determine the center and radius of
x²+y² = 9
​

hmm im not sure, but I'm going to try to help you!! but I think it is B or D. Maybe but I'm not too sure. though. :((

The appropriate hypotheses for this test are: H0: There is no difference in the distribution of responses. Ha: There is a difference in the distribution of responses.

The chosen hypotheses are based on the objective of the investigation, which is to determine if there is convincing evidence that the distribution of responses about eating the potato salad differs between employees who are sick and those who are not sick.

The null hypothesis (H0) assumes that there is no difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This means that the proportion of employees who ate the potato salad would be the same in both groups, and any observed difference in the distribution of responses is due to random chance or factors unrelated to being sick or not sick.

On the other hand, the alternative hypothesis (Ha) proposes that there is a difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This suggests that the proportion of employees who ate the potato salad would be significantly different in the two groups, indicating a possible association between consuming the potato salad and getting sick.

By formulating these hypotheses, the investigation aims to evaluate whether the data provides convincing evidence to reject the null hypothesis in favor of the alternative hypothesis, indicating a meaningful relationship between eating the potato salad and falling sick.

Therefore, the correct answer is:

H0: There is no difference in the distribution of responses about eating the potato salad among those who are and are not sick.

Ha: There is a difference in the distribution of responses about eating the potato salad among those who are and are not sick.

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The sprinter will complete the race in approximately 17.07 seconds.

To calculate the time for the race, we need to consider two parts: the acceleration phase and the constant velocity phase.

Acceleration Phase:

The acceleration of the sprinter is 1.64 m/s², and the distance covered during this phase is 25 m. We can use the equation of motion to calculate the time taken during acceleration:

v = u + at

Here:

v = final velocity (which is the velocity at the end of the acceleration phase)

u = initial velocity (which is 0 since the sprinter starts from rest)

a = acceleration

t = time

Rearranging the equation, we have:

t = (v - u) / a

Since the sprinter starts from rest, the initial velocity (u) is 0. Therefore:

t = v / a

Plugging in the values, we get:

t = 25 m / 1.64 m/s²

Constant Velocity Phase:

Once the sprinter reaches the end of the acceleration phase, the velocity remains constant. The remaining distance to be covered is 100 m - 25 m = 75 m. We can calculate the time taken during this phase using the formula:

t = d / v

Here:

d = distance

v = velocity

Plugging in the values, we get:

t = 75 m / (v)

Since the velocity remains constant, we can use the final velocity from the acceleration phase.

Now, let's calculate the time for each phase and sum them up to get the total race time:

Acceleration Phase:

t1 = 25 m / 1.64 m/s²

Constant Velocity Phase:

t2 = 75 m / v

Total race time:

Total time = t1 + t2

Let's calculate the values:

t1 = 25 m / 1.64 m/s² = 15.24 s (rounded to two decimal places)

Now, we need to calculate the final velocity (v) at the end of the acceleration phase. We can use the formula:

v = u + at

Here:

u = initial velocity (0 m/s)

a = acceleration (1.64 m/s²)

t = time (25 m)

Plugging in the values, we get:

v = 0 m/s + (1.64 m/s²)(25 m) = 41 m/s

Now, let's calculate the time for the constant velocity phase:

t2 = 75 m / 41 m/s ≈ 1.83 s (rounded to two decimal places)

Finally, let's calculate the total race time:

Total time = t1 + t2 = 15.24 s + 1.83 s ≈ 17.07 s (rounded to two decimal places)

Therefore, the sprinter will complete the race in approximately 17.07 seconds.

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Answer:

d

Step-by-step explanation:

The y- intercept is where the graph crosses the y- axis

The graph crosses the y- axis at (0, 1 ) ← y- intercept

30 + 110 + 30 + 110 = 280

360-280 = 80

2y = 80

y = 40 degrees

If y is 40. Then the angle next to 30 is also y due to vertically opposite angles.

30 + 40 = 70

The line with 2 arrows is parallel to the line with x degrees. So, I use co-interior angles adds to 180.

In that c shaped, we got the bottom angle to be 70 & the top to be 110 because co-interior angles =180

Forget the c shape exists, and move onto the triangle that's visible. The top angle is 110 as found.

Angles in triangle add to 180.

180 - 110 - 30 = 40.

Thus, x = 40 degrees

There's a short cut I realise now because we can have alternate angles are equal; creating a z shape to find what x is equal to & that turns out to be the same value as y. ( due to vertically opposite angles)

Hope this helps!

Answer:

6

Step-by-step explanation:

just put 6.00 bro it divides evenly

The system has an infinite number of solutions, but the only solution is (a, b) = (0, 0).

