Write the equation of each circle. center at (-4, 3), radius 9
Answers
Answer:
(x-h)²+(y-k)²=r²
putting respective value
(x--4)²+(y-3)²=9²
(x+4)²+(y-3)²=81
Answer:
(x + 4)^2 + (y - 3)^2 = 9^2
Step-by-step explanation:
Here our center is at (-4, 3), so h = -4 and k = 3. Radius, r, is 9.
Insert these values into the standard equation of a circle centered at (h, k) with radius r:
(x - h)^2 + (y - k)^2 = r^2 becomes:
(x + 4)^2 + (y - 3)^2 = 9^2
Related Questions
The company ALTA Ltd issued a bank accepted bill to fund its working capital requirement. The bill is issued for 60 days, with a face value of $150,000 and a yield of 2.5% per annum to the original discounter. After 25 days, the bank bill is sold by the wwwwww original discounter into the secondary market for $138,222. The purchaser holds the bill to maturity. What is the yield received by the holder of the bill at the date of maturity?
Answers
the yield received by the holder of the bill at the date of maturity is approximately 10.15%.
To calculate the yield received by the holder of the bill at the date of maturity, we need to use the formula for yield to maturity. The formula is:
Yield to Maturity = (Face Value - Purchase Price) / Purchase Price * (365 / Days to Maturity)
In this case:
Face Value = $150,000
Purchase Price = $138,222
Days to Maturity = 60 - 25 = 35
these values in the formula, we can calculate the yield to maturity:
Yield to Maturity = ($150,000 - $138,222) / $138,222 * (365 / 35)
Yield to Maturity ≈ 0.1015 or 10.15%
Therefore, the yield received by the holder of the bill at the date of maturity is approximately 10.15%.
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what does the highest point on a bell-shaped curve represent?
Answers
The highest point on a bell-shaped curve represents the peak or maximum value of the distribution. This point is known as the mode of the distribution.
In a bell-shaped curve, also known as a normal distribution or Gaussian distribution, the data is symmetrically distributed around the mean. The curve is characterized by a central peak, and the highest point on this peak corresponds to the mode.
The mode represents the most frequently occurring value or the value that has the highest frequency in the dataset. It is the point of highest density in the distribution.
The bell-shaped curve is often used to model naturally occurring phenomena and is widely applied in statistics and probability theory. The mode provides information about the most common or typical value in the dataset and is useful for understanding the central tendency of the distribution.
While the mean and median also have significance in a normal distribution, the highest point on the bell-shaped curve specifically represents the mode, indicating the value with the highest occurrence in the dataset.
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give all possible polar coordinates for the point (−7,−73–√) given in rectangular coordinates.
Answers
The other set of polar coordinates for the point (-7, -7√3) is (14, 4π/3) or (14, 240°) in degrees.
To find the polar coordinates for a point given in rectangular coordinates, we use the formulas: r = √(x^2 + y^2) and θ = tan^-1(y/x).
Using these formulas, we can find the polar coordinates for the point (-7, -7√3):
r = √((-7)^2 + (-7√3)^2) = √(49 + 147) = √196 = 14
θ = tan^-1((-7√3)/-7) = tan^-1(√3) = π/3
Therefore, the polar coordinates for the point (-7, -7√3) are (14, π/3) or (14, 60°) in degrees.
It is important to note that there is another set of polar coordinates for this point, since the point (-7, -7√3) is in the third quadrant, and angles in the third and fourth quadrants are measured with respect to the negative x-axis. So, we add π to our angle to get:
θ = tan^-1((-7√3)/-7) + π = tan^-1(√3) + π = 4π/3
Therefore, the other set of polar coordinates for the point (-7, -7√3) is (14, 4π/3) or (14, 240°) in degrees.
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How do you write an equation of a line through points (3,1) and (4,-4)?
