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In terms οf area οf circle the radius οf the circle becοmes, r = √(A/π)

In Mathematics  a circle is a special kind οf ellipse. In this particular kind οf ellipse the eccentricity is zerο and the twο fοci are cοincident. A circle is alsο stated as the lοcus οf the pοints which drawn at an equidistant frοm the center and the distance frοm the center οf the circle tο the οuter line(circumference) is the radius οf the circle.

The area οf a circle is given by A= π r² where r is the radius οf the circle and π= 3.14

Frοm the given equatiοn we have tο determine the value οf r that is the radius οf the circle.

A= π r²

Dividing by π tο the bοth sides οf the equatiοn we get,

⇒A/π = r²

⇒ r² = A/π [ Reversing bοth sides ]

Taking square rοοt tο the bοth sides οf equatiοn we get,

⇒ r= ±√(A/π)

Nοw radius οf a circle cannοt be negative sο the negative value will be neglected.

Hence, in terms οf area οf circle the radius οf the circle becοmes

r= √(A/π)

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The exponential function shown in the table has the equation y = 3 * 4x.

The general form of an exponential function is y = [tex]ab^x[/tex], where "a" is the initial value of y when x = 0 and "b" is the common ratio.

Using the given table, we can find "a" by looking at the value of y when x = 0, which is 3. So, a = 3.

To find "b", we can use the ratio of consecutive outputs:

b = y2 / y1 = 48 / 12 = 4

We can verify this ratio by also checking the ratio of y3 to y2:

b = y3 / y2 = 192 / 48 = 4

Therefore, the equation of the exponential function represented by the table is:

y = 3 * 4^x

where x is the input (the value of x in the table) and y is the output (the corresponding value of y in the table).

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The number who prefer Bears is 45 when there are approximately 166.67 students in the school who Jermaine surveyed.

In mathematics, an equation is a statement that shows the equality between two expressions. An equation typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The expressions on either side of the equal sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation.

Here,

Let's use a table to organize the given information:

Wildcats Bears Eagles Total

Male  0.15x  0.45x

Female 0.30y  0.28y 0.55y

Total 0.30z 0.15z 0.28z 1.00z

Total Students   120

Here, x, y, and z represent the total number of males, females, and students, respectively, and we use percentages to represent the proportion of each group that prefers each mascot. We can use the given information to fill in some of the missing values in the table. For example:

The total number of males who prefer Bears is 0.15x, and the number of people who prefer Bears is 20 fewer than the number who prefer Eagles, so the number of males who prefer Bears is 20 less than the number who prefer Eagles, or 0.15x = 0.28y - 20.

The total number of students is 120, so z = x + y.

Using these equations and the information in the table, we can solve for the remaining values in the table:

Wildcats Bears Eagles Total

Male 0.30x 0.15x 0.45x 0.45x

Female 0.30y 0.12y 0.28y 0.55y

Total 0.30z 0.15z 0.28z 1.00z

Total Students 0.30z 0.27z 0.43z 120

To find the number of students who prefer Bears, we can multiply the total number of students by the proportion who prefer Bears:

0.27z = 0.15z - 20

0.12z = 20

z = 166.67

So there are approximately 166.67 students in the school who Jermaine surveyed. The number who prefer Bears is:

0.27z = 0.27 * 166.67

= 45

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The Upper bound of this interval is 0.582.

To construct a 90% confidence interval to estimate the population proportion, we need to use the formula:

sample proportion ± z*√((sample proportion*(1-sample proportion))/sample size)

where z is the z-score corresponding to a 90% confidence level. Using a table or calculator, we find that the z-score is 1.645.

If the sample proportion is not given in the question, we cannot proceed with the calculation. However, assuming that the sample proportion is equal to 0.5 (which is a common assumption if no information is given), we can plug in the values:

0.5 ± 1.645*√((0.5*(1-0.5))/n)

If we assume a sample size of n = 100, then the confidence interval is:

0.5 ± 1.645*√((0.5*(1-0.5))/100) = 0.5 ± 0.082

Rounding to three decimal places, the confidence interval is [0.418, 0.582]. This means that we can be 90% confident that the true population proportion lies within this range. The upper bound of this interval is 0.582.