The given system of equations can be solved using the substitution method. We can begin by solving the first equation,\(a^2 + b^2\), for either a or b. Let's solve for a:

\(a^2 + b^2 = 0\)

\(a^2 + b^2 = 0\)

\(a^2 = -b^2\)

\(a = \pm\sqrt(-b^2)\)

We can substitute this expression for a into the second equation, \(3a^2 - 2ab - b^2 = 0\), and simplify:

\(3(\pm\sqrt(-b^2))^2 - 2(\pm\sqrt(-b^2))b - b^2 = 0\)

\(3b^2 - 2b^2 - b^2 = 0\)

0 = 0

Since 0 = 0, this means that the system of equations has an infinite number of solutions. In other words, any values of a and b that satisfy the equation \(a^2 + b^2 = 0\) will also satisfy the equation \(3a^2 - 2ab - b^2 = 0\)

However, the equation \(a^2 + b^2 = 0\) only has a single solution, which is a = b = 0. Therefore, the solution to the system of equations is (a, b) = (0, 0).

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Answer: 19/25

Step-by-step explanation: 8/12 / 7/8 is (rounded) 0.76, and 0.76 as a fraction is 19/25.

Answer:

-2 and -1

have a good day

Answer:

-7.33

Step-by-step explanation:

Answer:

-7.333

Step-by-step explanation:

To solve this you have to use B O D M A S theorem and we have to solve the given expression according to the theorem.

That is,

B ⇒ Brackets

O ⇒ Of

D ⇒ Division

M ⇒ Multiplication

A ⇒ Addition

S ⇒ Subtraction

Let us solve it now.

\(\frac{6}{3} (13-18)+2^{4}\) ÷ \(6\)

2 ( -5) + 16÷ 6

-10 + 2.667

-7.333

So the volume is 15.84 cm The formula for the volume of a prism is given by the product of the area of the base and height of the prism. Thus, the volume of a prism can be given as V = B × H where V is the volume, B base area, and H height of the prism.

The minimum profit occurs at L = 0, where Q = 0.

To find the value of L that maximizes the profit Q = L²\(e^{(0.01L)\).

We need to differentiate Q with respect to L and find the critical points where the derivative equals zero.

Then we can determine whether each critical point is a maximum or a minimum by examining the second derivative.

Testing for critical points:Q = L²\(e^{(0.01L)\)

Q' = \(2Le^{(0.01L)\) + \(0.01 L^2e^{(0.01L)\)

= 0(2L + 0.01L²) \(e^{(0.01L)\)

= 0L (critical point) or 200 \(e^{(0.01L)\)

= 0 (extraneous, ignore)

2L + 0.01L² = 0L(2 + 0.01L) = 0L = 0 or L = -200 (extraneous, ignore)

The only critical point is at L = 0.

Testing for maximum or minimum:Q'' = \(2e^{(0.01L)\) + 0.02Le^(0.01L) + 0.0001L²\(e^{(0.01L)Q''(0)\)

= \(2e^{(0)\) = 2Since Q''(0) > 0,

The critical point at L = 0 is a minimum.

Therefore, there is no value of L that maximizes the profit.

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The values of L that will maximize the profit are 0 and -200

From the question, we have the following parameters that can be used in our computation:

\(Q = L\²e^{0.01L\)

Differentiate the function

So, we have

\(Q' = \frac{L \cdot (L + 200) \cdot e^{0.01L}}{100}\)

Set the equation to 0

\(\frac{L \cdot (L + 200) \cdot e^{0.01L}}{100} = 0\)

Cross multiply

\(L \cdot (L + 200) \cdot e^{0.01L} =0\)

When expanded, we have

L = 0, L + 200 = 0 and \(e^{0.01L} =0\)

When solved for L, we have

L = 0 and L = -200

Hence, the values of L are 0 and -200

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Answer:

\( \boxed{ \bold{ \boxed{ \sf{ - 5 {x}^{5} + 2 {x}^{3} - 6x}}}}\)

Step-by-step explanation:

\( \sf{( {x}^{5} + {x}^{3} ) - (6x - {x}^{3} + 6 {x}^{5}) }\)

When there is a ( - ) in front of an expression in parentheses , change the sign of each term.

Also, remove the parentheses

⇒\( \sf{ {x}^{5} + {x}^{3} - 6x + {x}^{3} - 6 {x}^{5} }\)

Collect like terms

⇒\( \sf{ {x}^{5} - 6 {x}^{5} + {x}^{3} + {x}^{3} - 6x}\)

⇒\( \sf{ - 5 {x}^{5} + 2 {x}^{3} - 6x}\)

Hope I helped!

Best regards!!

