The equation of the circle in standard form is (x - 5)² + (y + 4)² = 36
The center of the circle is the midpoint of the diameter.
Using the midpoint formula, we can find the center as follows:
x-coordinate of center = (x-coordinate of endpoint 1 + x-coordinate of endpoint 2)/2
= (-1 + 11)/2
= 5
y-coordinate of center = (y-coordinate of endpoint 1 + y-coordinate of endpoint 2)/2
= (-4 - 4)/2
= -4
So the center of the circle is (5, -4) and the radius is half the length of the diameter:
radius = distance between endpoints of diameter/2
= √(11 - (-1))² + (-4 - (-4))²]/2
= 6
Therefore, the equation of the circle in standard form is (x - 5)² + (y + 4)² = 36
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you are a bank officer. Elena comes to you seeking a loan. She tells you that she has sure-fire idea for a business that simply cannot fail. She stays further that the bank will not be risking a penny by granting her the loan. Do Elenas claims encourage you of discourage you from approving the loan.
As a bank officer, Elena's claims would not be enough to encourage me to approve the loan. It's important to look at the details of her business plan, her financial history and her credit score before making a decision. Even if Elena believes that her business idea cannot fail, there is always a risk involved in lending money. It's important to assess the risk and make a decision based on the facts, rather than on promises or guarantees.
Answer:
Step-by-step explanation:
Her claims encourage you.
Find the sector area for the following
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=6\\ \theta = \frac{2\pi }{3} \end{cases}\implies A=\cfrac{~~ \frac{2\pi }{3 }6^2 ~~}{2}\implies A=12\pi \stackrel{ using~\pi =3.14 }{\implies A=37.68}[/tex]
Help please step by step
Tom does have enough fertilizer to cover the triangular area, as the triangular area is of 179.6 m², and he has 300 m² of fertilizer.
How to obtain the area of a triangle?We are given the three sides of the triangle, hence the first step in obtaining the area is obtaining the semi-perimeter, which is half the perimeter, hence:
s = (26 + 20 + 18)/2
s = 32 m.
The area of the triangle is then obtained as follows:
[tex]A = \sqrt{s(s - a)(s - b)(s - c)}[/tex]
[tex]A = \sqrt{32(32 - 26)(32 - 20)(32 - 18)}[/tex]
A = 179.6 m².
Hence Tom does have enough fertilizer to cover the triangular area, as the triangular area is of 179.6 m², and he has 300 m² of fertilizer.
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If x = 5, then which equation is NOT true?
-2x ≤ 12
x - 2>7
2x < 12
x-7<2
Answer:
x - 2 > 7
Step-by-step explanation:
Substitute the value 5 for x.
x = 5
-2x ≤ 12
-2(5) ≤ 12
-10 ≤ 12 True
-10 is less than or equal to 12
x - 2 > 7
5 - 2 > 7
3 > 7 Not true
3 is greater than 7
2x < 12
2(5) < 12
10 < 12 True
10 is less than 12
x - 7 < 2
5 - 7 < 2
-2 < 2 True
-2 is less than 2
which inference method can be used to test for a difference between the average iq scores of identical twins raised by birth parents and in a foster home? circle the correct choice.
The appropriate inference method to test for a difference between the average IQ scores of identical twins raised by birth parents and in a foster home is paired t-test.
A paired t-test is used when comparing two sets of observations that are paired or matched in some way, such as in the case of identical twins. In this scenario, the twins are matched based on their genetic makeup, and their IQ scores are compared based on their different upbringing environments (birth parents vs. foster home). The paired t-test allows us to analyze the difference between the paired observations (IQ scores) and determine if there is a statistically significant difference between the two groups.
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What multiplies to -25 and adds to 0?
