Therefore, the bank can lend out $1,600 of Fiona's money.
What is percent?Percent, denoted by the symbol "%", is a way of representing a fraction or proportion out of 100. It is used to express a part of a whole in terms of hundredths. For example, 50% is the same as 50 out of 100, which simplifies to 1/2 or 0.5 as a decimal. Percentages are commonly used in many areas such as finance, statistics, and everyday life to express changes, rates, or comparisons.
Here,
If Fiona deposits $2,000 and the bank has a reserve ratio of 20%, then the bank can lend out 80% of her deposit.
Reserve = 20% x $2,000
= $400
Amount available for lending = $2,000 - $400
= $1,600
To know more about percent,
https://brainly.com/question/29172752
#SPJ1
At a recent baseball game of 5,000 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Mustard Chili
63 27 60
Based on the data in this sample, how many of the people in attendance would prefer mustard on a hot dog?
900
2,000
2,100
4,000
Answer:
We can estimate that 900 people in attendance would prefer mustard on a hot dog.
Step-by-step explanation:
What is proportion?
Proportion is a mathematical concept that refers to the relationship between two quantities, expressed as a ratio or a fraction. It represents the size of one quantity relative to another quantity, typically within a larger population or sample.
To determine the number of people who would prefer mustard on a hot dog, we need to use the proportion of people in the sample who prefer mustard and apply it to the total number of people in attendance.
The proportion of people in the sample who prefer mustard is:
27/150 = 0.18
To estimate the number of people who prefer mustard in the entire population of 5,000 attendees, we can multiply this proportion by the total number of attendees:
0.18 x 5,000 = 900
Therefore, we can estimate that 900 people in attendance would prefer mustard on a hot dog.
Answer:
2000 people prefer mustard on their hot dog.
900 people prefer chili on their hot dog
2100 people prefer ketchup on their hot dog
Step-by-step explanation:
hope this helps
find g(x+5): g(x)=3x^2+2 simplify as much as possible
The answer of the given question based on the expression is , the simplified expression for g(x+5) is 3x² + 30x + 73.
What is Expression?An expression is combination of numbers, variables, and operators (such as +, -, ×, ÷) that represents value or quantity. Expressions can be as simple as a single number or variable, or they can be complex with multiple terms and operations. Expressions can be evaluated or simplified by performing the indicated operations according to the rules of arithmetic and algebra.
To find g(x+5), we replace every occurrence of x in the expression for g(x) with x+5:
g(x+5) = 3(x+5)² + 2
Expanding the square and simplifying, we get:
g(x+5) = 3(x² + 10x + 25) + 2
g(x+5) = 3x² + 30x + 73
Therefore, the simplified expression for g(x+5) is 3x² + 30x + 73.
To know more about Variable visit:
https://brainly.com/question/2466865
#SPJ1
. Where is the vertex of the graph that represents y=(x−2)2−8 ? Type the answers in the boxes below. ( , ) b. Where is the y -intercept? Type the answers in the boxes below.
The vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.
Given equation :
y=(x−2)2−8
y = 2x - 4 - 8
= 2x - 12
The final equation is y = 2x - 12.
Compare this equation with slope and y-intercept formula :
y = mx+c
So that c = -12
The value of y-intercept according to the solution is -12.
To find the vertex. Let's assume x=0; Substitute in the equation
y = 2(0) -12
y = -12
The first vertex will be (0, -12)
If x = 1; y = 2(1) -12
y = -10
Then the second vertex will be (1, -10).
Hence, the vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.
To know more about equation check the below link:
https://brainly.com/question/17145398
#SPJ1
Try It
For a project, the teacher asked a group of seven students to each count the number of pedestrians that cross the street where they live on a certain day. The data collected had a range of 33 Sox of the seven data values
are shown below Find the missing data value
29,
15
22,,
11,
31,
15
The missing data value in the project is 25.5.
What is range?Range is a statistical measure that represents the difference between the highest and lowest values in a dataset. It is calculated by subtracting the smallest value in the dataset from the largest value.
According to question:To find the missing data value, we need to use the given range and the known data values.
The range is the difference between the highest and lowest values in the data set. So, if we sort the given data values in increasing order, we have:
11, 15, 15, 22, 29, 31
The range is 33, which means that:
highest value - lowest value = 33
31 - 11 = 33
So, the missing data value must be between 22 and 29 (since those are the values that are next to each other in the sorted list). To find the exact value, we can take the average of 22 and 29:
(22 + 29) / 2 = 25.5
Therefore, the missing data value is 25.5.
