The margin of error can be calculated as half the width of the confidence interval. So, the margin of error is:
(0.257 - 0.183) / 2 = 0.037
Therefore, the answer is (a) 0.037.
The margin of error for this confidence interval can be calculated by finding the difference between the upper bound and the lower bound, and then dividing by 2.
In this case, the confidence interval is (0.183, 0.257).
Margin of error = (0.257 - 0.183) / 2 = 0.074.
So the answer is b. 0.074.
The margin of error is a measure of the precision of an estimate or a statistic, often used in opinion polls and surveys. It represents the amount of sampling error that is expected in the results due to random variation.
In statistical terms, the margin of error is calculated as a range of values around the estimated statistic, within which the true population parameter is likely to fall with a certain degree of confidence. The most common way to express the margin of error is as a plus or minus value, typically represented as a percentage of the sample size.
For example, if a survey of 1,000 people finds that 60% of them support a particular political candidate, with a margin of error of +/- 3%, this means that there is a 95% chance that the true level of support in the population falls between 57% and 63%. In other words, if the survey were to be repeated many times, 95% of the resulting confidence intervals would contain the true level of support.
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Lesson 10.1.3 - Review and Preview
ANSWERS ARE NEEDED ASAP APEPRICATED AND WILL TRY TO PUT YOU AS BRAINLIEST WHEN IM ACTIVE (FIRST ONE THAT SOLVES THE PROBLEM AND SHOWS STEPS)
The calculated volume of the prism is 104 cubic feet
From the question, we have the following parameters that can be used in our computation:
Volume of right pyramid = 312 cubic feet
The volume of the prism next to it is calculated as
Volume = 1/3 * Volume of right pyramid
Substitute the known values in the above equation, so, we have the following representation
Volume = 1/3 * 312 cubic feet
Evaluate
Volume = 104 cubic feet
Hence, the volume is 104 cubic feet
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Evaluate the expression 2x^2 + 5xy - 3y^2 for x = 2 and y = -1
The answer for the value of the expression 2x² + 5xy - 3y², which is a quadratic equation, for x = 2 and y=-1, is 1.
The values of the unknown variable x that satisfy the equation are known as the roots or zeros of a quadratic equation. A quadratic equation of the type:
ax² + bx + c = 0 with a 0 can have solutions found using the quadratic formula. Given in the question, solutions are given as x= 2 and y=-1.
To evaluate the expression 2x² + 5xy - 3y² for x = 2 and y = -1, we substitute these values into the expression and simplify:
2x² + 5xy - 3y²
= 2(2)² + 5(2)⁻¹ - 3(-1)²
= 8 - 10 + 3
= 1
Therefore, the value of the expression 2x² + 5xy - 3y² for x = 2 and y = -1 is 1.
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Kenton compared gas mileage for three cars.
Car A—340 miles for 17 gallons
Car B—361 miles for 19 gallons
Car C—450 miles for 18 gallons
Which car has the best rate of miles per gallon?
Car A has the best rate at 20 miles per gallon.
Car B has the best rate at 19 miles per gallon.
Car C has the best rate at 25 miles per gallon.
All three cars had the same rate of miles per gallon.
Answer:
The answer to your problem is, C. Car C has the best rate at 25 miles per gallon.
Step-by-step explanation:
Well given,
Car C = 450 / 18 = 25
Car B = 361 / 19 = 19
Car A = 340 / 17 = 20
We can see that Car C has the best MPG.
Thus the answer to your problem is, C. Car C has the best rate at 25 miles per gallon.
The average Math SAT score of 36 randomly selected students in a certain state is 525.6 and the standard deviation is 69.5. Does this result provide significant evidence that the overall average Math SAT score in that state differs from the national average of 514 points? Use an appropriate p-value to draw and explain your conclusion
There isn't significant evidence to conclude that the overall average Math SAT score in the state differs from the national average of 514 points based on this sample.
To determine if the average Math SAT score of the 36 randomly selected students significantly differs from the national average of 514 points, we can use a t-test with the given information.
1. Null hypothesis (H₀): The overall average Math SAT score in the state is equal to the national average (μ = 514).
2. Alternative hypothesis (Hₐ): The overall average Math SAT score in the state differs from the national average (μ ≠ 514).