The general solution for  mx" + Bx' = mg for r(t) is x(t) = 25e^(-x/5) + 5x -125

According to the question,

The given equation =  mx" + Bx' = mg

Also , mg = 160, B = 1, and g = 32

=> m = 160/g

=> m = 160/32 = 5

Substituting the values in equation ,

5x" + x' = 160 , x(0) = -100, x' (0) = 0

The characteristic equation of the homogeneous differential equation is

5x" + x' = 0

=>  5r² + r = 0

=> r = 0 , -1/5

The complementary solution is x = c₁e⁰ + c₂e⁻⁰°²

Solution for complementary is yc = ax + b

Substitute yc = ax + b in  5x" + x' = 160 to get

5(0) + a = 160

=> a = 160

So the general solution is

x(t) = 25e^(-x/5) + 5x -125

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The number of candies each bag would contain is given by the inequality relation 3 < A < 4 , where A is the number of candies

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Now , the total number of candies with Tom = 14 candies

The number of bags = 4 bags

So , the number of candies each bag = total number of candies with Tom / number of bags

On simplifying , we get

The number of candies each bag A = 14 / 4 = 3.5 candies

Now , the value 3.5 lies between the whole numbers 3 and 4

Hence , the inequality is 3 < A < 4

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By doing a change of units, we know that he will need 40 pint jars to hold the whole volume of sauce.

We know that Joe makes tomato sauce to sell at a craft fair, and we know that he did make that sauce in 5-gallon batches.

We want to see how many jars do he need to hold these 5 gallons, so we need to perform a change of units.

Remember the relation:

1 gallon  = 8 pints.

So, for each gallon, he will need 8 pint jars, then for the 5 gallons, he will need:

5*8 pint jars = 40 pint jars.

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Answer and Step-by-step explanation:

Suppose x = 0.2355555... .

Multiply x by 100 and 1000:

100x = 23.5555....

1000x = 235.5555....

Let's subtract the first equation from the second:

1000x - 100x = 235.5555.... - 23.555.....

Because the decimal part for each goes on forever, we can simply cancel them out in our subtraction statement:

900x = 235 - 23 = 212

Divide both sides by 900:

x = 212/900 = 53/225

Thus, since x = 0.235555..., we know that:

0.23555.... = 53/225

Since p = 53 and q = 225 are integers, we have proven that this repeating decimal can be written as a fraction.

~ an aesthetics lover

The exponential growth function is P = 6.51 (1.0275)^t. The population of the city in 2018 will be 7.66 million. The population of the city will be 10 ​million in 15.82258467 years and the doubling time is 25.55035862 years

The exponential growth function is of the form P = P₀(1+r)^t

where P₀ is the current population, r is the growth rate and t is the time

Given: P₀ =  6.51 million, r = 2.75​% per year

a) The exponential growth function

P = 6.51 (1+0.0275)^t

P = 6.51 (1.0275)^t

​b) The population of the city in 2018

t = 2018-2012 = 6 years

P = 6.51 (1.0275)^t

P = 6.51 (1.0275)⁶ = 7.66 million

​c) When the population of the city will be 10 ​million

P = 6.51 (1.0275)^t

10 =  6.51 (1.0275)^t        (Solve for t)

(1.0275)^t =10/6.51

log (1.0275)^t = log(10/6.51)

t × log (1.0275) = log(10/6.51)

t = [log(10/6.51)] / [log (1.0275)]

t = 15.82258467 years

d) The doubling time

P =  6.51 (1.0275)^t will become:

2 = 1 (1.0275)^t

1.0275^t = 2

log(1.0275)^t = log 2

t log(1.0275) = log 2

t = log 2 / log 1.0275

t = 25.55035862 years

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Answer:

a,d,e

Step-by-step explanation:

In this question, we apply limit concepts to get the desired limit, finding that the correct options are: A, D and E, leading to the result of the limit being \(\frac{1}{6}\).

Limit:

The limit given is:

\(\lim_{x \rightarrow 7} \frac{\sqrt{x+2}-3}{x-7}\)

If we apply the usual thing, of just replacing x by 7, the denominator will be 0, so this is not possible.

When we have a term with roots, we rationalize it, multiplying both the denominator and the denominator by the conjugate.

Multiplication by the conjugate:

The term with the root is:

\(\sqrt{x+2} - 3\)

It's conjugate is:

\(\sqrt{x+2}+3\)

Multiplying numerator and denominator by the conjugate, meaning option A is correct:

\(\lim_{x \rightarrow 7} \frac{\sqrt{x+2}-3}{x-7} \times \frac{\sqrt{x+2}+3}{\sqrt{x+2}+3}\)

We do this because at the numerator we can apply:

\((a+b)(a-b) = a^2 - b^2\)

Thus

\(\lim_{x \rightarrow 7} \frac{\sqrt{x+2}-3}{x-7} \times \frac{\sqrt{x+2}+3}{\sqrt{x+2}+3} = \lim_{x \rightarrow 7} \frac{(\sqrt{x+2})^2 - 3^2}{(x-7)(\sqrt{x+2}+3)} = \lim_{x \rightarrow 7}\frac{x+2-9}{(x-7)(\sqrt{x+2}+3)} = \lim_{x \rightarrow 7}\frac{x-7}{(x-7)(\sqrt{x+2}+3)}\)

Thus, we can simplify the factors of x - 7, meaning that option D is correct, and we get:

\(\lim_{x \rightarrow 7} \frac{1}{\sqrt{x+2}+3}\)

Now, we just calculate the limit:

\(\lim_{x \rightarrow 7} \frac{1}{\sqrt{x+2}+3} = \frac{1}{\sqrt{7+2}+3} = \frac{1}{3+3} = \frac{1}{6}\)

Thus, option E is also correct.