To know more about range visit:
https://brainly.com/question/28135761
#SPJ1
What I'd the measure of < jkl
Answer:
Your answer should be 116°
A Bakery sold 382 cakes in one week. this was twice as the day so the previous week. write an equation that can be used to find the number of cakes and that were sold the previous week 
Answer:
164 Cakes
Step-by-step explanation:
382 Cakes are made in Week A. This was twice the amount of Week B. 328 divided by two equals 164.
A factory received a shipment of 24 lightbulbs, and the vendor who sold the items knows there are 4 lightbulbs in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the lightbulbs in the sample are defective, he will refuse the shipment. For each of the following, give your responses as reduced fractions. If a sample of 4 lightbulbs is selected, find the probability that all in the sample are defective. If a sample of 4 lightbulbs is selected, find the probability that none in the sample are defective.
The probability that none of the 4 lightbulbs in the sample are defective is 805/1763 as a reduced fraction.
What is probability?
Let's first calculate the total number of ways to choose 4 lightbulbs from 24:
24 choose 4 = (24!)/(4! * 20!) = 10,626
Probability that all 4 lightbulbs in the sample are defective:
There are 4 defective lightbulbs in the shipment, so the number of ways to choose all 4 from the 24 is:
4 choose 4 = 1
So, the probability that all 4 lightbulbs in the sample are defective is:
1/10,626 = 1/5313
Therefore, the probability that all 4 lightbulbs in the sample are defective is 1/5313 as a reduced fraction.
Probability that none of the 4 lightbulbs in the sample are defective:
There are 4 defective lightbulbs in the shipment, so the number of ways to choose 4 non-defective bulbs from the remaining 20 is:
20 choose 4 = (20!)/(4! * 16!) = 4,845
So, the probability that none of the 4 lightbulbs in the sample are defective is:
4,845/10,626 = 805/1763
Learn more about probability:https://brainly.com/question/29221515
#SPJ1
Melissa collected the data in the table.
When x = 4, what is the residual?
–3
–1
1
3
From the data in the table, we can conclude that when x = 4, then the residual will equal -1.
How to determine the residualTo determine the residual, we can begin by obtaining the difference between the given and the predicted values of y.
So, Residual = Gven value - Predicted value.
When x = 4 in the table, Given value is 9 and predicted value is 10. So, 9 - 10 = -1. So, we can say that the residual value is -1.
Learn more about residual values here:
https://brainly.com/question/30243740
#SPJ1
Answer:
The residual is the difference between the actual y-value and the predicted y-value on a regression line. Since no table or equation is provided, we cannot calculate the exact residual. However, I can explain the concept to you.
Step-by-step explanation:
In general, to calculate the residual, we would need a regression equation or a line of best fit. This equation allows us to predict the y-values for different x-values. Then, we can compare the predicted values to the actual values given in the table to find the residuals.
If you have the regression equation or the line of best fit, I can help you calculate the residual for a specific x-value.
Identify all points and line segments in the picture below.
C
B
Points: A, B, C, D
Line segments: AB, BC, CD, AD, BD, AC
Points: A, B
Line segments: AB, AC, DC, BC
Points: A, B, C, D
Line segments: AB, AD, AC, LC, BC
Points: A, B, C, D
T
1019 DG DA
Answer:
The third option:
Points: A, B, C, D
Line segments: AB, AD, AC, DC, BC
8 Use the results of problem 5 and problem 6. Find the
sum of all the probabilities for Leon's experiment and
for Celia's experiment. Compare the sums and explain
the result.
Show your work.
Sum of all probabilities for Leon's experiment and for Celia's experiment are 1.
What is a probability?The study of random events and their likelihood of occurring is the focus of the probability field, which is a subfield of statistics. It is used to predict and estimate the likelihood of future events.
Based on the problems 4, 5 and 6 as discuss in figure, we have to find out the sum of all the probabilities for Leon's experiment and for Celia's experiment.
The Results of problem 5 and problem 6 are shown in below figure.
So, The sum of all the probabilities for Leon's experiment and for Celia's experiment are;
Leon: [tex]\frac{2}{20} + \frac{3}{20} + \frac{5}{20} +\frac{4}{20} +\frac{6}{20} = \frac{20}{20} =1[/tex]
Celia: [tex]\frac{4}{24} + \frac{3}{24} + \frac{7}{24} +\frac{6}{24} +\frac{4}{24} = \frac{24}{24} =1[/tex]
Solution: Sum of all probabilities for Leon's experiment and for Celia's experiment are 1.
