to 3/5.
What is percent?Percent is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%". Percentages are used in many areas, including finance, statistics, and science, to represent relative values or changes.
According to question:I choose 60%.
60% means 60 out of 100 or 60/100 or 3/5. It represents a fraction of a whole or a part of a group that is equivalent to 60 parts per 100 parts, or 3 parts per 5 parts.
For example, if there are 100 students in a class and 60 of them are girls, then 60% of the class are girls. Another example could be if a store is offering a 60% discount on a $100 item, then the discounted price would be $40.
Two fractions that also represent 60% are 6/10 and 12/20, which can be simplified to 3/5.
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URGENT!! Will give brainliest if right :)
If the formula X=.
Ex, is used to find the mean of the following sample,
what is the value of n?
51, 37, 83, 44, 52, 19, 99, 7, 36, 88
A. 11
B. 10
C. 9
D. 12
Answer:
Correct option is Option A
Step-by-step explanation:
Help which one I am very confused
Answer:
A. y=[x+4]-2
Step-by-step explanation:
what type of relation exists between the number of absences and the final grade? be sure to state the type, direction, and strength
There is a linear relationship between the number of absences and grade point average.
Number of absencesThe total number of absences depend on the number of students enrolled in a class. Therefore, a measure independent of the number of students is needed. This leads to the introduction of the concept of normalized absences.
It is defined as: Number of Absences / (Number of Students x Number of Contact Hours).
final gradeA Final Grade is the installation of specific materials - such as screened topsoil - on top of a clay base called, "Rough Grade" that promotes proper drainage and flow of excess water away from existing structures.
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Awarding 15 points for best answer!
Answer:
Step-by-step explanation:
First
what is the probability that a randomly selected person would be a protestant and at the same time bea democrat or a republican?
The probability of picking a red ball is 2/3.
As given in the student question,
The probability that a randomly selected person would be a protestant and at the same time be a democrat or a republican is not given in the problem statement.
Hence, it cannot be determined without further information.
Probability is the branch of mathematics that deals with the study of uncertainty.
It provides a framework for analyzing random events that occur in the real world.
Probability helps us to estimate the likelihood of a particular event occurring. It helps us to make informed decisions when faced with uncertain outcomes.
It plays a critical role in many fields such as science, engineering, economics, and finance.
Probability formula:
The probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes.
The formula for probability is given by:
P (A) = Number of favorable outcomes/ Total number of outcomes
where P (A) represents the probability of event A.
Example:
Suppose we have a bag containing 10 red balls and 5 blue balls.
The total number of outcomes = 10 + 5 = 15
The number of favorable outcomes = 10P (Red ball) = 10/15 = 2/3
Therefore, the probability of picking a red ball is 2/3.
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Felipe used 40 percent off coupon on single item at the craft store which saved him $16.42. What would be the item have cost if he had not used the coupon?
Answer:
41.05
Step-by-step explanation:
Given that-
Felipe used 40% off couponSaved him $16.42Original Cost [?]Solve-
Let, "p" represents his original cost.
0.4p = $16.42
0.4p/0.4 = $16.42/0.4 >> Divide both sides by 0.4
p = $16.42/0.40 >> $16.42/0.40 = $41.05
Answer- $41.05
The price of the item was $41.05 if he had not used the coupon.
RevyBreeze
Answer:
$41.05
Step-by-step explanation:
.40c = $16.42
c = $41.05
I NEED HELP ON THIS ASAP!!!
I hope this answer helps.
Select the correct answer. What are the solutions of this quadratic equation? x2 + 8x + 3 = 0 A. B. C. D. Reset Next
The sοlutiοns οf the quadratic equatiοn [tex]x^2 + 8x + 3 = 0[/tex] are:
[tex]x = -4 + \sqrt{(13)[/tex] and [tex]x = -4 - \sqrt{(13)[/tex]
What is quadratic equatiοn?it's a secοnd-degree quadratic equatiοn which is an algebraic equatiοn in x.
Tο find the sοlutiοns οf the quadratic equatiοn [tex]x^2 + 8x + 3 = 0[/tex], we can use the quadratic fοrmula:
[tex]x = (-b \± \sqrt{(b^2 - 4ac)}) / 2a[/tex]
where a = 1, b = 8, and c = 3.
Substituting these values intο the fοrmula, we get:
[tex]x = (-8 \± \sqrt{(8^2 - 4(1)(3))}) / 2(1)[/tex]
[tex]x = (-8\± \sqrt{(64 - 12)}) / 2[/tex]
[tex]x = (-8 \± \sqrt{(52)}) / 2[/tex]
[tex]x = (-8 \± 2\sqrt{(13)}) / 2[/tex]
[tex]x = -4 \± \sqrt{(13)[/tex]
Therefοre, the sοlutiοns οf the quadratic equatiοn [tex]x^2 + 8x + 3 = 0[/tex]are:
[tex]x = -4 + \sqrt{(13)[/tex] and[tex]x = -4 - \sqrt{(13)[/tex]
Sο the answer is οptiοn C.
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Complete Question:
What are the solutions of this quadratic equation?
x² + 8x + 3 = 0 A. B. C. D.
which of the following statements is an example of computer-readable data? a handwritten note brain waves a physical photograph a digital spreadsheet filled with measurements about the air quality of different major cities
The correct answer is d. A detailed spreadsheet filled with measurements about the air quality of different major cities is an example of computer-readable data.
Computer-readable data refers to any information that can be interpreted and processed by a computer system. A handwritten note, brain waves, and a physical photograph cannot be read and interpreted by a computer without undergoing a digitization process first.
On the other hand, a detailed spreadsheet containing well-structured data that can be easily read by a computer, such as in the case of air quality measurements, can be easily processed and analyzed by computer software. This data can be used to generate visualizations, perform statistical analysis, and extract insights that can inform decision-making.
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The question is -
Which of the following statements is an example of computer-readable data?
a. A handwritten note
b. Brain waves
c. A physical photograph
d. A detailed Spreadsheet filled with measurements about the air quality of different major cities
This circle is centered at the point (2, 6), and the length of its radius is 4. What is the equation of the circle?
Option D: [tex](x-2)^2+(y-6)^2=16[/tex] is the equation of the circle.
Explanation:
Given that the circle is centered at the point and the length of its radius is 4.
We need to determine the equation of the circle.
The equation of the circle with center and radius r is given by the equation,
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Substituting the center and the radius in the above formula, we get,
[tex](x-2)^2+(y-6)^2=4^2[/tex]
Simplifying the radius, we get,
[tex](x-2)^2+(y-6)^2=16[/tex]
Thus, the equation of the circle is [tex](x-2)^2+(y-6)^2=16[/tex]
Hence, Option D is the correct answer.
Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−6, −6), B(6, 6), C(0, 6). Determine the scale factor used.
2
one half
3
one third
Answer:
the scale factor is 2
Step-by-step explanation:
Take each x and y value and multiply it by 2 and you get the coordinates for the image.
Helping in the name of Jesus.
The scale factor is 2. Point B goes from (3,3) to (6,6). 6/3 is 2. Similar triangles have the same shape and the three angles' measurements are likewise the same.
Their sides are the only thing that differs. The scale factor, which is what is referred to here as this, is the ratio of one triangle's sides to those of another triangle. To calculate the scale factor for the smaller triangle to the bigger triangle, divide one of the sides in the bigger triangle by its corresponding side in the smaller triangle. In the example, the scale factor would be 2 if you divided 40 by 20.
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