3. Calculate the test statistic (t-value) using the formula: t = (sample mean - population mean) / (standard deviation / √sample size)
t = (525.6 - 514) / (69.5 / √36) = 11.6 / 11.583 = 1
4. Determine the degrees of freedom (df): df = sample size - 1 = 36 - 1 = 35
5. Choose a significance level (α), commonly 0.05.
6. Compare the t-value with the critical t-value from a t-distribution table using the chosen α level and degrees of freedom. For a two-tailed test with α = 0.05 and df = 35, the critical t-values are approximately ±2.03.
Since the calculated t-value (1) is not greater than the critical t-value (±2.03), we fail to reject the null hypothesis.
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Determine the number of solutions that 5x^2 + 3x + 8 has without solving the equation.
The number of solutions that the quadratic equation, 5x² + 3x + 8 can have without solving the equation using discriminant is 0.
Given equation is,
5x² + 3x + 8
This is a quadratic equation.
It can have atmost 2 solutions.
So there can't be any solutions, there can be one solution or 2 solutions.
We can find the discriminant to know this.
Discriminant = √(b² - 4ac)
Here,
discriminant = √(3² - (4 × 5 × 8)) = √(9 - 160) = √(-154)
Discriminant is less than 0.
So there are no solutions.
Hence the number of solutions is 0.
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how many tennis balls do you need to balance out the scale
Answer: 3 Possibly.
Step-by-step explanation:
I just know:)
PLEASE give THANKS!
ABCD is a parallelogram where A is (2,-1), B is (6,2) and C is (11,-2).
(a) State the coordinates of the midpoint AC.
(b) Hence find the coordinates of D.
(c) Find the equations of the diagonals of the parallelogram.
the answer is produced by chatgpt, it is a good study tool, you can take it as reference
(a) The coordinates of the midpoint AC can be found by taking the average of the x-coordinates and the average of the y-coordinates of points A and C. Therefore, the midpoint AC is at:
((2+11)/2, (-1-2)/2) = (6.5,-1.5)
(b) Since ABCD is a parallelogram, the midpoint of BD is also at (6.5,-1.5). Let D have coordinates (x,y). Then the midpoint of BD is:
((6+x)/2, (2+y)/2) = (6.5,-1.5)
Solving for x and y, we get:
x = 7 and y = -5
Therefore, the coordinates of D are (7,-5).
(c) The two diagonals of a parallelogram bisect each other. Since AC is one diagonal and it passes through the midpoint of BD, the equation of AC can be found using the two given points A and C:
Slope of AC = (y2 - y1)/(x2 - x1) = (-2 - (-1))/(11 - 2) = -1/9
Using point-slope form of a line, the equation of AC is:
y - (-1) = (-1/9)*(x - 2)
y = (-1/9)*x + (17/9)
Similarly, the other diagonal BD can be found using the two points B and D:
Slope of BD = (y2 - y1)/(x2 - x1) = (-5 - 2)/(7 - 6) = -7
Using point-slope form of a line, the equation of BD is:
y - 2 = (-7)*(x - 6)
y = -7x + 44
Therefore, the equations of the diagonals of the parallelogram are:
AC: y = (-1/9)*x + (17/9)
BD: y = -7x + 44
Which is greater, an angle measured at 40° or an angle measured at 0.7 radians? Explain.
Answer:
0.7 radians
Step-by-step explanation:
The equation for converting radians to degrees is:
X radians * 180/pi = degrees
Plugging in 0.7 radians,
we have 0.7 * 180/pi
= approx 40.1070457 degrees.
40.1070457 > 40 degrees,
so 0.7 radians is greater than 40 degrees
estimate the value(s) of c that satisfy the conclusion of the mean value theorem on the interval [2, 6]. (enter your answers as a comma-separated list. round your answers to one decimal places. if an answer does not exist, enter dne.)
The mean value theorem states that if a function f(x) is continuous on the interval [a, b] and differentiable on (a, b), then there exists a value c in (a, b) such that:
f'(c) = (f(b) - f(a))/(b - a)
In this case, the interval is [2, 6]. So, we need to find the value(s) of c that satisfy:
f'(c) = (f(6) - f(2))/(6 - 2)
We can make an estimate based on the graph of the function.
If the graph of f(x) is a straight line between (2, f(2)) and (6, f(6)), then the derivative is constant over the interval [2, 6]. In this case, we can use the formula:
f'(c) = (f(6) - f(2))/(6 - 2) = (y2 - y1)/(x2 - x1)
where (x1, y1) = (2, f(2)) and (x2, y2) = (6, f(6)).
Solving for c, we get:
c = (x1 + x2)/2 = (2 + 6)/2 = 4
This is the only value of c that satisfies the conclusion of the mean value theorem in this case.
