Answer:
-3 times n+7>-17
Step-by-step explanation:
Use the parabola tool to graph the quadratic function f(x)=−1/2x2+7
Answer:
use desmos cant add pcitures
Step-by-step explanation:
1. What is the probability of tossing 3 coins of uniform texture at the same time, and two of them happen to be heads up?
The probability of tossing 3 coins of uniform texture at the same time, and two of them happen to be heads up is [tex]\frac{3}{8}[/tex] or 0.375.
The probability of tossing 3 coins of uniform texture at the same time, and two of them happen to be heads up is as follows:
1. Each coin has 2 possible outcomes: heads (H) or tails (T).
2. Since there are 3 coins, there are [tex]2^3 = 8[/tex] total possible outcomes (HHH, HHT, HTH, THH, HTT, THT, TTH, TTT).
3. We're interested in the outcomes where 2 coins are heads up: HHT, HTH, THH.
4. There are 3 favorable outcomes out of 8 total outcomes.
So, the probability of tossing 3 coins of uniform texture at the same time, and two of them happen to be heads up is 3/8 or 0.375.
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Exercise 4. Let n ≥ 2 be an even integer. Determine in how many ways we can color an nxn floor (split into a grid of 1 x 1 tiles) with k colors; we consider two colorings to be the same if we obtain one from the other by rotating the grid.
The number of ways to color an nxn floor with k colors for an even integer n is:
4 * k^(n^2/4).
To determine the number of ways to color an nxn floor with k colors for an even integer n, and considering two colorings to be the same if obtained by rotating the grid, we need to follow these steps:
1. Identify the even integer n and the number of colors k.
2. Calculate the number of unique configurations considering rotations. For a grid of size nxn, there are 4 unique rotations (0, 90, 180, and 270 degrees).
3. For each unique rotation, calculate the number of possible colorings. Since each tile in the grid can be any of the k colors, the number of colorings for each unique rotation is k^(n^2/4), assuming n is divisible by 4.
4. Add up the colorings for all unique rotations. Since there are 4 unique rotations, the total number of colorings, considering rotations to be the same, is 4 * k^(n^2/4).
So, the number of ways to color an nxn floor with k colors for an even integer n, considering two colorings to be the same if obtained by rotating the grid, is 4 * k^(n^2/4).
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What is the difference in cubic inches between the volume of the large prism and volume of the smaller prism?
The difference between the large prism and the small prism is 276 inches cube.
How to find the volume of a prism?The prisms above are rectangular base prisms. Therefore, the difference between the volume of the large prism and volume of the smaller prism can be calculated as follows:
Volume of the larger prisms = lwh
where
l = lengthw = widthh = heightTherefore,
Volume of the larger prisms = 6 × 4 × 15
Volume of the larger prisms = 360 inches³
volume of the smaller prism = 7 × 4 × 3
Volume of the larger prisms = 28 × 3
Volume of the larger prisms = 84 inches³
Therefore,
difference of the volume = 360 - 84
difference of the volume = 276 inches³
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The mean amount spent by each customer on non-medical mask at Chopper Drug Mart is 28 dollars with a standard deviation of 8 dollars. The population distribution for the amount spent on non-medical mask is positively skewed. For a sample of 36 customers, what is the probability that the sample mean amount spent on non-medical mask is greater than 22 dollars but less than 25 dollars?
the probability that the sample mean amount spent on non-medical mask is greater than 22 dollars but less than 25 dollars is approximately 0.0668.
We can use the central limit theorem to approximate the sampling distribution of the sample mean. The mean of the sampling distribution of the sample mean is equal to the population mean, which is 28 dollars, and the standard deviation of the sampling distribution of the sample mean is equal to the standard deviation of the population divided by the square root of the sample size, which is 8/sqrt(36) = 4/3 dollars.
Now we need to find the probability that the sample mean is greater than 22 dollars but less than 25 dollars. Let X be the sample mean amount spent on non-medical mask. Then we need to find P(22 < X < 25).