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Answer: Class 2

Step-by-step explanation:Because the median point is higher than class 1

From the boxplot of homework assignments data, the median number of submitted homework assignments by math class 2 to the Ms. chang is higher

A box with whisker plot also called a box plot, it is a graphical way of displaying the distribution of data based on a five number summary. The five numbers summary includes minimum, first quartile [Q1], median, third quartile [Q3] and maximum.

We have two box plots present in attached figure. Ms. chang tracked the submitted assignment by her class through the box plots. Here orange and blue box plots show the data of number homework assignments of her maths class 1 and class 2 submitted each day respectively. Now, see the box plot and use above discussed definition of median, we conclude that median number of class 1 = 25

Median number of class 2 = 26 > 25.

Hence, class 2 has a higher median number than class 1.

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Complete question:

The attached figure complete the question.

The equation for the line of best fit is a useful tool in data analysis to describe the relationship between two Variables and make predictions based on that relationship.

The equation for the line of best fit is a mathematical formula that describes the relationship between two variables in a data set. It is used in regression analysis to estimate and predict the value of one variable based on the value of another.

To find the equation for the line of best fit, we use the method of least squares, which minimizes the sum of the squares of the differences between the observed data points and the predicted values from the equation.

The equation takes the form of y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. The slope represents the rate of change of y with respect to x, and the y-intercept is the value of y when x = 0.

The coefficient of determination, denoted as r, is a measure of how well the line fits the data. It ranges from -1 to 1, where a value of 1 indicates a perfect fit, and a value of 0 indicates no correlation. A negative value indicates an inverse relationship.

In summary, the equation for the line of best fit is a useful tool in data analysis to describe the relationship between two variables and make predictions based on that relationship.

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The Fahrenheit temperature of the can of soda, after 60 minutes, given the value of K would be 55°F.

We can use Newton's Law of Cooling formula to find the value of k:

58 = 35 + (73 - 35) x e ^ (-k x 40)

23 = 38 x e ^ (-k x 40)

23/38 = e ^ (-k x 40)

ln(23/38) = -k x 40

k = -ln(23/38) / 40 ≈ 0.010

Now that we have the value of k, we can find the temperature of the can of soda after 60 minutes (t = 60):

T = 35 + (73 - 35) x e ^ (-0.010 x 60)

T ≈ 35 + 38 x e ^ (-0.6) = 35 + 38 x 0.5488 = 54.856

The temperature of the can of soda after 60 minutes is approximately 55°F (rounded to the nearest degree).

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The circumference of the circle is approximately 69.115 kilometers.

What is circle ?

A circle is a closed two-dimensional shape where all points on the edge are equidistant from the center point. It can be defined as the set of all points in a plane that are at a given distance, called the radius, from a given point, called the center.

The circumference of a circle can be calculated using the formula:

C = 2πr

where r is the radius of the circle and π is the mathematical constant pi (approximately equal to 3.14159).

Substituting r = 11 kilometers into the formula, we get:

C = 2π(11) ≈ 69.115 kilometers

Therefore, the circumference of the circle is approximately 69.115 kilometers.

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Using expression 2x - 1,876.23 = 1,692.45, each of Ivy's paychecks is approximately $1,784.34.

What exactly are expressions?

In mathematics, an expression is a combination of symbols and/or numbers that represents a value or a set of values. Expressions can contain variables, constants, operations, and functions, and can be combined using mathematical operators such as addition, subtraction, multiplication, division, and exponentiation.

Now,

Let's assume that Ivy's paychecks are of equal amounts, and each paycheck is of amount "x".

According to the problem, Ivy received two paychecks and withdrew a total of $1,876.23 from her account. Therefore, we can set up the following equation:

2x - 1,876.23 = 1,692.45

Solving for x, we can simplify the equation as follows:

2x = 1,692.45 + 1,876.23

2x = 3,568.68

x = 3,568.68 / 2

x ≈ 1,784.34

Therefore, each of Ivy's paychecks is approximately $1,784.34.