If the graph of f(x) is not a straight line, then we cannot make a simple estimate for c based on the graph alone.
To estimate the value(s) of c that satisfy the conclusion of the Mean Value Theorem (MVT) on the interval [2, 6], you need to follow these steps:
1. Identify the function, f(x), that you're working with.
2. Ensure the function is continuous on the interval [2, 6] and differentiable on the open interval (2, 6). This is required for MVT to be applicable.
3. Calculate the average rate of change (mean value) of the function over the interval [2, 6] by using the formula (f(6) - f(2)) / (6 - 2).
4. Take the derivative of the function, f'(x).
5. Set f'(x) equal to the mean value calculated in step 3 and solve for the value(s) of x, which will give you the value(s) of c that satisfy the MVT.
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what are the coordinates of point q that partitions AB into the ratio 1:3 where (-3,6) and B (6,0)
The coordinates of point Q that partitions line segment AB into the ratio 1:3 is (-0.75, 4.5).
How to determine the coordinates of point Q?In this scenario, line ratio would be used to determine the coordinates of the point Q on the directed line segment AB that partitions the segment into a ratio of 1 to 3.
In Mathematics, line ratio can be used to determine the coordinates of Q and this is modeled by the following mathematical expression:
Q(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
By substituting the given points into the formula for line ratio, we have;
Q(x, y) = [(1(6) + 3(-3))/(1 + 3)], [(1(0) + 3(6))/(1 + 3)]
Q(x, y) = [(6 - 9)/(4)], [(0 + 18)/4]
Q(x, y) = [-3/4], [18/(4)]
Q(x, y) = [-0.75, 4.5]
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Practice
Example 1
Write each equation in exponential form.
1. log₁5 225 = 2
4. log3 243 = 5
10. ()³ = 343
Example 2
Write each equation in logarithmic form.
7. 27 = 128
Example 3
Evaluate each expression.
13. log2 64
16. log27 81
2. 1093 27 = -3
19. logg 512
5. log4 64 = 3
8. 3-4 = 1
11. 29 = 512
14. log100 100,000
17. 1094 32
20. log, 1
Practice
3. logs 25= -2
6. log432 = 5/2
9. 7-2 = 49
12. 643 = 16
15. log5 625
ace
18. log₁0 0.00001
21. logg 4
Answer: 546
Step-by-step explanation:
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Assignment #2 Question No.1 Evaluate this complex number in rectangular form 6 e/300 + j5 - 3 + 450
The evaluated complex number in rectangular form is (6cos(300) - 3) + (6sin(300) + j5).
To evaluate the complex number 6 e/300 + j5 - 3 + 450 in rectangular form, we need to convert it from polar form to rectangular form.
The polar form of a complex number is given by r e^(jθ), where r is the magnitude and θ is the angle in radians. In this case, we have:
r = 6
θ = 300 degrees = (5π/6) radians
Using Euler's formula e^(jθ) = cos(θ) + j sin(θ), we can write:
6 e^(j300) = 6 (cos(5π/6) + j sin(5π/6))
= 6 (-1/2 + j √3/2)
= -3 + j3√3
Now we can add this to the real number -3 + 450, to get:
-3 + j3√3 + (-3 + 450)
= 444 + j3√3
Therefore, the rectangular form of the complex number 6 e/300 + j5 - 3 + 450 is 444 + j3√3.
To evaluate the complex number in rectangular form, given the expression 6e^(300) + j5 - 3 + 450, follow these steps:
1. Convert the exponential form (6e^(300)) to rectangular form.
2. Combine the real parts and imaginary parts.
Step 1: Converting exponential form to rectangular form:
6e^(300) = 6(cos(300) + jsin(300))
Step 2: Combining real and imaginary parts:
Real part: 6cos(300) - 3
Imaginary part: 6sin(300) + j5
So, the evaluated complex number in rectangular form is (6cos(300) - 3) + (6sin(300) + j5).
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the jenkins family is having a family reunion. 15 people are each bringing 2 tables each. there are the same amount of people sitting at each table. if 90 people attend the reunion how many people will sit at each table
If 15 people are each bringing 2 tables, then there will be a total of 30 tables at the family reunion.
Since there are the same amount of people sitting at each table, we can divide the total number of people (90) by the total number of tables (30).
90 ÷ 30 = 3
Therefore, there will be 3 people sitting at each table.
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PLEASE HELP WITH BOTH QUESTIONSSSS!!!!!!!!!!!!!!