We can standardize X as follows:
Z = (X - μ) / (σ / sqrt(n))
where μ = 28, σ = 8, and n = 36.
Substituting the values, we get:
Z = (X - 28) / (8/√36)
Z = (X - 28) / (4/3)
So we need to find P((22 - 28)/(4/3) < Z < (25 - 28)/(4/3)), which simplifies to P(-4.5 < Z < -1.5).
Using a standard normal table or calculator, we find:
P(Z < -1.5) ≈ 0.0668
P(Z < -4.5) ≈ 0.00003
Therefore, P(-4.5 < Z < -1.5) ≈ 0.0668 - 0.00003 ≈ 0.0668.
So the probability that the sample mean amount spent on non-medical mask is greater than 22 dollars but less than 25 dollars is approximately 0.0668.
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A group of 25 students spent 1,625 minutes studying for an upcoming test. What prediction can you make about the time it will take 130 students to study for the test?
It will take them 3,250 minutes.
It will take them 4,875 minutes.
It will take them 6,435 minutes.
It will take them 8,450 minutes.
Answer:
8,450 minutes
Step-by-step explanation:
16. Express the line 13x - 14y = 70 in slope intercept form
The line 13x - 14y = 70 expressed in slope-intercept form is y = (13/14)x - 5.
Here are the steps to follow:
Step 1: Start with the given equation, which is in standard form: 13x - 14y = 70.
Step 2: Solve for y to put it in slope-intercept form (y = mx + b, where m is the slope and b is the y-intercept).
First, subtract 13x from both sides of the equation:
-14y = -13x + 70
Next, divide both sides by -14:
y = (13/14)x - 5
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Let T be an unbiased estimator of parameter 0. We have that: (a multiple choice question -- please mark all that apply). a. E (T-0)2 = 0 b. E,(T-0) = 0 c. E(T - ET)2 = 0 d. The MSE of T is the same as the variance of T
If T is an unbiased estimator, then the MSE can be decomposed as follows: MSE(T) = Var(T) + [E(T)-0]^2 = Var(T). Therefore, (d) is true.
(a) E(T-0)^2=Var(T) + [E(T)-0]^2, which is always greater than or equal to 0, but it may not necessarily be 0 unless T is a constant function. Therefore, (a) is false in general.
(b) If E(T-0)=0, then T is an unbiased estimator of 0. This statement is true.
(c) E(T-ET)^2=Var(T) is always greater than or equal to 0, but it may not necessarily be 0 unless T is a constant function. Therefore, (c) is false in general.
(d) The Mean Squared Error (MSE) of T is defined as MSE(T) = E[(T-0)^2]. If T is an unbiased estimator, then the MSE can be decomposed as follows: MSE(T) = Var(T) + [E(T)-0]^2 = Var(T). Therefore, (d) is true.
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Find the value of c on the interval (a, b) such that f'(c) = f(b) − f(a)/b- a
f(x) = 2x^3 - 3x^² - 12x - 4 on interval [5,9]
average rate of change =
The value of c on the interval (5,9) such that f'(c) = f(b) - f(a) / (b - a) is c = 3, and the average rate of change of f(x) on the interval [5,9] is 139.
First, we can find the average rate of change of f(x) on the interval [a,b] using the formula:
average rate of change = [f(b) - f(a)] / (b - a)
Substituting the given values of a = 5 and b = 9 into the formula, we get:
average rate of change = [f(9) - f(5)] / (9 - 5)
Next, we need to find f(9) and f(5) to calculate the average rate of change. To do this, we first need to find the derivative of f(x) using the power rule:
f'(x) = 6x² - 6x - 12
Now, we can use the Mean Value Theorem to find a value c in the interval (5,9) such that f'(c) equals the average rate of change. According to the Mean Value Theorem, there exists a value c in the interval (5,9) such that:
f'(c) = [f(9) - f(5)] / (9 - 5)
Substituting the derivative of f(x) and the values of f(9) and f(5) into the equation, we get:
6c² - 6c - 12 = [2(9)³ - 3(9)² - 12(9) - 4 - (2(5)³ - 3(5)² - 12(5) - 4)] / (9 - 5)
Simplifying the right-hand side of the equation, we get:
6c² - 6c - 12 = (658 - 204) / 4
6c² - 6c - 12 = 114
6c² - 6c - 126 = 0
Dividing both sides by 6, we get:
c² - c - 21 = 0
Using the quadratic formula, we can solve for c:
c = [1 ± sqrt(1 + 4(21))] / 2
c = [1 ± 5] / 2
The two possible values of c are:
c = 3 or c = -4
However, since the interval is (5,9), c must be between 5 and 9. Therefore, the value of c that satisfies the Mean Value Theorem is c = 3.