Possible explanation: It is certain that 1 of the 5 possible outcomes will result. The probability of any of the outcomes occurring is 1.
To know more about probability, visit:
https://brainly.com/question/13604758
#SPJ1
Full question -
You deposit $3000 each year into an account earning 6% interest compounded annually. How much will you have in the account in 30 years?
Answer:
$232,241.07
Step-by-step explanation:
To calculate the total amount in the account after 30 years of depositing $3,000 each year and earning 6% interest compounded annually, we can use the formula for the future value of an annuity:
FV = P * (((1 + r)^n - 1) / r)
where:
FV is the future value of the annuity
P is the periodic payment (in this case, $3,000 per year)
r is the interest rate per compounding period (in this case, 6% per year, compounded annually)
n is the number of compounding periods (in this case, 30 years)
Substituting the given values, we get:
FV = $3,000 * (((1 + 0.06)^30 - 1) / 0.06)
Using a calculator, we get:
FV ≈ $232,241.07
Therefore, the total amount in the account after 30 years, rounded to the nearest cent, is $232,241.07.
differentiate with respect to x the implicit function sin(y)+x^2y^3-cos(x)=2y
Answer:
To differentiate the implicit function sin(y) + x^2y^3 - cos(x) = 2y with respect to x, we will use the chain rule and product rule.
First, we will take the derivative of both sides of the equation with respect to x:
d/dx [sin(y) + x^2y^3 - cos(x)] = d/dx [2y]
Next, we will differentiate each term on the left side of the equation:
cos(x) - 2xy^2 dx/dx + 3x^2y^2 + sin(y) dy/dx = 2 dy/dx
We can simplify this equation by moving all the terms involving dy/dx to the left side:
cos(x) - 2xy^2 - 2 dy/dx sin(y) = dy/dx [2 - sin(y)]
Now we can solve for dy/dx by isolating it on one side of the equation:
dy/dx [2 - sin(y)] = cos(x) - 2xy^2
dy/dx = (cos(x) - 2xy^2) / [2 - sin(y)]
Therefore, the derivative of the implicit function sin(y) + x^2y^3 - cos(x) = 2y with respect to x is:
dy/dx = (cos(x) - 2xy^2) / [2 - sin(y)]
help please!! state the key features for this graph
Axis of symmetry: x = 1[tex]\\[/tex]
Vertex: (0,1)
Y-intercept: (0,1)
Min / Max: 0 / infinity
Domain: -infinity ≥ x ≥ infinity
Range: 0 ≥ y ≥ infinity
350 cm = m
pls help me with this
Answer:
0.35 m
Step-by-step explanation:
1 m = 1000 cm
350 cm = ? m
We Take
350 / 1000 = 0.35 m
So, 350 cm = 0.35 m
1.3.1 1.3.2 1.3.3 1.3.4 Government receives income from various sources, like tax and loans. This income is then distributed to the different sectors. TABLE 3 below shows the source of the income and the expenditure for the 2019/20 tax year. SOURCE Tax INCOME Loans ASC QP Other income Non-tax income AMOUNT (in billion rand) 1370 242.7 180.3 31.5 EXPENDITURE SECTOR Social Development Basic Education Health Peace and safety Economic development Community Development Debt service cost AMOUNT (in billion rand) Further Education and Training Other 278.4 262.4 222.6 211.0 209.2 208.5 202.2 APRIL 2021 112.7 B 1823.72 TOTAL A Write the amount received from loans as a number in millions (1) (3) (3) Calculate the missing value A Calculate the missing value B. Show ALL calculations. Determine the amount allocated for Community Development as a percentage of the total expenditure. (4)
The amount received from loans as a number in millions is 242,700 million rand.
How to calculate the valueDeducing value A requires computation of collective income sources, for which the following summation suffices:
Total Income = Tax + Loans + ASC + QP + Other income + Non-tax income = 1370 + 242.7 + 180.3 + 31.5 + A + 0 = 1825.5 + A
In this context, it follows that A amounts to (1825.5 - 1370 - 242.7 - 180.3 - 31.5) = 0 million rand.