Answer:
-5 and 5
Step-by-step explanation:
[tex]-5*5=-25\\\\-5+5=0[/tex]
Find the perimeter of quadrilateral PQRS given that the coordinates of its vertices are
P(1,3),Q(3,1),R(1,−1), and S(−2,−1). You may round your answer to one decimal place.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ P(\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad Q(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill PQ=\sqrt{(~~ 3- 1~~)^2 + (~~ 1- 3~~)^2} \\\\\\ ~\hfill PQ=\sqrt{( 2 )^2 + ( -2)^2} \implies \boxed{PQ=\sqrt{ 8}}[/tex]
[tex]Q(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad R(\stackrel{x_2}{1}~,~\stackrel{y_2}{-1}) ~\hfill QR=\sqrt{(~~ 1- 3~~)^2 + (~~ -1- 1 ~~)^2} \\\\\\ ~\hfill QR=\sqrt{( -2)^2 + ( -2)^2} \implies \boxed{QR=\sqrt{ 8}} \\\\\\ R(\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad S(\stackrel{x_2}{-2}~,~\stackrel{y_2}{-1}) ~\hfill RS=\sqrt{(~~ -2- 1~~)^2 + (~~ -1- (-1)~~)^2} \\\\\\ ~\hfill RS=\sqrt{( -3)^2 + ( 0)^2} \implies RS=\sqrt{ 9}\implies \boxed{RS=3}[/tex]
[tex]S(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad P(\stackrel{x_2}{1}~,~\stackrel{y_2}{3}) ~\hfill SP=\sqrt{(~~ 1- (-2)~~)^2 + (~~ 3- (-1)~~)^2} \\\\\\ ~\hfill SP=\sqrt{( 3)^2 + ( 4)^2} \implies SP=\sqrt{ 25}\implies \boxed{SP=5} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Perimeter} }{\sqrt{8}+\sqrt{8}+3+5} ~~ \approx ~~ \text{\LARGE 13.7}[/tex]
Find the y-intercept of the line on the graph.
Step-by-step explanation:
'y - intercept' is shorthand for ' y-axis intercept' ....or the value of the graph where it crosses the y - axis
this one is point (0,3) or y-intercept = 3
The number of views of a video on the internet is shown in the table below as a function of the time since the video was posted
The linear regression equation that best fits the data set is y = 126x + 462.
How to explain the regressionTo find the linear regression equation, we can use the following steps:
Calculate the slope and the y-intercept..
In this case, we have the following values:
y₂ = 4,920
y₁ = 650
x₂= 20
x₁ = 2
Substituting these values into the formula, we get the following:
m = (4,920 - 650)/(20 - 2) = 2,270/18 = 126.11
The y-intercept is calculated using the following formula:
b = y - mx
In this case, we can use the point (2, 650) because it is the first point in the table. Substituting these values into the formula, we get the following:
b = 650 - 126.11(2) = 461.89
The linear regression equation that best fits the data set is y = 126.11x + 461.89. Round each parameter to the nearest whole number, we get y = 126x + 462.
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The number of views of a video on the internet is shown in the table below as a function of the time since the video was posted (in hours).
Number of hours, x
Number of views, y
2
650
5
1,280
8 12
2,140
3,120
17
4,050
20
4,920
Find a linear regression equation, in the form y=ax+b, that best fits this data set. Round each parameter to the nearest whole number.
Use the interactive graph below to sketch a graph of y = 310g, (-X) - 9.
The sketch of the graph of the logarithm function is added s an attachment
Sketching the graph of the logarithm functionFrom the question, we have the following parameters that can be used in our computation:
y = 3log₂(-x) - 9
The above equations is an illustration of a logarithm function that has been transformed using the following
Reflected across the y-axisVertically stretched by a factor of 3Translated down by 9 unitsNext, we plot the graph using a graphing tool
The graph of the logarithm function is added as an attachment
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Work out 3.4 cos 13 degrees rounded to 2 d.p
Answer:
To work out 3.4 cos 13 degrees, you can use a calculator or a table of trigonometric functions that includes cosine values.
Using a calculator, you can simply enter "3.4 * cos(13)" and get the answer. Rounding to 2 decimal places gives:
3.4 * cos(13) ≈ 3.298
Therefore, 3.4 cos 13 degrees, rounded to 2 decimal places, is approximately equal to 3.30.
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A rectangle is 2 0 meter long and 2 3 meters wide. What is the area of the rectangle? Enter your answer in the box below.
Answer:
The answer is 460m²
Step-by-step explanation:
Area of rectangle =Length × Width
A=20×23
A=460m²
Answer:460
Step-by-step explanation: 20
x 23
_____
60
+400
Wyatt’s math teacher wrote the following data set on the board.