A graph of each of the function is shown below.
The domain is x = -2, x = 0, x = 1, x = 2.
The range is [-1, -1] U [3, 3].
What is a piecewise-defined function?In Mathematics, a piecewise-defined function is a type of function that is defined by two (2) or more mathematical expressions over a specific domain.
Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of the given piecewise-defined function, we can reasonably infer and logically deduce that it is constant over the interval x < -2 and x ≥ -2.
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Pls help I need answer and how to get the answer btw click on the text to see pic
Answer:
The answer for the Area is 847in²
Step-by-step explanation:
Area of shape=Area of square + Area of trapezoid
A=L²+1/2(a+b)h
A=22²+1/2(11+22)22
A=484+33×11
A=484+363
A=847in²
What Proportion Go to Maximum Pressure? We see that 75 of the 264 people in the study allowed the pressure to reach its maximum level of 300 mmHg, without ever saying that the pain was too much (MaxPressure=yes). Use this information to estimate the proportion of people who would allow the pressure to reach its maximum level.
The estimated proportion of people who would allow the pressure to reach its maximum level is approximately 0.284 or 28.4%.
Based on the given information, we know that out of the 264 people in the study, 75 allowed the pressure to reach its maximum level of 300 mmHg (MaxPressure=yes). Therefore, the proportion of people who would allow the pressure to reach its maximum level can be estimated by dividing the number of people who allowed the pressure to reach its maximum level (75) by the total number of people in the study (264):
Proportion = 75/264
Using a calculator, we can simplify this to:
Proportion ≈ 0.284
Therefore, approximately 28.4% of people in the study allowed the pressure to reach its maximum level of 300 mmHg without indicating that the pain was too much.
To estimate the proportion of people who allowed the pressure to reach its maximum level, follow these steps:
1. Determine the total number of people in the study: 264 people
2. Find the number of people who allowed the pressure to reach its maximum level (300 mmHg) without ever saying the pain was too much: 75 people
3. Calculate the proportion by dividing the number of people who reached maximum pressure by the total number of people in the study.
Proportion = (Number of people who reached maximum pressure) / (Total number of people in the study)
Proportion = 75 / 264 ≈ 0.284 (rounded to three decimal places)
The estimated proportion of people who would allow the pressure to reach its maximum level is approximately 0.284 or 28.4%.
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which term should be inserted in the blank space of x^2 +____+9y^2 to make it perfect square
the perfect square is : (x+3y)² the term is 6xy
Why is it important to analyze the relationships between a sample and full population?
To bring diverging data into analysis
To limit variance
To find out how many data points are necessary to be statistically valid
To help make more informed statements about a population
Answer:
It is important to analyze the relationships between a sample and full population for several reasons:
To help make more informed statements about a population: Analyzing the relationships between a sample and full population helps us to make more accurate and informed statements about the population. By examining a sample, we can draw conclusions about the characteristics of the larger population.
To bring diverging data into analysis: Sometimes, a sample may not accurately reflect the larger population, particularly if the sample is small or biased. Analyzing the relationship between the sample and population can help to identify any diverging data and adjust the analysis accordingly.
To limit variance: Variance is a measure of how much the data varies from the mean. By analyzing the relationship between the sample and population, we can better understand the variance and take steps to limit it.
To find out how many data points are necessary to be statistically valid: Analyzing the relationship between the sample and population can help us to determine the sample size needed to be statistically valid. This can help us to avoid drawing inaccurate conclusions based on a sample that is too small.
Overall, analyzing the relationship between a sample and full population is important for ensuring that our analysis is accurate, representative, and informative.
It is important to analyze the relationships between a sample and the full population to limit variance and to help make more informed statements about a population.
Analyzing the relationships between a sample and the full population is important because it helps limit variance in the data and brings diverging data into the analysis. It also helps to determine how many data points are necessary to be statistically valid and make more informed statements about the population.
By examining a sample and comparing it to the full population, we can identify any biases or errors in our data and ensure that our conclusions are accurate and representative of the entire population. Additionally, understanding the relationship between the sample and the population can help us make predictions and draw conclusions with greater confidence and precision.
By understanding the relationship, you can ensure that the sample accurately represents the population, leading to better inferences and decision-making.