Conversely determining missing value B necessitates subtraction of total expenditure from accumulated revenue, giving rise to the subsequent formula:
Total Income - Total Expenditure = B
(1825.5 - 112.7 - 278.4 - 262.4 - 222.6 - 211.0 - 209.2 - 208.5 - 202.2 - 0) = B
Following calculation, B equates to -77.1 million rand, indicating an overage in expenses during fiscal year 2019/20.
Learn more about word problem on
https://brainly.com/question/21405634
#SPJ1
Write the complex number in rectangular form. If necessary, round to the nearest tenth.
24( cos 275° + i sin 275°)
Answer:
Step-by-step explanation:
We first have to find cos 275 and sin 275 and then put them into the formula:
cos 275 = .0872
sin 275 = -.9962
Therefore,
24(.0872 - .9962i) distributes to
2.1 - 23.9i
help asp--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
For given trapezoid, the measures of angles A, B, and D are 40 degrees and 50 degrees, respectively.
What is trapezoid?A trapezoid is a quadrilateral with one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The legs may be of equal length, or they may be different lengths.
According to given information:Since trapezoid ABCD has two parallel sides, we know that angle A + angle D = 180 degrees. Similarly, angle B + angle C = 180 degrees.
Therefore, we can write:
angle A + angle B + angle C + angle D = 360 degrees
Substituting angle A = angle B and angle C = angle D, we get:
2(angle A) + 2(angle C) = 360 degrees
Simplifying:
2(angle A) + 2(50)= 180 degrees
2(angle A) = 180 degree-100 degree
2(angle A) = 80 degree
angle A= 80 degree/2
angle A = 40 degree
Since we know that angle A = angle B
angle B= 40 degree
Therefore,
angle A = angle B = 40 degrees
angle D = angle C = 50 degrees
So the measures of angles A, B, and D are 40 degrees and 50 degrees, respectively.
To know more about trapezoid visit:
https://brainly.com/question/1410008
#SPJ1
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The true statements are:
1. The radius of the circle is 3 units
2. The standard form of the equation is (x-1)^2+y^2=3
3. The center of the circle lies on X-axis
4. The radius of this circle is the same as the radius of the circle whose equation is x^2+y^2=9
The given equation is: x^2+y^2-2x-8=0
The equation in the standard form of the circle can be written as (x-h)^2+(y-k)^2=r^2, where h= center of the circle and r= radius of the circle
The given equation in standard form can be written as
(x^2-2x+1)+y^2-9=0
(x-1)^2+y^2=3^2
Hence from the above equation, the center of the circle is at (1,0) and the radius is 3 units.
To learn more about problems on the equation of a circle refer to:
https://brainly.com/question/23799314?referrer=searchResults
Write this in System of Equations from Context
A company produces fruity drinks that contain a percentage of real fruit juice. Drink A contains 20% real fruit juice and Drink B contains 10% real fruit juice. The company used 70 liters of real fruit juice to make 3 times as many liters of Drink A as liters of Drink B. Write a system of equations that could be used to determine the number of liters of Drink A made and the number of liters of Drink B made. Define the variables that you use to write the system.
Therefore, the system of equations that could be used to determine the number of liters of Drink A made and the number of liters of Drink B made is.
[tex]0.1x + 0.2y = 70[/tex]
[tex]y = 3x[/tex]
Where x represents the number of liters of Drink B made, and y represents the number of liters of Drink A made.
Let's define the variables as follows:
Let x be the number of liters of Drink B produced.
Since the company produced 3 times as many liters of Drink A as liters of Drink B, let y be the number of liters of Drink A produced, so y = 3x.
Now, let's write the system of equations:
The total amount of real fruit juice used is 70 liters, so we can write:
[tex]0.1x + 0.2y = 70[/tex]
Substituting y = 3x into the above equation, we get:
[tex]0.1x + 0.2(3x) = 70[/tex]
Simplifying the equation:
[tex]0.1x + 0.6x = 70[/tex]
[tex]0.7x = 70[/tex]
[tex]x = 100[/tex]
So, the company made 100 liters of Drink B and 3 times as many liters of Drink A, or 300 liters of Drink A.
Therefore, the system of equations that could be used to determine the number of liters of Drink A made and the number of liters of Drink B made is:
[tex]0.1x + 0.2y = 70[/tex]
[tex]y = 3x[/tex]
Where x represents the number of liters of Drink B made, and y represents the number of liters of Drink A made.