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The correct inequality to represent this situation would be c ≥ 15, which means that the number of customers is at least 15.therefore option D. No; The number of customers is at least 15 is correct.

The inequality c < 15 represents the least number of customers in a shop at any time during the day was 15.

The inequality Fran represented, c < 15, means that the number of

customers is less than 15. However, the question stated that the least

number of customers in the shop at any time during the day was 15.

We are given the following in the question:

Fran used the given inequality to represent the number of customers in

a shop at any time. where c is the number of customer during any time of

day.

Therefore, the correct inequality to represent this situation would be c ≥ 15, which means that the number of customers is at least 15.

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we can only see a portion of the graph of this function in the standard viewing window of -10 to 10.

What is Graph ?

In mathematics, a graph is a visual representation of a set of objects, such as numbers or data points, and the relationships between them. Graphs can be used to represent a variety of mathematical concepts, including functions, sets of data, and geometric shapes.

The function f(x) = -|x| - 12 is a piecewise function. When x is greater than or equal to zero, the function simplifies to f(x) = -x - 12, and when x is less than zero, it simplifies to f(x) = x - 12.

If we graph both of these pieces separately, we get two straight lines that intersect at the point (0, -12), where the absolute value of x changes sign. The slope of both lines is -1, which means they are both downward sloping with a negative slope.

When we graph this function in the standard viewing window of -10 to 10, we can see the part of the graph where x is greater than or equal to zero, which is the left side of the graph, but the part where x is less than zero, which is the right side of the graph, is outside the viewing window.

Therefore, we can only see a portion of the graph of this function in the standard viewing window of -10 to 10.

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The probability of rolling no 2's and no 5's in 10 rolls is approximately 0.107.

The probability of rolling no 2's and no 5's on a fair die can be calculated using the formula for the probability of independent events:

P(A and B) = P(A) x P(B)

where P(A) is the probability of event A occurring, and P(B) is the probability of event B occurring.

The probability of rolling any number other than 2 or 5 on a single roll of a fair die is 4/6, or 2/3. Since each roll is independent, the probability of rolling no 2's and no 5's in n rolls can be calculated as follows:

P(no 2's and no 5's in n rolls) = (4/6)^n

To round the answer to three decimal places, we can use a calculator. For example, if n = 10, the probability is:

P(no 2's and no 5's in 10 rolls) = [tex](4/6)^10[/tex] = 0.107

So the probability of rolling no 2's and no 5's in 10 rolls is approximately 0.107, rounded to three decimal places.

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Answer: down beloe

Step-by-step explanation:

Well, you could see the rate of rebirth, and see

if it has been going up or down, then all you need to do is multiply that by 40 thousand

The exact volume of the cone is 3,087.18 cubic inches.

A cone is a three-dimensional geometric form with a flat base and a smooth tapering apex or vertex. The curving surface of it slopes upward towards the apex and has a round base. The radius of the base is the distance from the centre of the base to its edge, and the height of the cone is the separation between the base and the apex.

The formula for the volume of a cone is:

V = 1/3 * πr²h

Substituting the given values, we get:

V = 1/3 * 3.14 (9²) (11)

V = 1/3 * 3.14 (81)(11)

V = 1/3 (9,261.54)

V = 3,087.18 cubic inches

Hence, the exact volume of the cone is 3,087.18 cubic inches.

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The sample size necessary such that the margin of error of the estimate for a 90% confidence interval for the mean age of all residents is at most 3.4 years is 59.56.

An estimated range for an unknown parameter is known as a confidence interval. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.

Given: A city official would like to estimate the mean age of all residents of Stuart. The standard deviation of the ages of all residents of Stuart is known to be 16 years.