Answers
Answer:
y = - 5x + 16
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (3, 1 ) and (x₂, y₂ ) = (4, - 4 )
m = \(\frac{-4-1}{4-3}\) = \(\frac{-5}{1}\) = - 5 , then
y = - 5x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (3, 1 )
1 = - 5(3) + c = - 15 + c ( add 15 to both sides )
16 = c
y = - 5x + 16 ← equation of line
x = 25 21 = 120° 42 = [?]° 5x -5 2x + 10
![x = 25 21 = 120 42 = [?] 5x -5 2x + 10](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/siq5MK6arLebs4BtzhhmrSCmUa378Vt8.jpeg)
Answers
Answer:
It should be 60 degrees
Step-by-step explanation:
A clinical trial was conducted to test the effectiveness of the drug zopiclone for treating insomrua in older subjects. Before treatment with zopiclone, 16 subjects had a mean wake time of 102.8 min. After treatment with zopiclone, the 16 subjects had a mean wake time of 98.9 min and a standard deviation of 42.3 min (based on data from "Cognitive Behavioral Therapy vs Zopiclone for Treatment of Chronic Primary Insomrua in Older Adults," by Sivertsen et al., Journal of the American Medical Association, Vol. 295, No. 24). Assume that the 16 sample values appear to be from a normally distributed population, and test the claim that after treatment with zopiclone, subjects have a mean wake time of less than 102.8 min. Does zopiclone appear to be effective?
Answers
A 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments is 74.26 to 125.54.
What is a confidence interval?
A confidence interval (CI) is a range of values that, with a particular level of certainty, is likely to encompass a population value. A population mean that sits between an upper and lower interval is frequently stated as a percentage.
Here,
From the standard normal table, the z-critical value at 98% confidence interval is 2.33 so,
98%C.I. = µ ± z * σ / n = 98.90 ± 2.33 * 42.30 / sqrt of 16 = 98.90 ± 24.64 = 74.26 to 125.54
The mean wake time of 102.80 minutes before the treatment due to the mean wake time of 102.80 minutes included in the 98% confidence interval which is between 74.26 and 125.54. Zopiclone does not appear effective.
Hence, A 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments is 74.26 to 125.54.
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A = {multiples of 3 between 20 and 32}
B = {odd numbers between 20 and 32}
C = {even numbers between 20 and 32}
a) List the members of A U B
Answers
Answer:
A={21,24,27,30}
B={21,27}
C={24,30}
Step-by-step explanation:
a)A U B={21,24,27,30}
b)A n C ={24,30}
9514 1404 393
Answer:
A ∪ B = {21, 23, 24, 25, 27, 29, 30, 31}
A ∩ C = {24, 30}
Step-by-step explanation:
A = {21, 24, 27, 30} . . . . . . . . . . . . . multiples of 3
B = {21, 23, 25, 27, 29, 31} . . . . . . . odd numbers
C = {20, 22, 24, 26, 28, 30, 32} . . . even numbers
The union is the list of numbers in either set.
A ∪ B = {21, 23, 24, 25, 27, 29, 30, 31}
The intersection is the list of numbers in both sets.
A ∩ C = {24, 30}
Find laplace transform l{e2−t u(t −2)}
Answers
The Laplace transform of the given function is L{ \(e^(2-t^)\) u(t-2)} = \(e^-^2^s\) * e² * (1/(s + 1)).
The Laplace transform L{ \(e^(2-t^)\) u(t-2)} can be found using the following steps:
1. Identify the function: f(t) = \(e^(2-t^)\) u(t-2)
2. Apply the time-shift property: L{ \(e^(2-t^)\) u(t-2)} = \(e^-^2^s\) * L{e² * \(e^-^t\) }
3. Calculate the Laplace transform: L{e² * \(e^-^t\) } = e² * L{ \(e^-^t\) }
4. Apply the formula: L{ \(e^-^t\) } = 1/(s + 1)
5. Multiply: \(e^-^2^s\) * e² * (1/(s + 1))
In this process, we first identified the given function and then applied the time-shift property to simplify it.
Next, we calculated the Laplace transform of the simplified function using the formula for the Laplace transform of an exponential function. Finally, we combined the results to obtain the Laplace transform of the original function.
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Solve 5 - 2x < 7.
A.) x<-1
B.) x>-1
C.) x<-12
D.) x>-12
Answers
Answer:
B
Step-by-step explanation:
-2x<7-5
-2x<2 multiplied by -1 gives 2x>-2 and devided by 2 you have x>-1
1. What does the mean of a dataset represent? What does knowing
the standard deviation of a
dataset add?
2. What is a p value? What is the meaning of a p value?
3. Define alpha. How is it related to p
Answers
1. The mean of a dataset represents the average value of the entire set of numbers. It is calculated by adding up all the values and dividing by the number of values in the dataset. Knowing the standard deviation of a dataset adds information about how much the values deviate from the mean.
A high standard deviation indicates that the values are more spread out from the mean, while a low standard deviation indicates that the values are closer to the mean. It can help to identify outliers and the overall variability of the dataset.