To know more about times visit:
https://brainly.com/question/28050940
#SPJ1
The probability of choosing a green grape out of the bag that contains red and green grapes without looking is 11/15 . Which term best describes this probability?
Answer:
Likely
Step-by-step explanation:
Find the value of x. x =______ °
Answer:
x=26
Step-by-step explanation:
5x=3x+52
5x-3x=52
2x=52
2x/2=52/2
x=52/2
x=26
You take out a loan in the amount of your tuition and fees cost $70,000. The loan has a monthly interest rate of 0.25% and a monthly payment of $250. How long will it take you to pay off the loan? Use the formula N= (-log(1-i*A/P))/(log(1+i)) to determine the number of months it will take you to pay off the loan. Let N represent the number of monthly payments that will need to be made, i represent the interest rate in decimal form, A represent the amount owed (total amount of the loan), and P represent the amount of your monthly payment. Be sure to show your work for all calculations made.
With given compound interest, it will take approximately 31 years and 5 months to pay off the loan.
What is Compound interest?
Compound interest is computed on both the starting principal and the accrued interest from prior periods. In other words, it is the interest gained not just on the principle amount but also on any past interest earned.
Now,
Using the given formula:
N = (-log(1 - i * A / P)) / (log(1 + i))
where i = 0.0025 (0.25% monthly interest rate), A = $70,000, and P = $250
N = (-log(1 - 0.0025 * 70000 / 250)) / (log(1 + 0.0025))
N = (-log(1 - 175)) / (log(1.0025))
N = (-log(0.9883)) / (0.0025)
N = 376.48
Rounding up to the nearest whole number, it will take 377 months to pay off the loan.
Therefore, it will take approximately 31 years and 5 months to pay off the loan.
To know more about Compound Interest visit the link
brainly.com/question/14295570
#SPJ1
Malachi asks students in his class, "How long does it take you to get to school?" The histogram shows the data. Which statement best describes the distribution?
The data from the distribution shows a symmetric distribution.
When is the data from a distribution symmetric?The data from a distribution can be described as symmetric when the values of the data are evenly distributed around its center point. This mans that if the data is folded along its center point and the two halves overlap perfectly, then the distribution is said to be symmetric.
In the histogram, we see an example of symmetric data because the center value that has the frequency of 10 ahs even distribution on both sides.
Learn more about histograms here:
https://brainly.com/question/2962546
#SPJ1
Bhavik bought 3 liters of milk and 5 loaves of bread for a total of $11. A month later, he bought 4 liters of milk and 4 44 loaves of bread at the same prices, for a total of $10. How much does a liter of milk cost, and how much does a loaf of bread cost?
The cost of a liter of milk is $2.50 and the cost of a loaf of bread is $2.50.
What is cost?Cost is the value of goods or services measured in money or other forms of exchange. It is the amount that must be given up in exchange for something else. Costs are typically incurred in the production of goods and services, and can include both tangible and intangible elements, such as labor, materials, overhead, and financing.
The total cost for 3 liters of milk and 5 loaves of bread was $11. Therefore, the cost for 1 liter of milk was ($11 / 3) = $3.67. The cost for 1 loaf of bread was ($11 / 5)
= $2.20.
The total cost for 4 liters of milk and 4 loaves of bread was $10. Therefore, the cost for 1 liter of milk was ($10 / 4) = $2.50. The cost for 1 loaf of bread was ($10 / 4)
= $2.50.
Therefore, the cost of a liter of milk is $2.50 and the cost of a loaf of bread is $2.50.
To learn more about cost
https://brainly.com/question/2292799
#SPJ1
f(x) = 4(1+ 0.1/0.5)^0.5x is
Answer:
f(x) = 4(1.095)^x.
Step-by-step explanation:
The function f(x) = 4(1+0.1/0.5)^0.5x can be simplified using the order of operations, which is PEMDAS (parentheses, exponents, multiplication and division, and addition and subtraction).
First, we can simplify 0.1/0.5 to get 0.2.
Next, we can simplify (1 + 0.2) to get 1.2.
Then, we can simplify (1.2)^0.5 to get approximately 1.095.
Finally, we can multiply 4 by 1.095^x to get the simplified function:
Leah said on her birthday: “Today I am exactly three times as old as I was four years ago.“ And that was true. In how many years can Leah truthfully say on her birthday: “Today I am exactly twice as old as I was four years ago“?
in 2 years, Leah will be exactly twice as old as she was four years ago. Therefore, the answer is 2 years.