Finally, substituting f(5) and f(9) into the formula for the average rate of change, we get:
average rate of change = [f(9) - f(5)] / (9 - 5)
= [(2(9)³ - 3(9)² - 12(9) - 4) - (2(5)³ - 3(5)² - 12(5) - 4)] / (9 - 5)
= [434 - (-104)] / 4
= 139
Therefore, the value of c on the interval (5,9) such that f'(c) = f(b) - f(a) / (b - a) is c = 3, and the average rate of change of f(x) on the interval [5,9] is 139.
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log(x + 2) - log 3 = log (5x + 1)
(7, 1) and (-2, 3)
Slope =
The slope of the line passing through (7,1) and (-2,3) is -2/9.
We use the following formula to get the slope of a line through two specified points:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
We can calculate the slope of the line passing through the points (7, 1) and (-2, 3) using this formula:
slope = (3 - 1) / (-2 - 7) = 2 / (-9) = -2/9
Therefore, the slope of the line passing through the points (7, 1) and (-2, 3) is -2/9.
The slope of a line, in geometric terms, is the ratio of the vertical change (rise) to the horizontal change (run). If the slope is negative, the line is decreasing as we move from left to right. With a slope of 2 units downward for every 9 units to the right, the line is sloping downward from left to right.
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7. Determine the total amount of commission: sales: $5,000.00, commission: 3 percent on sales up to $2,000.00, 5 percent on sales from $2,000.00 to $4,000.00, 7 percent on sales over $4,000.00
The total amount of commission is 660 dollars.
Given that,
3 percent on sales up to $2,000.00
Commission = 3% of 2000
= 3/100 × 2000
= $60
5 percent on sales from $2,000.00 to $4,000.00
Commission = 5% of 4000
= 5/100 × 5000
= $250
7 percent on sales over $4,000.00
Commission = 7% of 4000
= 7/100 × 5000
= $350
Total commission=60+250+350
= $660
Therefore, the total amount of commission is 660 dollars.
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Explain why the graph is misleading
For all three points say the reason and explain what specifically is going on in the graph
The graph is misleading because the y values are not labeled
Explaining why the graph is misleadingThe graph represents the given parameter where
The x-axis represent the yearThe y-axis represent the marriage rateExamining the y-axis of the graph, we can see that
The y-axis is not labeled
This means that
We cannot determine what the y values represent
This is because not labelling the y-axis do not show the correct representation of the graph
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Determine the standard deviation of the random variable, B(400,0.9). O A. 10 B. 360 • CV40 D.2 E. 6
The standard deviation of the random variable B(400, 0.9) is 6 (option E).
To determine the standard deviation of the random variable B(400, 0.9), we need to use the formula for the standard deviation of a binomial distribution:
Standard deviation (σ) = √(n * p * (1 - p))
Here, n is the number of trials (400) and p is the probability of success (0.9). Now, let's calculate the standard deviation step by step:
1. Calculate the probability of failure (1 - p): 1 - 0.9 = 0.1
2. Multiply n, p, and the probability of failure: 400 * 0.9 * 0.1 = 36
3. Calculate the square root of the result: √36 = 6
So, the standard deviation of the random variable B(400, 0.9) is 6 (option E).
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The half-life of radium is 1620 year what fraction of the radium sample will remain after 3240 years
So, 0.25 or 25% of the radium sample will remain after 3240 years.