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Factorise completely 49xy+56x
Answer:
[tex]49xy + 56x = 7x(7y + 8)[/tex]
Find the slope of the line tangent to the following polar curve at the given point. At the point where the curve intersects the origin (if this occurs), find the equationn of the tangent line in polar coordinates. r = 9 + 7 cos theta; (16,0) and (2, pi) Find the slope of the line tangent to r = 9 + 7 cos theta at (16,0). Select the correct choice below and fill in any answer boxes within your choice. Find the slope of the line tangent to r = 9 + 7 cos theta at (2, pi). Select the correct choice below and fill in any answer boxes within your choice. At the point where the curve intersects the origin (if this occurs), find the equationn of the tangent line in polar coordinates. Select the correct choice below and fill in any answer boxes within your choice. The equationn of the tangent line when the curve intersects the origin is The curve does not intersect the origin.
To find the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (16, 0), we can use the formula:
dy/dx = (dy/dtheta) / (dx/dtheta) = (r' sin(theta) + r cos(theta)) / (r' cos(theta) - r sin(theta))
where r' = dr/dtheta.
First, we need to find r' by taking the derivative of r with respect to theta:
r' = dr/dtheta = -7 sin(theta)
Then, we can plug in the given values to find the slope at (16, 0):
dy/dx = [(r' sin(theta) + r cos(theta)] / [r' cos(theta) - r sin(theta)]
= [(-7 sin(0) sin(0) + (9 + 7 cos(0)) cos(0))] / [(-7 sin(0) cos(0)) - (9 + 7 cos(0)) sin(0))]
= (9 + 7) / (-9) = -2
Therefore, the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (16, 0) is -2.
To find the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (2, pi), we can use the same formula as above:
dy/dx = (r' sin(theta) + r cos(theta)) / (r' cos(theta) - r sin(theta))
First, we need to find r' by taking the derivative of r with respect to theta:
r' = dr/dtheta = -7 sin(theta)
Then, we can plug in the given values to find the slope at (2, pi):
dy/dx = [(r' sin(theta) + r cos(theta)] / [r' cos(theta) - r sin(theta)]
= [(-7 sin(pi) sin(2) + (9 + 7 cos(pi)) cos(2))] / [(-7 sin(pi) cos(2)) - (9 + 7 cos(pi)) sin(2))]
= (-2) / (7)
Therefore, the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (2, pi) is -2/7.
The polar curve r = 9 + 7 cos(theta) intersects the origin when r = 0, which occurs when cos(theta) = -9/7, which is not possible since the range of cosine function is [-1, 1]. Therefore, the curve does not intersect the origin.
Since the curve does not intersect the origin, the answer is "The curve does not intersect the origin" for the equation of the tangent line in polar coordinates.
Is vector v with an initial point of (0,0) and a terminal point of (50,120) equal to vector u with an initial point of (50,120) and a terminal point of (0,0)?
The vectors u and v are not equal because they have different direction.
If the initial point is (x₁, y₁) and terminal point is (x₂, y₂) then the vector is
Vector =(x₂-x₁)i+(y₂-y₁)j
Vector v with an initial point of (0, 0) and a terminal point of (50,120).
Vector v = 50i+120j..(1)
Vector u with an initial point of (50, 120) and a terminal point of (0,0).
Vector u = (0-50)i+(0-120)j
=-50i-120j..(2)
Hence, the vectors u and v are not equal because they have different direction.
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James has completed 3/4 of his homework. Marcus has completed 2/3 of his homework. Draw 2 number lines to represent these fractions . Who has more homework left to complete
The two number lines to represent these fractions are shown in the image attached below.
Marcus has more homework left to complete.
What is a number line?In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
For James, he has completed 3x/4 of his homework while Marcus has completed 2x/3 of his homework and as such, Marcus has more homework left to complete.
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plsss help!!! giving 100 B and brainliest.
29. The percentage of change is -39.66%.
30. The percentage of change is 35.29%
31. The percentage of change is 150.38%.
32. The percentage of change is -62.5%
How to calculate the percentageA percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
The percentage of change is
= (-2300 / 5800) × 100
= -39.66%.
The percentage of change is:
= 6/17 × 100
= 35.29%
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the noise level in a restaurant is normally distributed with an average of 30 decibels. 99% of the time it is below what value?
According to the given information, the noise level in a restaurant is normally distributed with an average of 30 decibels. To find the value below which 99% of the time the noise level is, we need to use the Z-table.
We know that 99% of the area under the normal curve is below a Z-score of 2.33 (found from the Z-table).
To find the corresponding noise level value, we use the formula:
Z-score = (X - μ) / σ
where X is the noise level value we want to find, μ is the average (30 decibels), and σ is the standard deviation (which is not given in this question).