How to determine In how many years can Leah truthfully say on her birthday: “Today I am exactly twice as old as I was four years ago“Let's start by setting up an equation based on the given information.
Let Leah's current age be represented by "x". Then, we know that:
x = 3(x-4)
Expanding the right side of the equation:
x = 3x - 12
Bringing the "x" term to the left side and simplifying:
2x = 12
x = 6
So Leah is currently 6 years old. Now we want to find out how many years it will take for her to be exactly twice as old as she was four years ago. Let's represent this number of years as "y". Then we can set up another equation:
6 + y = 2(6 - 4 + y)
Simplifying:
6 + y = 2(2 + y)
6 + y = 4 + 2y
2 = y
So in 2 years, Leah will be exactly twice as old as she was four years ago. Therefore, the answer is 2 years.
Learn more about word problems at https://brainly.com/question/21405634
#SPJ1
Determine the number of solutions to the system of linear equations shown on the graph.
No solution
Infinitely many solutions
One solution at (−3, 2)
One solution at (2, −3)
Answer:
explanation:A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line).
Consider two points A(0,0) and B(1, 1) on a Cartesian plane. The equation of the axis of the segment AB is: A. y = 1 2 − B. y = 2 − C. y = 1 − 2 D. y = 1 − E. y = 1 − 2
So, the equation of the axis of the segment AB is (A) y = 1/2 - x/2.
What is slope?
In mathematics, slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for every unit change in the independent variable.
The slope of the line passing through points A and B can be calculated as follows:
slope = (change in y) / (change in x) = (1-0) / (1-0) = 1/1 = 1
The equation of a line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
To find the y-intercept, we can use point A (0,0) and substitute the slope value.
y = mx + b
0 = 1(0) + b
b = 0
Therefore, the equation of the line passing through points A and B is:
y = 1x + 0
Simplifying, we get:
y = x
So, the answer is (A) y = 1/2 - x/2. However, this is not one of the given answer choices. We can also write the equation in point-slope form as y - y1 = m(x - x1) using point A, which gives:
y - 0 = 1(x - 0)
y = x
This confirms our earlier answer.
To learn more about slope from the given link:
https://brainly.com/question/2491620
#SPJ1
in row 2, write the standard form equation of a circle whose diameter endpoints are shown here (-3,4) (2,1)
The standard form equation of a circle whose diameter endpoints are (-3,4) (2,1) is [tex](x - (-0.5))^2 + (y - 2.5)^2[/tex] = 6.5
What is the general form of equation of a circle?The general form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r represents the radius. This equation is derived using the Pythagorean theorem, which states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse. By setting (x - h)² and (y - k)² equal to r² and then combining the two equations, we get the standard form equation of a circle.
The center of the circle lies in the middle of the diameter, so we find the midpoint of the end points:
[tex](\frac{-3+2}{2} , \frac{4+1}{2} )[/tex] = (-0.5, 2.5)
And radius of the circle is half of the diameter, which is:
[tex]\frac{\sqrt{( 2-(-3))^2 + (1-4)^2 )}}{2}[/tex] = [tex]\frac{\sqrt{26}}{2}[/tex]
Therefore, the circle equation is:
[tex](x - (-0.5))^2 + (y - 2.5)^2[/tex] = [tex](\frac{\sqrt{26} }{2} )^2[/tex] = 26/4 = 6.5
[tex](x - (-0.5))^2 + (y - 2.5)^2[/tex] = 6.5
To know more about circle equation visit:
brainly.com/question/29288238
#SPJ1
Find the surface area and volume of the composite solid.
According to the information, the surface area of the solid is 758m² and the volume is 594m³
How to find the surface area of the solid?To find the surface area of the solid we have to perform the following procedure:
12m * 11m = 132m²
132m² * 2 = 264m²
16m * 9m = 144m²
144m² - 18m² = 126m²
126m² * 2 = 252m²
16m * 11m = 176m²
176m² - 66m² = 110m²
3m * 11m = 33m²
33m² * 2 = 66m²
6m * 11m = 66m²
264m² + 66m² + 66m² + 110m² +252m² = 758m²
To find the volume we have to perform the following procedure:
8m * 11m * 9m = 792m³
792m³ - 198m³ = 594m³
Learn more about surface area in: https://brainly.com/question/29298005
#SPJ1