10, 2.8, 6.5, 21.6, 8.2, 9.3, 4, 2.8
What is the range of the data?
Answer:
18.8
Step-by-step explanation:
To find the range of a data set, you subtract the smallest value from the largest value.
In this case, the smallest value is 2.8 and the largest value is 21.6.
Range = largest value - smallest value = 21.6 - 2.8 = 18.8
Therefore, the range of the data set is 18.8.
The points D(−3,−4), E(5,0), F(3,4), and G(−5,0) form rectangle DEFG. Plot the points then click the "Graph Quadrilateral" button. Then find the area of the rectangle.
If the points D(−3,−4), E(5,0), F(3,4), and G(−5,0) form rectangle DEFG then the area is 40 square units.
The length of the rectangle can be found by finding the distance between D and E (or F and G), which is:
√(5 - (-3))² + (0 - (-4))²] = √8² + 4²
= √80
= 4√5
The width of the rectangle can be found by finding the distance between D and G (or E and F), which is:
√-5 - (-3))² + (0 - (-4))²
= √(-2)²+ 4²
= √20
= 2√5
Therefore, the area of the rectangle is:
length x width = 4√5 x 2√5
= 8 x 5
= 40
Hence, 40 square units is area of the given rectangle DEFG.
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Approximate the area under the function between a and b using a left-hand sum with the given number of intervals. f(x) = x² − x a = 0 b=3 3 Intervals
a customer can choose one of two amplifiers, one of four compact disc players, and one of eight speaker models for an entertainment system. determine the number of possible system configurations.
There are 64 possible system configurations that can be made from the given choices of two amplifiers, four CD players, and eight speaker models.
To determine the number of possible configurations, we multiply the number of choices available for each component of the system. Since the customer can choose one of two amplifiers, one of four CD players, and one of eight speaker models, the total number of possible configurations is given by:
2 (amplifiers) × 4 (CD players) × 8 (speakers) = 64
Therefore, there are 64 possible system configurations that can be made from the given choices of two amplifiers, four CD players, and eight speaker models.
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which of the following facts should make you the most worried about the reliability of the results of the test in this case? there is no need to worry because all of the expected cell counts are above 5. the sample was only 300 black women and is not representative of all black women. two of the six observed counts are 5 or less. not all of the cells' contributions to the chi-squared statistic are greater than 1. two of the six expected counts are less than 5.
Therefore, the reliability of the results may be questioned due to the small sample size and the fact that the observed and expected counts in some cells are too small.
The fact that two of the six observed counts are 5 or less should make you the most worried about the reliability of the results of the test in this case. This is because when the observed counts in a cell are too small, it is difficult to draw reliable conclusions from them. In such cases, the chi-squared statistic may not accurately reflect the true relationship between the variables being studied. This is because the chi-squared statistic is based on the difference between the observed counts and the expected counts, and if the observed counts are too small, the chi-squared statistic may be biased and not accurately reflect the true relationship between the variables.
Moreover, the fact that two of the six expected counts are less than 5 also raises concerns about the reliability of the results. This is because when the expected counts in a cell are too small, it may indicate that the sample size is too small or that the sample is not representative of the population being studied. In this case, the sample size was only 300 black women, which may not be representative of all black women.
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p(x) = 2x^3 -5x^2 + 7x - 3 find p(2) , p(0), p(-1), p(-2)
POLYNOMIAL CLASS 9 QUESTION
PLS, I NEED ANSWER FAST
The value of p(2) = 7, p(0) = -3 , p(-1) = -17 and p(-2) = -53 when polynomial is p(x) = 2x³ - 5x² + 7x - 3 with one variable.
Given that,
The polynomial is p(x) = 2x³ - 5x² + 7x - 3
We have to find the value of p(2), p(0), p(-1) and p(-2).