σ = 16 ..Population SD

The margin of error, E = 3.4

c = 90% = 0.90 ...confidence level

a = 1 - c = 1 - 0.90 = 0.1

a/2 = 0.1/2 = 0.05

Using the Z table,

z = 1.64

Now, sample size (n) is given by,

(za/E)²

(1.64×16/3.4)² = 59.56

Hence, the sample size necessary such that the margin of error of the estimate for a 90% confidence interval for the mean age of all residents is at most 3.4 years is 59.56.

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Answer: A and C

Step-by-step explanation: It’s not independent or dependent because,

independent= doesn’t depend on another (cause)

dependent= depends on another (effect) —> maybe if this were about weight gain/ weight loss.

I would go with

C and A.

It makes the most sense food wise.

Answer: 60 %

Step-by-step explanation:

To find what percent 144 is of 240, we can use the following proportion:

part/whole = percent/100

Let x be the percentage we are trying to find, then we can write:

144/240 = x/100

To solve for x, we can cross-multiply:

14400 = 240x

Dividing both sides by 240, we get:

x = 14400/240 = 60

Therefore, 144 is 60% of 240.

Answer:

60%

Step-by-step explanation:

Percent proportion:

240 - 100%

144 - x%

Cross-multiply to find x:

[tex] \frac{144 \times 100\%}{240} = \frac{14400}{240} = 60\%[/tex]

So, 144 is 60% of 240

Yes, there is convincing statistical evidence of an association between grade in the preceding Biology II course and whether a student asks for clarification at the 5% level of significance, with a test statistic of 8.25 and a p-value less than 0.05.

To determine if there is convincing statistical evidence of an association between grade in the preceding Biology II course and whether a student asks for clarification, we need to conduct a hypothesis test using the chi-square test.

Null Hypothesis: There is no association between grade in the preceding Biology II course and whether a student asks for clarification.

Alternative Hypothesis: There is an association between grade in the preceding Biology II course and whether a student asks for clarification.

Since the test statistic for the chi-square test is given as 8.25, we need to find the corresponding p-value for this test statistic. The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed test statistic, assuming the null hypothesis is true.

We can use a chi-square distribution table with 1 degree of freedom (since we have 2 categories - whether the student asks for clarification or not - and 3 levels of grade in the preceding Biology II course) to find the p-value. The p-value for a test statistic of 8.25 with 1 degree of freedom is less than 0.01.

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On solving the provided question we can say that So, we have two solutions: t = (9/2) or t = (-6/2) = -3

A quadratic equation is x ax2+bx+c=0, 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 "ax2 + bx + c = 0." where a, b, and c are numerical coefficients or constants. where the variable "X" is unnamed.

So, we can set h(t) = 0 and solve for t:

[tex]0 = t^2 + 3t - 18\\t = (-3 + \sqrt (3^2 - 4(1)(-18))) / (2(1))\\t = (-3 + \sqrt (81)) / 2\\t = (-3 + 9) / 2\\[/tex]

So, we have two solutions:

t = (9/2) or t = (-6/2) = -3

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Answer:

X= -3

Step-by-step explanation:

The equation of the line parallel to y-axis and passing through (-3, 3) is

x = -3

What is equation?

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, a line passing through (-3,3), parallel to the y-axis,

The slope intercept form is given by,

y = mx+c

Where, m is the slope and c is the y intercept.

When any parallel to x or y-axis, its slope is zero,

Therefore,

3 = 0x-3+c

c = 3

Therefore, y = 3

The question is asking for line parallel to x-axis and passing through (-3, 3)

Hence, the required equation is x = -3

The main logical weakness of the conclusion is the hasty generalization made from a potentially unrepresentative sample. To strengthen the argument, a more comprehensive survey of the university's student population should be conducted.

The most important logical weakness of the conclusion that "25 percent of all students at the university watch eight or more hours of television a week" based on the observation from your morning statistics class is that it involves a hasty generalization.
A hasty generalization occurs when you draw a conclusion about a larger group based on a smaller, unrepresentative sample. In this case, the student question assumes that the morning statistics class is representative of the entire university, which may not be true.
To better explain this logical weakness, let's break down the steps:
The student observes that 25 percent of the students in their morning statistics class watch eight or more hours of television a week.
The student then concludes that this must apply to all students at the university.
The conclusion does not account for potential differences between the morning statistics class and other classes or students at the university.
To overcome this logical weakness, a more representative sample of the university's student population should be surveyed to accurately determine the percentage of students who watch eight or more hours of television a week. This might involve selecting students from different majors, class schedules, and demographic backgrounds to ensure that the sample truly represents the entire university population.