2. A p-value is a statistical measure that helps to determine whether the null hypothesis (there is no significant difference between two groups) is true or false.
It is the probability of obtaining a result as extreme or more extreme than the observed result, assuming that the null hypothesis is true. A p-value of less than 0.05 (typically) is considered statistically significant, which means that there is strong evidence to reject the null hypothesis and accept the alternative hypothesis (there is a significant difference between the two groups).
3. Alpha is the level of significance that is set to determine whether a p-value is statistically significant or not. It is typically set at 0.05, which means that if the p-value is less than 0.05, then the result is considered statistically significant and the null hypothesis is rejected.
If the p-value is greater than 0.05, then the result is not statistically significant and the null hypothesis cannot be rejected. In summary, alpha and p-value are related because alpha sets the threshold for determining whether a p-value is statistically significant or not.
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A=5. Move the dot to -(-A) on the number line
Answers
Please help quick I still can’t figure it out
Answers
Step-by-step explanation:
3+21+7+3+21+7
2x = 5x - 30 how do i get x
Answers
-3x = -30
Then divide both sides by -3 to get x = 10
Have a nice day.
Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (1,6) and perpendicular to 3 x + 7y = 1.a) The equation of the line in slope-intercept form is enter your response here
Answers
The equation
\(3x+7y=1\)\(7y=-3x+1\)\(y=\frac{-3x}{7}+\frac{1}{7}\)has slope -3/7.
The product of perpendicular lines must be -1, so the slope of the new equation must be:
\(m\cdot-\frac{3}{7}=-1\)\(m=\frac{-1\cdot7}{-3}=\frac{7}{3}\)The line with that slope and that passes throught (1,6) is:
\((y-6)=m(x-1)\)\((y-6)=\frac{7}{3}(x-1)\)\(y-6=\frac{7}{3}x-\frac{7}{3}\)\(y=\frac{7}{3}x-\frac{7}{3}+6\)\(y=\frac{7}{3}x-\frac{7}{3}+\frac{18}{3}\)\(y=\frac{7}{3}x+\frac{11}{3}\)The following graph shows both equations:
\(y=\frac{7}{3}x+\frac{11}{3}\)\(3\cdot y=(\frac{7}{3}x+\frac{11}{3})\cdot3\)\(3y=7x+11\)\(-7x+3y=11\)
Eight cars are to be parked in a row for viewing at a fair. Three of the cars are the same colour and are to be kept together in the viewing row. Determine the number of possible arrangements of the cars, given that the three cars of the same colour are kept together.
Answers
Answer:
720 possible arrangements.
Step-by-step explanation:
The possible arrangement of the cars, given that the three cars of the same color are kept together is 4320.
What is combination?The combination is a way of selecting items from a collection where the order of selection does not matter.
We have,
Number of cars = 8
Number of cars that are the same in color = 3
Cars that are the same in color can be arranged = 3!
There are 8 cars such that,
1 2 3 4 5 6 7 8
Three cars of the same color are taken out and we have,
1 2 3 4 5
We see that there are six spaces = 6!
where we can put the same color cars together so,
The possible arrangement of the cars, given that the three cars of the same color are kept together:
= 3! x 6!
= 3 x 2 x 1 x 6 x 5 x 4 x 3 x 2 x 1
= 4320
Thus,
The possible arrangement of the cars, given that the three cars of the same color are kept together is 4320.
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in isosceles triangle ABC,AB=AC.If B=55,calculate A
Answers
The measure of angle A in the isosceles triangle ABC is 62.5 degrees.
In an isosceles triangle ABC, where AB = AC, we are given that angle B (denoted as ∠B) measures 55 degrees. We need to calculate the measure of angle A (denoted as ∠A).
Since AB = AC, we know that angles A and C are congruent (denoted as ∠A ≅ ∠C). In an isosceles triangle, the base angles (the angles opposite the equal sides) are congruent.
Therefore, we have:
∠A ≅ ∠C
Also, the sum of the angles in a triangle is always 180 degrees. Hence, we can write:
∠A + ∠B + ∠C = 180
Substituting the given values:
∠A + 55 + ∠A = 180
Combining like terms:
2∠A + 55 = 180
Subtracting 55 from both sides:
2∠A = 180 - 55
2∠A = 125
Dividing by 2:
∠A = 125 / 2
∠A = 62.5
Therefore, the measure of angle A in the isosceles triangle ABC is 62.5 degrees.