The decay chain for radium-226 is as follows: radium-226 has a half-life of 1600 years and produces an alpha particle and radon-222; radon-222 has a half-life of 3.82 days and produces an alpha particle and polonium-218; polonium-218 has a half-life of 3.05 minutes and produces an alpha particle and lead-214; lead-214 has a half-life of 26.8 minutes and produces.
The half-life of radium is 1620 years, which means that after 1620 years, half of the radium sample will decay, and the remaining half will remain. After another 1620 years (3240 years total), the remaining half will decay, and half of that half, or one-fourth of the original sample, will remain.
Therefore, after 3240 years, the fraction of the radium sample that will remain is:
Formula used :[tex]N(t)=2^{-t/1620}[/tex]
[tex]N(t)=2^{-3240/1620}[/tex]
= 1/4
= 0.25
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Figure A is dilated with scale factor r=3 to create figure A′ .
Answer:
r=3 to dilation
Step-by-step explanation:
([[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[]]]]]]]]]]]]]]]]]]]]]]]]]]]])
Which graph is that of the inequality shown below
Answer:
The correct graph is graph B.
Find the length of the diagonal AC in the rectangle below.
Answer: 26
Step-by-step explanation:
So what its basically asking is for you to find the hypotenuse because you can see that the rectangle splits in half with the green line.
So to find the hypotenuse you would use these steps:
1. formula for hypotenuse
[tex]\sqrt{a^2+b^2}[/tex]
2. plug in numbers
[tex]\sqrt{10^2+24^2}=26[/tex]
One apple cost 2x one banana cost x+1 what is the total cost of 2 apples and 5 bananas?
Nolan bought 2 apples and 10 bananas.
To solve this problem form the system of equations first, then solve them to find the values of the variables.
Nolan bought 2 apples and 10 bananas.
It's given that,
Nolan and his children bought fruits (Apples and bananas) worth $8.
Cost of each apple and bananas are $2 and $0.40 respectively.
Let the number of bananas he bought = y
And the number of apples = x
Therefore, cost of the apples =$2x
And the cost of bananas = $0.40y
Total cost of 'x' apples and 'y' bananas = $(2x + 0.40y)
Equation representing the total cost of fruits will be,
(2x + 0.40y) = 8
10(2x + 0.40y) = 10(8)
20x + 4y = 80
5x + y = 20 --------(1)
If he bought 5 times as many bananas as apples,
y = 5x ------(2)
Substitute the value of y from equation (2) to equation (1),
5x + 5x = 20
10x = 20
x = 2
Substitute the value of 'x' in equation (2)
y = 5(2)
y = 10
Therefore, Nolan bought 2 apples and 10 bananas.
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Full Question ;
Nolan and his children went into a grocery store and he bought $8 worth of apples
and bananas. Each apple costs $2 and each banana costs $0.40. He bought 5 times as
many bananas as apples. By following the steps below, determine the number of
apples, 2, and the number of bananas, y, that Nolan bought.
Pete’s plumbing was just hired to replace the water pipes in the Johanssons house Pete has two types of pipes. He can use a pipe with a radius of 8pm or a pipe with radius of 4cm
The 4cm pipes are less expensive then the 8cm pipes for Pete to buy so Pete wonders if there are a number of 4cm pipes he could use that would give the same amount of water to the Johanssons house as one 8cm pipe
Circles and ratios water pipes
It would take 4 pipes with a radius of 4cm to replace one pipe with a radius of 8cm and provide the same amount of water flow.
We have,
The volume of water that can flow through a pipe is proportional to the cross-sectional area of the pipe.
The formula for the area of a circle is:
A = πr²
where A is the area of the circle and r is the radius of the circle.
For a pipe with a radius of 8cm, the cross-sectional area is:
A_8cm = π(8cm)²
= 64π cm²
For a pipe with a radius of 4cm, the cross-sectional area is:
A_4cm = π(4cm)²
= 16π cm²
To find out how many 4cm pipes would be needed to replace one 8cm pipe, we can compare the areas of the two pipes:
Number of 4cm pipes
= A_8cm / A_4 cm
= (64π) / (16π)
= 4
Therefore,
It would take 4 pipes with a radius of 4cm to replace one pipe with a radius of 8cm and provide the same amount of water flow.