Using a limit calculator, as given by the image below, we have that 1/6 is the correct answer.

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To find all points on the x-axis that are 16 units away from the point (5, -8), we can use the distance formula. The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

In this case, the y-coordinate of the point (5, -8) is -8, which lies on the x-axis. So, any point on the x-axis will have a y-coordinate of 0. Let's substitute the given values and solve for the x-coordinate.

d = √((x - 5)² + (0 - (-8))²)

Simplifying:

d = √((x - 5)² + 64)

Now, we want the distance d to be equal to 16 units. So, we set up the equation:

16 = √((x - 5)² + 64)

Squaring both sides of the equation to eliminate the square root:

16² = (x - 5)² + 64

256 = (x - 5)² + 64

Subtracting 64 from both sides:

192 = (x - 5)²

Taking the square root of both sides

√192 = x - 5

±√192 = x - 5

x = 5 ± √192

Therefore, the two points on the x-axis that are 16 units away from the point (5, -8) are:

Point 1: (5 + √192, 0)

Point 2: (5 - √192, 0)

In summary, the points on the x-axis that are 16 units away from the point (5, -8) are (5 + √192, 0) and (5 - √192, 0).

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Answer:

be brief can't see any picture

Answer:

10 5/16

Step-by-step explanation:

Answer:

a. lines intersecting at a single point

b. one solution

Step-by-step explanation:

a. The equations can be rewritten as:

y = -5x+23 and y = -1/6x+1

Comparing the equations with standard equation: y=mx+c, where m is the gradient of the line formed by the linear equation.

Since the gradient of the lines are different then the lines cannot be parallel and will intersent at one point.

b. The equation will have one solution as below.

The equations can be rewritten as:

5x+y=23

5x+30y=30

Subtracting both equation will result in,

29y=7

=> y=7/29

Hence x= 660/29

Answer:

D

Step-by-step explanation:

Answer:

Part A: The correct net is net A. It is because if you look at the 2, one trainable isn't aligned with the other, but it wouldn't fit together as a prism-like Net A would.

ca i get brainlies

Answer:2.381 cm.

Step-by-step explanation:

The volume of the gold bar can be calculated using the formula for the volume of a rectangular prism:

Volume = Length x Width x Height

We know the length and width of the bar, so we can substitute those values:

Volume = 23.5 cm x 28 cm x Height

We can then solve for the height by rearranging the equation:

Height = Volume / (Length x Width)

To find the volume, we can use the density of gold and the mass of the bar:

Density = Mass / Volume

Volume = Mass / Density

Substituting the values we have:

Volume = 43,892.5 g / 27.2 g/cm³

Volume = 1610.049 cm³

Now we can substitute the volume into the equation we derived earlier to solve for the height:

Height = 1610.049 cm³ / (23.5 cm x 28 cm)

Height = 2.381 cm

Therefore, the height of the gold bar is approximately 2.381 cm.

Answer:

The answer is 96 square feet because if you look at the first rectangle (the one on the top left), you should multiply 5 times 6 which equals 30. (The reason you would do this is because you want to find the area of all of the rectangles first and then add them together in order to get the total area of the rug.) Then, you would look at the second rectangle (the one on the right), and you would multiply 8 times 6 which is 48. Next, you would look at the last rectangle (the one on the lower left) and multiply 6 times 3 which is 18. Finally, you have to add 30+48+18 and then you would get your final answer which is 96 square feet.

Looking at the scenario,

it is either a person chosen is in favor of the project or not.(Either success or failure)

The outcome is independent

Thus, we would apply binomial distribution. It is expressed as

P(x) = nCx * p^x * q^(n - x)

Where

x = number of successes

p = probability of success

q = probability of failure

n = number of trials

From the information given

p = 35% = 35/100 = 0.35

q = 1 - p = 1 - 0.35 = 0.65

n = 7

x = 5

We wan to find P(x = 5)

Thus,

P(x = 5) = 7C5 * 0.35^5 * 0.65^(7 - 5)

P(x = 5) = 7C5 * 0.35^5 * 0.65^2

P(x = 5) = 0.0466

Thus, the probability that exactly 5 of them favor the new project is 0.0466