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If sam can eat 4 pies in every 1/3 minute how many pies per minute can sam eat
\(help\)
Answers
Answer: 12
Step-by-step explanation: 4x3= 12 hope it helps! :)
a sample of 50 11th graders were asked to select a favorite pattern
Answers
A mathematical process called subtraction reflects the elimination of items from a collection. There are 14 pupils that enjoy pink polka dots.
How does subtraction work?A mathematical process called subtraction reflects the elimination of items from a collection.
Subtraction is symbolised by the negative sign.
Considering that there were 50 students in the sample as a whole, the number of pupils who enjoy pink polka dots is as follows:
50 students divided by (4+9+11+9+3) yields 14 students.
Thus, there are 14 students that enjoy pink polka dots.
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The complete question is:
A sample of 50 11th graders was asked to select a favorite pattern out of 6 choices. the following display shows what their favorite color patterns were.
blue on grey 4
green 9
pink polka dots?
purple 11
red and orange stripes 9
yellow 3
The counts have been recorded in the accompanying table according to pattern and the number of students who selected the pattern. what is the missing value in the table?
please help with solving systtems of equation by graphing I'm lost
Answers
Answer:
Solution is (3, -3)
Step-by-step explanation:
To solve by graphing, you literally have to graph both lines to see where they intersect. That point of intersection is the solution to the given system.
Given the following linear equations:
y = - x where the slope (m) = -1, and the y-intercept (b) = 0.
y = x - 6 where the slope (m) = 1, and the y-intercept (b) = -6.
Plot the intercepts (0, 0) for the first line, and (0, -6) for the second line, as a starting point, then use the given slopes (rise over run) of each line to plot the next points. Repeat the process until you have enough points to connect with and create a line.
Attached is a screenshot of the graphed systems of linear equations. It shows that the solution is (3, -3).
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How do I solve this arithmetic sequence?
Answers
In other words, a1 = 13, then
a2 = a1 + 4 = 13 + 4 = 17
a3 = a2 + 4 = 17 + 4 = 21
And so on.
There is a formula to find larger terms.
Since a2 = a1 + 4
a3 = a2 + 4
= (a1 + 4) + 4
= a1 + 2*4
a4 = a3 + 4
= a1 + 2*4 + 4
= a1 + 3*4
And so on, notice the pattern:
an = a1 + (n-1)*d
a6 = a1 + 5*d = 13 + 5*4 = 13 + 20 = 33
Answer:
The 6ᵗʰ term of this sequence is 82
Step-by-step explanation:
Here,
First Term = a₁ = 13
Common Difference = (d) = 4
Now, For 6ᵗʰ term, n = 16
aₙ = a + (n - 1)d
a₆ = 13 + (6 - 1) × 4
a₆ = 13 + 5 × 4
a₆ = 13 + 20
a₆ = 33
Thus, The 6ᵗʰ term of this sequence is 33
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give an expression to 2.5 x +(-5x) -2.5 by combining like terms. PLEASE I NEED THIS RIGHT NOW
URGENT
Answers
Answer:
- 5x
Step-by-step explanation:
note that + (-) = -
2.5x + (- 5x) - 2.5
= 2.5x - 5x - 2.5 ← collect like terms
= 2.5 - 2.5 - 5x
= 0 - 5x
= - 5x
Identify the property demonstrated.
4(3 + 5) = 4 • 3 + 4 • 5
Answers
Answer: Distributive Property
Step-by-step explanation:
The first 300 natural numbers are written in an ascending order of sequence. Now all the numbers at the odd places of this sequence are removed and, thus a new sequence is formed. From this new sequence, all the numbers at odd places are removed once again. This process continues till only one number remains at the end. What is this number?
Answers
The final number remaining in this sequence is the number 2.
We start with the first 300 natural numbers written in ascending order. We remove the numbers at odd places, which means we remove all the numbers at positions 1, 3, 5, and so on.
After the first removal, we are left with the numbers at even positions: 2, 4, 6, and so on.
Now, we repeat the process and remove the numbers at odd positions again. We remove numbers at positions 1, 3, 5, and so on from the remaining sequence.
After the second removal, we are left with the numbers at even positions again: 4, 8, 12, and so on.
We can observe that in each removal, the sequence reduces to half its size, and we are left with the numbers at even positions.
Continuing this process, we will eventually reach a point where we have only one number left.
Since we start with 300 numbers, after the first removal, we have 150 numbers. After the second removal, we have 75 numbers. After the third removal, we have 38 numbers. After the fourth removal, we have 19 numbers. After the fifth removal, we have 10 numbers. After the sixth removal, we have 5 numbers. After the seventh removal, we have 3 numbers. After the eighth removal, we have 2 numbers. Finally, after the ninth and last removal, we are left with a single number.
Therefore, the final number remaining in this sequence is the number 2.
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Use the compound angle formulae to find the following in surd form: tan 225°
Answers
Answer:
On the trig unit circle,
tan 225 = tan (45 + 180) = tan 45 = 1
Chi-square distributions that are positively skewed have a research hypothesis that is?
Answers
Answer:
A one tailed test
Step-by-step explanation:
Chi-Square Distributions That Are Positively Skewed Have A Research Hypothesis That Is A One-Tailed Test.
Chi-Square distributions are positively skewed, with the degree of skew decreasing with increasing degrees of freedom.
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One-Tailed Test
In probability theory and statistics, the chi-square distribution with k degrees of freedom is the distribution of the sum of squares of k independent standard normal random variables. The chi-square distribution is a continuous probability distribution. The shape of the chi-square distribution depends on its degrees of freedom k. It is used to describe the distribution of the sum of squares of random variables. The chi-square distribution is positively skewed, with decreasing skewness as the degrees of freedom increase. The chi-squre distribution approaches the normal distribution on increase of degree of freedom.Chi-Square distributions that are positively skewed have a research hypothesis that is a One-Tailed Test.
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1
2
-17
+
X
5
+ 1 = 2
4
= 21
Answers
Answer:
21
Step-by-step explanation:
You got it right.
What is the perimeter of 2x + 5 + 6x -1
Answers
Answer:
8x + 4
Step-by-step explanation:
Subtract the numbers: 2x + 5 + 6x - 1 2x + 4 + 6x
Then, you combine them like terms: 2x + 4 + 6x = 8x + 4
Which expression is equivalent to (3a + 7) (2a – 5)?
Answers
Answer:
6a^2-a-35
Step-by-step explanation:
(3a + 7) (2a – 5)
F: 6a^2
O: -15a
I: 14a
L: -35
combine like terms
6a^2-a-35
Find the curvature of r(t) =< t^2,ln t,t ln t > at the point
Answers
To find the curvature of the curve defined by the vector function r(t) = < t^2, ln(t), t ln(t) > at a given point, we need to calculate the curvature using the formula:
κ = |dT/ds| / ||dT/ds||,
where dT/ds is the unit tangent vector and ||dT/ds|| is its magnitude.
Let's proceed with the calculations:
Step 1: Find the first derivative of r(t) to get the tangent vector T(t):
r'(t) = < 2t, 1/t, ln(t) + t/t > = < 2t, 1/t, ln(t) + 1 >.
Step 2: Calculate the magnitude of the tangent vector:
||r'(t)|| = sqrt((2t)^2 + (1/t)^2 + (ln(t) + 1)^2)
= sqrt(4t^2 + 1/t^2 + ln(t)^2 + 2ln(t) + 1).
Step 3: Differentiate r'(t) to find the second derivative:
r''(t) = < 2, -1/t^2, 1/t + 2/t > = < 2, -1/t^2, (t + 2)/t >.
Step 4: Calculate the magnitude of the second derivative:
||r''(t)|| = sqrt(2^2 + (-1/t^2)^2 + ((t + 2)/t)^2)
= sqrt(4 + 1/t^4 + (t^2 + 4t + 4)/t^2)
= sqrt((t^6 + 4t^5 + 4t^4) + (t^2 + 4t + 4) + 4t^2).
Step 5: Calculate the curvature:
κ = |dT/ds| / ||dT/ds||
= (||r'(t)|| / ||r''(t)||^3)
= ((sqrt(4t^2 + 1/t^2 + ln(t)^2 + 2ln(t) + 1)) / (sqrt((t^6 + 4t^5 + 4t^4) + (t^2 + 4t + 4) + 4t^2))^3).
To find the curvature at a specific point, substitute the value of t into the expression for κ.
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Simplify each expression
Answers
Answer:
\(3. \: \: ( \frac{7}{8} ) ^{2} = \frac{ {7}^{2} }{ {8}^{2} } = \frac{49}{64} = 0.765 \)\(5. \: \: 8 + 5(7) = 8 + 35 = 43\)
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