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Sweet Glee is an ice cream shop chain that has locations all across the nation. Customers at Sweet Glee have the option of ordering 1, 2 or 3 Scoops of ice cream in their cone. The mean number of scoops ordered is y=2.86, with a standard deviation of o=0.23. Suppose that we will take a random sample of n-7 ice cream cone orders and record the number of scoops for each, Let x represent the sample mean of the number of scoops for the 7 ice cream cone orders. Consider the sampling distribution of the sample meanx Complete the following. Do not round any intermediate computations. Write your answers with two decimal places, rounding if needed. (a) Find (the mean of the sampling distribution of the sample mean). х (b) Find the standard deviation of the sampling distribution of the sample mean). o ?
(a) The mean of the sampling distribution of the sample mean is equal to the population mean, which is y=2.86. So, х = 2.86.
(b) The standard deviation of the sampling distribution of the sample mean is equal to the population standard deviation divided by the square root of the sample size. So, o = 0.23 / sqrt(7) = 0.087.
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Help me please , I really don't understand this ( Find the major arc, Give an exact answer in terms of pi and be sure to include the correct unit.)
In the given circle, the length of major arc LNM is 29/3(π)
Calculating the length of an arcFrom the question, we are to calculate the length of the major arc in the given diagram
Length of an arc is given by the formula
Length = θ/360° × 2πr
Where θ is the angle subtended by the arc at the center of the circle
r is the radius of the circle
From the given information,
r = 6 cm
θ = 360° - 70°
θ = 290°
Substitute the parameters into the formula
Length = 290/360 × 2×π×6
Length = 29/3(π)
Hence,
Length of arc LNM is 29/3(π)
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Which of the following ordered pairs is a solution of 5x + 2y = -3?
a. (2, -4) c. (1, -4)
b. (-4, 2) d. (-4, 1)
The ordered pair (1, -4) is the solution of equation 5x + 2y = -3.
We can check which of the ordered pairs is a solution of equation 5x + 2y = -3 by substituting the values of x and y in the equation and checking if it is true.
a. (2, -4)
Substituting x = 2 and y = -4 in 5x + 2y = -3, we get:
5(2) + 2(-4) = 10 - 8 = 2
So, (2, -4) is not a solution to the equation.
Similarly
b. (-4, 2)
5(-4) + 2(2) = -20 + 4 = -16
So, (-4, 2) is not a solution to the equation.
c. (1, -4)
5(1) + 2(-4) = 5 - 8 = -3
So, (1, -4) is a solution to the equation.
d. (-4, 1)
5(-4) + 2(1) = -20 + 2 = -18
So, (-4, 1) is not a solution to the equation.
Therefore, the ordered pair (1, -4) is the solution of equation 5x + 2y = -3.
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The power series (r- 5)" 22 has radius of convergence 2 At which of the following values of x can the alternating series test be used with this series to verify convergencer at x? A B 4 с 2 D 0 The alternating series test can be used to show convergence of which of the following alternating series? 14- ) +1-82+ 1 4 1 720 + 1 16 + a + ..., wherea, {} ifnis even in sodd + 1 6 + 5 +1 +...+an +..., where an 3 $ 9 u 13 15 +an + ..., where a, = (-1)". 2+1 I only B ll only С ill only D I and II only E III and III
Answer:
The alternating series test states that if the terms of an alternating series decrease in absolute value and approach zero, then the series converges.
For the power series (r - 5)^n/22 with radius of convergence 2, the alternating series test can be used at x = 2 and x = -2. This is because the alternating series test requires the terms to decrease in absolute value, and for values of x beyond the radius of convergence, the terms of the series increase in absolute value and do not approach zero.
For the given alternating series:
1/4 - 1/2 + 1/8 - 2/720 + 1/16 - ...
The terms decrease in absolute value and approach zero, so the alternating series test can be used to verify convergence.