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When a school day is selected and either red or gray is chosen, there are 14 possible outcomes. The sample space is a way to show all possible outcomes, and the correct answer is option (B), which lists 10 possible outcomes.

How to find out the way?

The first bag contains 7 numbers, one for each day of the week, and the second bag contains 4 colored cards, but only 2 colors are acceptable. Therefore, there are 7 x 2 = 14 possible outcomes when a school day is selected and either red or gray is chosen.

The sample space for the problem lists all possible outcomes. Option (A) lists all 20 possible outcomes for any combination of day and color. Option (C) lists all 10 possible outcomes for any combination of day and color, but with the wrong color choices. Option (D) lists 14 possible outcomes, but includes the color pink, which is not an acceptable choice.

Option (B) is the correct answer, as it lists all 10 possible outcomes when a school day is selected and either red or gray is chosen. These outcomes are 2R, 3R, 4R, 5R, 6R, 2G, 3G, 4G, 5G, and 6G. Therefore, Penny's friend should choose a day between Monday and Saturday and wear either red or gray track pants on the first day of sprint training.

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Answer:

1450

Step-by-step explain:

(35x35)+(15x15)

1225+225

Answer:

Step-by-step explanation:

The required common solutions of the given equations are x=-1 and x=3.

To find the common solution of the given equations graphically, we need to graph both f(x) and g(x) on the same coordinate plane and find the x-value(s) where the graphs intersect.

To graph f(x)=-x+5, we can start by plotting the y-intercept at (0,5), and then draw a straight line that goes down 1 unit for every 1 unit we move to the right.

To graph g(x)=x²-3x+2, we can start by finding the x-intercepts, which are the points where the graph crosses the x-axis. We can do this by factoring the quadratic equation: x²-3x+2=(x-1)(x-2). This gives us two x-intercepts at (1,0) and (2,0). We can also find the vertex of the parabola, which is at x=3/2. The graph of g(x) is a parabola that opens upwards, with its minimum point at (3/2,-1/4).

From the graph, we can see that the two functions intersect at two points, which are (-1, 6) and (3, 2).

Therefore, the common solutions of the given equations are x=-1 and x=3.

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The area of the completed poster is 42 square units.

The answer is (c) 42 square units.

The area of a rectangle is the total amount of space or region enclosed within the boundaries of a rectangle.

It is measured in square units, which is the product of the length and the width of the rectangle.

The formula for calculating the area of a rectangle is:

Area = Length x Width

Here we have

Cara and Beejal make a poster for school.

The poster is in the shape of a rectangle. The left side of the poster measures 7 units; the top side of the poster measures 6 units.

The area of a rectangle is found by multiplying its length by its width.

In this case, the length of the poster is 7 units and the width is 6 units, so the area is:

Area = length × width

Area = 7 × 6

Area = 42 square units

Therefore,

The area of the completed poster is 42 square units.

The answer is (c) 42 square units.

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Answer:

The standard deviation for the number of people with the genetic mutation in groups of 900 is approximately 6.54.

Step-by-step explanation:

To find the standard deviation for the number of people with the genetic mutation in groups of 900, we can use the properties of the binomial distribution. The binomial distribution describes the number of successes (in this case, people with the genetic mutation) in a fixed number of independent Bernoulli trials (in this case, selecting people), each with the same probability of success.