However, we can use the empirical rule (68-95-99.7 rule) to estimate the standard deviation. According to the rule, 99.7% of the data falls within 3 standard deviations of the mean. So, if 99% of the time the noise level is below a Z-score of 2.33, then we can estimate that the standard deviation is approximately:
(2.33 x σ) = 3
Solving for σ, we get:
σ = 3 / 2.33 = 1.29 (approx.)
Now we can use the formula above to find the noise level value below which 99% of the time the noise level is:
2.33 = (X - 30) / 1.29
X - 30 = 2.33 x 1.29
X = 33.01
So, 99% of the time, the noise level in the restaurant is below 33.01 decibels (rounded to two decimal places).
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Write the equation in standard form for the circle with center (-10, 0) passing through
(-12,3/2)
Answer:
Step-by-step explanation:
the standard equation for the circle is:
(x-a)²+(y-b)² = r²
the center is : A(a,b) and ridus r
you have : a= -10 and b=0 r²= (-12+10)²+(3/2-0)²= 4+ 9/4
r² = 25/4 so : r = 5/2
the standard equation for the circle is:
(x+10)²+y² =25/4
Isabella opens a savings account with an initial deposit of $6,300. Isabella’s account pays 2% in compound interest. If Isabella makes no other deposits or withdrawals, how much money would Isabella have in the savings account after 2 years?
The required Isabella would have $6,574.92 in the savings account after 2 years.
After 1 year, Isabella's account would have grown to:
[tex]A = P(1 + r)^n[/tex]
[tex]A = $6,300(1 + 0.02)^1[/tex]
A = $6,426
After 2 years, the account would have grown to:
A = $6,300(1 + 0.02)
A = $6,574.92
Therefore, Isabella would have $6,574.92 in the savings account after 2 years.
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7. Which type of function best models the data in the table? Use the differences or ratios:
X. Y
-1. 2.5
0. 5
1. 10
2. 20
3. 40
The type of function that models the data in the table is an exponential function
Identifying the type of function that models the data in the table?From the question, we have the following table of values that can be used in our computation:
X. Y
-1. 2.5
0. 5
1. 10
2. 20
3. 40
The above definitions imply that we simply multiply 2 to the previous term to get the current term
This means that the function is an exponential function
Hence, the type of function that models the data in the table is an exponential function
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Question 9 of 10
The vertex of this parabola is at (2, -4). When the y-value is -3, the x-value is
-3. What is the coefficient of the squared term in the parabola's equation?
10
10+
-10
O A. -1
OB. -5
O C. 1
DE
← PREVIOUS
(2,-4)
10
The coefficient of the squared term in the parabola's equation is 1/25.
How to determine the factored form of a quadratic equation?In this exercise, you are required to determine the factored form of the given quadratic function that passes through the points (2, -4) and (-3, -3).
In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:
f(x) = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided above, we can determine the value of a as follows:
f(x) = a(x - h)² + k
-3 = a(-3 - 2)² - 4
-3 = 25a - 4
1 = 25a
a = 1/25
Therefore, the required quadratic function is given by:
f(x) = a(x - h)² + k
f(x) = y = 1/25(x - 2)² - 4
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Find the arc length
The arc length equals 18.85 yd
How to find the arc length?An arc length is given by L = Ф/360 × 2πr where
Ф = angle of arc and r = radius of circleTo find the arc length of the given circle, given that
Ф = 135° and r = 8 ydSo, substituting the values of the variables into the equation, we have that
L = Ф/360 × 2πr
L = 135°/360° × 2π × 8 yd
L = 135°/360° × 16π yd
L = 2160π/360° yd
L = 6785.84 yd/360
L = 18.85 yd
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Answer:
u still on here Delilah?
Step-by-step explanation:
Which of the following must be used to find the number of bit strings of length seven that either begin with two Os or end with three 1s? a. the inclusion-exclusion principle b. the sum rule c. the product rule d. the division rule
The correct answer is a. the inclusion-exclusion principle must be used to find the number of bit strings of length seven that either begin with two Os or end with three 1s.
This is because we need to subtract the number of bit strings that both begin with two Os and end with three 1s (which are counted twice if we simply add the number of bit strings that begin with two Os and the number that end with three 1s). The inclusion-exclusion principle allows us to do this by first adding the number of bit strings that begin with two Os and the number that end with three 1s, and then subtracting the number of bit strings that both begin with two Os and end with three 1s.
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