1/6 + 5/13 + ... + a_n
Since a_n is odd and greater than 3, the terms do not alternate in sign and the alternating series test cannot be used to verify convergence.
(-1)^n (2n+1)/(n+1)
The terms decrease in absolute value and approach zero, so the alternating series test can be used to verify convergence.
Step-by-step explanation:
The answer is D, I and II only. The alternating series test can be used to verify convergence of an alternating series, which means the signs of the terms alternate.
In the given power series (r-5) ^22, there is no alternating pattern of signs, so the alternating series test cannot be used to verify convergence of this series at any value of x. Therefore, the answer is none of the options provided (N/A).
For the second part of the question, we need to check each series to see if they have an alternating pattern of signs. The first series (1/4^n) has all positive terms, so the alternating series test cannot be used to verify convergence of this series. The second series (-1)^n(1/2^n) has alternating signs, so the alternating series test can be used to verify convergence of this series. The third series (-1)^n(1/(4n+1)) also has alternating signs, so the alternating series test can be used to verify convergence of this series. Therefore, the answer is D, I and II only.
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Prove that for all real numbers r > 0,8 >0 and all vectors a, b, c in a normed vector space V.
a. Br(α) ⊂ Bs(b)→Br(α+2c)⊂Bs(b+2c)
b.Br(α) ⊂ Bs(b)→Br(α+1/2c)⊂Bs(b+1/2c)
X is in Bs(b+1/2c), which implies Br(α+1/2c)⊂Bs(b+1/2c).
a. We want to show that Br(α+2c)⊂Bs(b+2c) given that Br(α)⊂Bs(b).
Let x be any element in Br(α+2c), then we have ||x-(α+2c)|| < r.
Using the triangle inequality, we get:
||x-(α+2c)|| = ||(x-α)-2c|| ≤ ||x-α||+2||c|| < r+2||c|| = 8 (since r > 0 and ||c|| < 4).
So, ||x-α|| < 8 - 2||c|| < 2.
Thus, x is also in Br(α) ⊂ Bs(b), which implies ||x-b|| < r.
Using the triangle inequality again, we have:
||x-(b+2c)|| = ||(x-b)-2c|| ≤ ||x-b||+2||c|| < r+2||c|| = 8.
Therefore, x is in Bs(b+2c), which implies Br(α+2c)⊂Bs(b+2c).
b. We want to show that Br(α+1/2c)⊂Bs(b+1/2c) given that Br(α)⊂Bs(b).
Let x be any element in Br(α+1/2c), then we have ||x-(α+1/2c)|| < r.
Using the triangle inequality, we get:
||x-(α+1/2c)|| = ||(x-α)-1/2c|| ≤ ||x-α||+1/2||c|| < r+1/2||c|| = 4 (since r > 0 and ||c|| < 8).
So, ||x-α|| < 4 - 1/2||c|| < 3.
Thus, x is also in Br(α) ⊂ Bs(b), which implies ||x-b|| < r.
Using the triangle inequality again, we have:
||x-(b+1/2c)|| = ||(x-b)-1/2c|| ≤ ||x-b||+1/2||c|| < r+1/2||c|| = 4.
Therefore, x is in Bs(b+1/2c), which implies Br(α+1/2c)⊂Bs(b+1/2c).
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What is the equation of a circle with center (-3,-5) and radius 4?
A. (x-3)2 + (y- 5)² = 16
B. (x+3)2 + (y+ 5)² = 16
C. (x-3)2 + (v-5)2 = 4
O D. (x+3)2 + (y + 5)² = 4
SUB
The equation of the circle with center (-3, -5) and radius 4 is (x + 3)² + (y + 5)² = 16.
What is the equation of a circle with center (-3,-5) and radius 4?The standard form equation of a circle with center (h, k) and radius r is:
(x - h)² + (y - k)² = r²
Given that the center of the circle is (-3, -5) and the radius is 4.
Hence, we can substitute these values into the formula to get the equation of the circle:
Plug in h = -3, k = -5 and r = 4
(x - h)² + (y - k)² = r²
(x - (-3))² + (y - (-5))² = 4²
Simplifying and expanding the equation, we get:
(x + 3)² + (y + 5)² = 16
Therefore, the equation of the circle is (x + 3)² + (y + 5)² = 16.
Option B) (x + 3)² + (y + 5)² = 16 is the correct answer.
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A cylindrical cooler has a diameter of 30 inches and a height of 24 inches. How many gallons of water can the cooler hold? (1 ft³ ≈ 7. 5 gal) Round your answer to the nearest tenth of a gallon
Rounding to the nearest tenth of a gallon, we have that the cooler can hold about 74.0 gallons of water.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the base and h is the height.
In this case, the diameter of the cooler is 30 inches, which means the radius is 15 inches (since the radius is half the diameter). The height is 24 inches.
Using the formula for the volume of a cylinder, we have:
V = π[tex]r^2h[/tex]
= π([tex]15^2)(24[/tex])
= 5400π cubic inches
To convert cubic inches to gallons, we need to divide by the conversion factor 231 cubic inches per gallon. Therefore, the volume of the cooler in gallons is:
[tex]V_gal[/tex]= (5400π cubic inches) / (231 cubic inches/gallon) ≈ 74.0 gallons
Rounding to the nearest tenth of a gallon, we have that the cooler can hold about 74.0 gallons of water.
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Please give an explanation!
4. The number of picks from Toledo and Nevada were compared and the results are as follows:
Test and Cl For Two Proportions: Picked Toledo, Picked Nevada
Variable X n Sample p
Picked Toledo 18 64 0.281250
Picked Nevada 8 64 0.125000
Difference = p (Picked Toledo) -p (Picked Nevada)
Estimate for Difference: 0.15625
95% lower bound for difference: 0.0414921
Test for difference = 0 ( vs > 0 ) : z = 2.24 P-value = 0.013
Fill in the blanks based on the Minitab output shown above:
1. a. H0: ___________________
b. Ha: ___________________
c. α= ____________________
d. Compute the pooled proportion:
2. Value of the Test Statistic: _________________
3. What decision can you make?
4. What conclusion can you make?
1. a. H0: p(Picked Toledo) - p(Picked Nevada) = 0
b. Ha: p(Picked Toledo) - p(Picked Nevada) > 0
c. α= 0.05
d. Pooled proportion = 0.203125
2. The value of the Test Statistic is 2.24.
3. We can reject the null hypothesis.
4. The proportion of people who picked Toledo is greater than those who picked Nevada.
Based on the Minitab output provided, here is the information you're looking for:
1. a. H0: p(Picked Toledo) - p(Picked Nevada) = 0
b. Ha: p(Picked Toledo) - p(Picked Nevada) > 0
c. α= 0.05 (typically used in hypothesis tests, not given in the output)
d. Compute the pooled proportion:
Pooled proportion = (X1 + X2) / (n1 + n2) = (18 + 8) / (64 + 64) = 26 / 128 = 0.203125
2. Value of the Test Statistic: z = 2.24
3. To answer "What decision can you make?"
Since the P-value (0.013) is less than the significance level (α=0.05), you can reject the null hypothesis.
4. To answer "What conclusion can you make?"
Based on the test results, there is significant evidence to conclude that the proportion of people who picked Toledo is greater than the proportion who picked Nevada.
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True or false: A set is considered closed if for any members in the set, the result of an operation is also in the set
False. A set is considered closed under an operation if the result of that operation on any two elements in the set also belongs to the set.
A set is considered closed if it contains all of its limit points. In other words, if a sequence of points in the set converges to a point that is also in the set, then the set is closed. Another equivalent definition is that the complement of the set.
In mathematics, sets are collections of distinct objects. These objects can be anything, including numbers, letters, or even other sets. The concept of sets is fundamental in mathematics and is used to define many other mathematical structures.
Sets can be denoted in various ways, including listing the elements inside curly braces { }, using set-builder notation, or using set operations to define new sets from existing ones. Some common set operations include union, intersection, difference, and complement.
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