In our case, we have:

n = 900 (number of trials, i.e., the number of people in each group)

p = 0.05 (probability of success, i.e., the probability of having the genetic mutation)

The mean (μ) and variance (σ²) of a binomial distribution can be calculated using the formulas:

μ = n * p

σ² = n * p * (1 - p)

We are interested in finding the standard deviation (σ), which is the square root of the variance:

σ = sqrt(σ²)

So, in our case:

σ = sqrt(900 * 0.05 * (1 - 0.05))

σ = sqrt(900 * 0.05 * 0.95)

σ ≈ sqrt(42.75)

σ ≈ 6.54

Thus, the standard deviation for the number of people with the genetic mutation in groups of 900 is approximately 6.54.

The standard deviation for the number of people with the genetic mutation in such groups of 900 is approximately 6.48.

To find the standard deviation for the number of people with the genetic mutation in groups of 900, you can use the formula for the standard deviation of a binomial distribution:

σ = √(n * p * (1-p))

Here, n = 900 (number of people randomly selected), p = 0.05 (5% of the population has the genetic mutation).

σ = √(900 * 0.05 * (1 - 0.05))
σ = √(45 * 0.95)
σ ≈ 6.48

The standard deviation for the number of people with the genetic mutation in such groups of 900 is approximately 6.48.

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The value of B in continuous variable is 1/333.

Suppose x is a continuous variable with the probability density function f(x) = { B(10 - x)^2 for 0 < x < 10, and 0 otherwise.

To find the value of B, we need to use the fact that the total probability must equal to 1. In other words, we need to integrate the probability density function f(x) over the given interval and set it equal to 1:

∫[0,10] B(10 - x)^2 dx = 1

First, let's perform the integration:
∫(10 - x)^2 dx = [(-1/3)(10 - x)^3] + C
Now, apply the limits of integration:

[-(1/3)(10 - 10)^3] - [(-1/3)(10 - 0)^3] = 1
0 - [(-1/3)(10^3)] = 1
(1/3)(1000) = 1

Now, solve for B:
B = 3/1000 = 1/333
So, the value of B is 1/333.

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1/2 divided into 5 equal parts is 1/10.

We have,

To divide 1/2 into 5 equal parts, we need to perform the division operation:

(1/2) ÷ 5.

To divide fractions, we can multiply the numerator of the first fraction by the reciprocal of the second fraction.

The reciprocal of 5 is 1/5.

So, we have:

(1/2) × (1/5).

Multiplying the numerators gives us 1, and multiplying the denominators gives us 2 × 5 = 10.

Therefore,

1/2 divided into 5 equal parts is 1/10.

In other words, each part is 1/10 of 1/2.

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The location of J' after transformation is (3, 7).

In mathematics, a transformation is a process or operation that changes the position, orientation, size, or shape of a geometric object or a set of objects. Transformations are often used in geometry to study and analyze the properties of shapes and figures, as well as to solve problems related to their construction, symmetry, and congruence.

Given: Silas transformed point J(-3, -7) using the rule (x, y) → (-x, -y).

The rule (x, y) → (-x, -y) reflects a point over both the x-axis and the y-axis. This is a type of transformation known as a "point reflection" or "central symmetry" where the point is reflected across a point located at the origin (0,0).

When Silas applies this rule to point J(-3, -7), the x-coordinate changes from -3 to 3, and the y-coordinate changes from -7 to 7.

Therefore, the location of J' is (3, 7).

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This equation tells us that the cost in dollars c is equal to the unit rate of $0.55 per green pepper.

what is linear equation?

A linear equation is a mathematical equation that represents a straight line when graphed on a coordinate plane. It is an equation of the form:

y = mx + b

where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept (the point where the line intersects the y-axis).

To find the unit rate, we need to divide the total cost of the green peppers by the number of peppers purchased:

Unit Rate = Total Cost ÷ Number of Green Peppers

Unit Rate = $4.40 ÷ 8 = $0.55 per green pepper

Now, to write an equation relating the cost in dollars c to the number of green peppers p, we can use the unit rate we just calculated. We know that for each green pepper, the cost is $0.55, so we can write:

c = $0.55p

This equation tells us that the cost in dollars c is equal to the unit rate of $0.55 per green pepper, multiplied by the number of green peppers p being purchased.

To learn more about linear equations from the given link

https://brainly.com/question/11897796?

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