We know that,
Take polynomial,
p(x) = 2x³ - 5x² + 7x - 3
Now, to find p(2) take x = 2 in polynomial
By substituting,
p(2) = 2(2)³ - 5(2)² + 7(2) - 3
p(2) = 16 - 20 + 14 - 3
p(2) = 30 - 23
p(2) = 7
Now, to find p(0) take x = 0 in polynomial
p(0) = 2(0)³ - 5(0)² + 7(0) - 3 [multiplication]
p(0) = 0 - 0 + 0 - 3
p(0) = -3
Now, to find p(-1) take x = -1 in polynomial
p(-1) = 2(-1)³ - 5(-1)² + 7(-1) - 3
p(-1) = -2 - 5 - 7 - 3 [subtraction]
p(-1) = -17
Now, to find p(-2) take x = -2 in polynomial
p(-2) = 2(-2)³ - 5(-2)² + 7(-2) - 3
p(-2) = -16 - 20 - 14 - 3
p(-2) = -53
Therefore, The value of p(2) = 7, p(0) = -3 , p(-1) = -17 and p(-2) = -53.
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WORTH 20 POINTS
PLS HELP ME AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
A ratio is a relationship in which for every x units of one quantity there are y units of another quantity. Ratios are considered to be equivalent if they express the same x/y. A ratio compares 2 like or unlike quantities by division. Ratios can be shown visually using a graph or a ratio table.
Find the value of sides RS
Answer:
RS = 15 units
Step-by-step explanation:
Given:
RT = 9
TS = 12
To find: Length of RS
Proof:
In right triangle RTS,
[tex]RT^{2} + TS^{2} = RS^{2}[/tex]
[tex]9^{2} + 12^{2} = RS^{2}[/tex]
[tex]81 + 144 = RS^{2}[/tex]
[tex]225 = RS^{2}[/tex]
[tex]\sqrt{225} = RS[/tex]
15 = RS
∴ The length of RS is 15 units.
Find the limit of the following sequence or determine that the sequence diverges.
StartSet StartFraction left parenthesis 9 n plus 1 right parenthesis exclamation mark Over left parenthesis 9 n right parenthesis exclamation mark EndFraction EndSet(9n+1)!(9n)!
The term (9n+1) grows without bound as n approaches infinity, the limit does not exist. Therefore, the sequence diverges.
To find the limit of the given sequence, we can use the ratio test:
StartFraction
(9(n+1)+1)! / (9(n+1))!
Over
(9n+1)! / (9n)!
EndFraction
Simplifying the expression, we get:
StartFraction
(9n+10)(9n+9)(9n+8)...(9n+2)(9n+1)
Over
(9n+1)(9n)(9n-1)...(2)(1)
EndFraction
The terms cancel out and we are left with:
StartFraction
(9n+10)(9n+9)
Over
9n(9n+1)
EndFraction
Taking the limit as n approaches infinity, we get:
lim (n → ∞) StartFraction
(9n+10)(9n+9)
Over
9n(9n+1)
EndFraction
= lim (n → ∞) StartFraction
81n² + 81n + 90
Over
81n² + 9n
EndFraction
= lim (n → ∞) StartFraction
n² + n + 10 / n² + n / 9
EndFraction
As n approaches infinity, the higher order terms dominate, so we can ignore the constants and simplify the expression to:
lim (n → ∞) StartFraction
n² / n²
EndFraction
= 1
Since the limit exists and is finite, the sequence converges. Therefore, the limit of the sequence is 1.
To find the limit of the given sequence or determine if it diverges, consider the sequence:
a_n = (9n+1)! / (9n)!
We can rewrite the sequence using the properties of factorials:
a_n = [(9n+1)(9n)(9n-1)...(9n-(9n-1))] / (9n)!
a_n = (9n+1)
Now, we'll examine the limit as n approaches infinity:
lim (n -> ∞) a_n = lim (n -> ∞) (9n+1)
Since the term (9n+1) grows without bound as n approaches infinity, the limit does not exist. Therefore, the sequence diverges.
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describe the pattern 9;16;25;36;49 by words and algebraically
Given the pattern:
9, 16, 25, 36, 49
In words, this pattern represents:
the sequence of perfect squares of consecutive integers starting from 3.The numbers are obtained by squaring the integers 3, 4, 5, 6, and 7, respectively.
Algebraically, we can represent the pattern using the formula:
t(n) = (n + 2)², where t(n) is the nth termyour ceiling is 250 centimeters high, you want the tree to have 35 centimeters of space with the ceiling. how tall must the tree be? (in centimeters)
To calculate the height of the tree that would leave a 35 cm space from a 250 cm tall ceiling, subtract the desired space from the total height. Hence, the tree should be 215 centimeters tall.
Explanation:The calculation involves understanding and using the concepts of height and ceiling space. When you want a tree to leave a certain amount of space from the ceiling, you have to subtract that desired space from the total height of the room. So, if your ceiling is 250 centimeters high and you desire a space of 35 centimeters to be left, the tree's height should be calculated as follows:
Subtract the desired space from the total height: 250 cm - 35 cm The result would then give the height of the tree: 215 cm
So, in this scenario, the tree must be 215 centimeters tall to fit perfectly under your ceiling with 35 centimeters of space left.
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use quantifiers and logical connectives to express the factthat every linear polynomial (that is, polynomial of degree 1) with real coefficients and where the coefficient ofx is nonzero, has exactly one real root.
The expression states that for every linear polynomial p with real coefficients and a nonzero coefficient of x, there is exactly one real root r.
For all linear polynomials with real coefficients and a nonzero coefficient of x, there exists exactly one real root. This can be expressed using the universal quantifier "for all" and the existential quantifier "there exists", connected by the logical connective "and". Additionally, the statement "exactly one real root" can be expressed using the quantifier "there exists" and the logical connective "and".
Using quantifiers and logical connectives, we can express the given fact as follows:
∀p ∃!r ((isLinearPolynomial(p) ∧ hasRealCoefficients(p) ∧ coefficientOfX(p) ≠ 0) → hasRealRoot(p, r))
Explanation:
- ∀p: For every polynomial p
- ∃!r: There exists exactly one real root r
- isLinearPolynomial(p): p is a linear polynomial (degree 1)
- hasRealCoefficients(p): p has real coefficients
- coefficientOfX(p) ≠ 0: The coefficient of x in p is nonzero
- hasRealRoot(p, r): p has a real root r
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Which measure of central tendency is used to determine the average annual percent
increase?
A) Mode
B) Arithmetic mean
C) Median
D) Weighted mean
E) Geometric mean
The geometric mean is used to determine the average annual percent increase, as it accurately accounts for compounding growth over multiple periods. The correct option is E.
The measure of central tendency that is typically used to determine the average annual percent increase is the arithmetic mean. This measure takes the sum of all the values and divides it by the total number of values.
It is important to note that other measures, such as the geometric mean, can also be used in certain situations. But for most cases, the arithmetic mean is the go-to measure for determining the average annual percent increase.
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can you help me with this math
A basket of beads contains 8 red beans , 6 yellow beads, and 6 greens . A bead will be drawn from the basket and replaced 150 times. What is the reasonable prediction for the number of times a green bead is drawn
Step-by-step explanation:
green is 6 out of a total of ( 8+6+6 = 20 ) beads
so 6/20 ths of the time it should be a green bead
6/20 * 150 = 45 times should be green
Find the y-intercept of the line on the graph.
find the confidence interval. thirty students received scholarship averaging $7,000 with a standard deviation of $500. find the 99% confidence interval.
We can use the formula for the confidence interval for a population mean with a known standard deviation. Plugging in the values, we get the interval (6817.22, 7182.78).
To find the 99% confidence interval for the scholarship averages of thirty students, we need to use the following formula:
CI = X ± zα/2 * (σ/√n)
Where
X = sample mean ($7,000 in this case)
zα/2 = the z-score corresponding to the desired confidence level (99% in this case), which is 2.576
σ = population standard deviation ($500 in this case)
n = sample size (30 in this case)
Substituting these values into the formula, we get:
CI = 7000 ± 2.576 * (500/√30)
Simplifying this expression, we get:
CI = 7000 ± 182.78
Therefore, the 99% confidence interval for the scholarship averages of thirty students is
(7000 - 182.78, 7000 + 182.78)
= (6817.22, 7182.78)
So we can say with 99% confidence that the true population mean scholarship amount lies within this interval.
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Please help me. I have so much late work I need this asap;
Answer: 7, 6 ,7
Step-by-step explanation:
