Which equation represents a circle that contains the point (-2, 8) and has a center at (4, 0)?

Distance formula: V(x2

1) + (V2 - )

O (x - 4)2 + y? = 100

O (x - 4)2 + y? = 10

O x2 + (y - 4)2 = 10

O x' + (y - 4)? = 100

Applying the secant-tangent theorem, the length of PQ is calculated as: 6 units.

In the image given, line segment QS is a secant while QP is a tangent. This, according to the secant-tangent theorem, we have:

(x - 3)(x - 3 + 5) = (x - 1)²

(x - 3)(x + 2) = (x - 1)(x - 1)

Expand:

x² - x - 6 = x² - 2x + 1

Combine like terms:

x² - x² - x + 2x = 6 + 1

x = 7

length of PQ = x - 1

Plug in the value of x:

length of PQ = 7 - 1 = 6 units.

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Answer:

-3.8

Step-by-step explanation:

-3.8+7.2=3.4

To find the area of the given triangle with a side length of 18 and an angle of 62 degrees, we can use the formula for the area of a triangle: A = 1/2 * base * height.

In this case, the base of the triangle is given as 18, but we need to find the height. To find the height, we can use the trigonometric relationship between the angle and the sides of the triangle. The height is equal to the length of the side opposite the given angle. Using trigonometry, we can determine the height by multiplying the length of the base by the sine of the angle: height = 18 * sin(62°).

Once we have the height, we can calculate the area using the formula: A = 1/2 * base * height. Plugging in the values, we get A = 1/2 * 18 * 18 * sin(62°). Finally, we round the answer to the nearest tenth to obtain the final result.

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a)1. True

2.False

3.True

4).False

b)Without knowing the sample size and standard deviation, we cannot determine the exact 90% confidence interval.

(a) For the content loaded Central Middle School data:

1. True: There is a 95% probability that μ (mean height) is between 54 and 58 inches.

This is the correct interpretation of the 95% confidence interval.

2. False: The confidence interval doesn't tell us the probability of the true mean or the margin of error being exactly as given. It only tells us the range where the true mean is likely to fall with 95% confidence.

3. True: If we took many additional random samples of the same size and from each computed a 95% confidence interval for μ, approximately 95% of these intervals would contain μ. This is the definition of a 95% confidence interval.

4. False: It's incorrect to say that μ would fall between 54 and 58 95% of the time. The correct interpretation is that if we computed multiple 95% confidence intervals, approximately 95% of those intervals would contain the true mean height.

(b) To determine the 90% confidence interval based on the same data:

Without knowing the sample size and standard deviation, any of the above answers could be the 90% confidence interval. Confidence intervals depend on the sample size, standard deviation, and desired confidence level. With the information given, we cannot determine the exact 90% confidence interval.

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Answer:

just sum all the number and x y's. Then you can find x!

Answer:

The Elimination Method ....

A. 1 pair of corresponding points are N and L or you could use S and H.

but i do not know the question B sorry.

Answer:

4.5 miles per hour

Step-by-step explanation:

2 1/4 x 2 = 4.5 (As decimal)

30 mins + 30 mins = 1 hour

1 hour = 4.5 miles per hour

Answer:

We combine like terms to get \(10x^{2} + 3x - 6\)

Hope this helps!

Answer:

\(\frac{6}{35}\)

Step-by-step explanation:

To find the ' middle ' add the 2 fractions and divide by 2 ( average )

\(\frac{1}{5}\) + \(\frac{1}{7}\) ( change denominators to 35 , the LCM of 5 and 7 )

= \(\frac{7}{35}\) + \(\frac{5}{35}\)

= \(\frac{12}{35}\)

midway = \(\frac{12}{35}\) ÷ 2 = \(\frac{6}{35}\)

The fraction is exactly midway between 1/5 and 1/7  is  \(\frac{6}{35}\) .

Sometimes you need to find the point that is exactly midway between two other points. For instance, you might need to find a line that bisects (divides into two equal halves) a given line segment. This middle point is called the "midpoint".

According to the question

The fraction is exactly midway between 1/5 and 1/7

Now ,

To find midway between 1/5 and 1/7

Step1 : Add fraction 1/5 and 1/7

= \(\frac{1}{5} +\frac{1}{7}\)

= \(\frac{12}{35}\)

Step2 : Divide the sum by 2 or multiply by 1/2

= \(\frac{12}{35}\) * \(\frac{1}{2}\)

= \(\frac{6}{35}\)

Hence, the fraction is exactly midway between 1/5 and 1/7  is  \(\frac{6}{35}\) .

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Answer:

No

Step-by-step explanation:

To determine if the point is a solution to either of the inequalities, substitute the variables with the point given. When y<-3.x+4 is substituted with (0,4), the inequality becomes 4<4, which proves that the point is inapplicable to the first inequality. Therefore, you do not need to continue to check its applicability with the second inequality.

The statement "if the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other" is true. The dot product of two vectors is zero if and only if the vectors are perpendicular.

The dot product of two vectors is defined as the product of their magnitudes and the cosine of the angle between them. When the dot product is zero, it means that the cosine of the angle between the vectors is zero, which occurs when the vectors are perpendicular.

In other words, the dot product being zero indicates that the vectors are at a 90-degree angle to each other, supporting the statement that they are perpendicular.

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Answer:

12-27+9Y=5+6=90X5=800

Step-by-step explanation:

The chart has been completed and the information has been given below:

Annually $9200 6% 15 9200(1+0.06)15 $22084.34

Semi-Annually $9200 6/2 = 3% 15*2 = 30 9200(1+0.03)30 $22330.81

Quaterly $9200 6/4 = 1.5% 15*4 = 60 9200(1+0.015)​​​​​60 $22477.62

Monthly $9200 6/(12*15) = 1/30 %

15*12*15 = 2700

9200(1+1/(30*100))2700

$22624.96

Weekly $9200 6/(15*52) = 1/130 15*52*15 = 11700

9200(1+1/(130*100))11700

$22627.57

Daily $9200 6/(15*365) = 2/1825

15*365*15 = 82125

9200(1+2/(1825*100))82125

$22628.24

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The cost of an adult ticket is £17 and a child ticket is £9.

Let's assume 'a'  for an adult ticket and 'c' for a child ticket

The cost of tickets for the Smith family of 2 adults and 3 children is £61

Equating, \(2a+3c=61\)

\(2a=61-3c\)

Dividing by 2, \(a=30.5-1.5c\)        (equation 1)

Now, the cost of tickets for the Jones family of three adults and five children is £96

Equating, \(3a+5c=96\)                 (equation 2)

Using equation 1, \(3(30.5-1.5c)+5c=96\)

\(91.5-4.5c+5c=96\)

\(91.5+0.5c=96\)

\(0.5c=96-91.5\)

\(0.5c=4.5\)

\(c = \frac{4.5}{0.5}\)

\(c=9\)

Similarly, putting the answer of equation 2 in equation 1

we get, \(a=30.5-1.5c\)

\(a=30.5-1.5(9)\)

\(a=17\)

Therefore, adult tickets cost £17 and child tickets cost £9

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The steady-state response is given by the expression below;x = X1sin(ωt − α)We know that; For a damped system with sinusoidal forcing, the steady-state amplitude is given by;X1 = (F0/m) / [(ωn2 − ω2)2 + (2ζωnω)2]0.5To find the phase angle α, we use;tan α = 2ζωnω / (ωn2 − ω2)

Hence, α = tan-1 [2ζωnω / (ωn2 − ω2)]Given ζ = 0.5, ωn = 13 rad/s and ω = 3.1 rad/s, Substituting in the expressions above;X1 = (150/1) / [(13² − 3.1²)² + (2 × 0.5 × 13 × 3.1)²]0.5 = 0.1062 rad

Substituting again;α = tan-1 [2 × 0.5 × 13 × 3.1 / (13² − 3.1²)] = 71.688° = 71.688°Therefore, α = 71.688° to 3 decimal places.

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MCC management plans to hire more staff in response to West Virginia's high divorce rate, using a probability distribution for X (number of divorces per 1000 people) to inform their decision.

The probability distribution for X provides insights into the likelihood of different divorce rates in West Virginia. This distribution helps the MCC management assess the potential demand for their services and determine the need for additional staff. By analyzing the data, they can estimate the probability of various divorce rates occurring and make informed decisions.

The probability distribution allows the MCC management to understand the range of possible outcomes and the likelihood of each outcome. This knowledge is crucial for resource allocation and planning. If the distribution indicates a high probability of divorce rates exceeding the current rate of 5 per 1000 people, it suggests a growing demand for marital counseling services. In such a case, hiring additional staff becomes a viable solution to meet the increased demand.

By utilizing the probability distribution, the management can make data-driven decisions and allocate their resources effectively. They can also monitor the divorce rates over time and adjust their staffing levels accordingly. This approach helps the Marital Counseling Center, Inc. adapt to the needs of West Virginia's population and provide adequate support to couples experiencing marital difficulties.

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Answer:

\(x=6+3\sqrt{2}\) is the size of the square

Step-by-step explanation:

Let the side of the square cut from the cardboard be “x”

Size of the square base = \(12 -2x\), height of the box = x

Volume of square box = Area * height = \((12-2x)^2 * x\)

Differentiating the above equation and equating it to zero, we get –  

d/dx \(((12-2x)^2 * x)\)

d/dx\({(144 + 4x^2 -48x)*x}\)= d/dx \((144x + 4x^3 -48x^2)\)

d/dx \((144x + 4x^3 -48x^2) = 0\)

\(144+8x^2-96X= 0\\18 +X^2-12X = 0\)

On solving above equation, we get –  

\(x=6+3\sqrt{2} \\ x=6-3\sqrt{2}\)

Answer:

Im pretty sure its 5

Step-by-step explanation:

5:1 due to 20/4 would be 5. I can give you more of an explaination if needed.

Answer:

5 triangles to 4 circles.

Answer:

Answer choice B.

Step-by-step explanation:

Standard form is written as ax + by = c, therefore our answer choice 10x + 8y = 20 is most likely the correct answer choice.

Answer: I hope this is what you are looking for

Step-by-step explanation:

so the answer is

x=y +v/b

The z test statistic needed for this hypothesis test is 0.75 .

Z test is a statistical test that is conducted on data that approximately follows a normal distribution. The z test can be performed on one sample, two samples, or on proportions for hypothesis testing. It checks if the means of two large samples are different or not when the population variance is known.

NOW,

sample proportion =  p = x / n = 0.23

Test statistics

z = ( p - p0 ) / \(\sqrt{ p0*(1-p0)}\) / n

= ( 0.23 - 0.20) /  \(\sqrt{ (0.20*0.80) / 100}\)

= 0.75

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Answer:

I'm not positive but it should be 16/625

Step-by-step explanation:

if it is brainlist would be nice

The coordinates of the center is (32, 40.5).

length of the radius of the circle is 73 units.

The coordinates of the center is solved using the formula for midpoints expressed as

Midpoint x-coordinate = (x₁ + x₂) / 2

Midpoint y-coordinate = (y₁ + y₂) / 2

Plugging in the values:

x₁ = 8 and y₁ = 13

x₂ = 56 and y₂ =68

Midpoint x-coordinate

= (8 + 56) /2

= 64/2

= 32

Midpoint y-coordinate

= (13 + 68) /2

= 81/ 2

= 40.5

distance formula will be used to find the length of the radius of the circle

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Plugging in the values:

= √[(56 - 8)² + (68 - 13)²]

= √(48² + 55²)

= √(2304 + 3025)

= √5329

= 73

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Given:

Required:

We need to find the percentage of the time will the police take 4 minutes or less to arrive.

Explanation:

Consider the z-score formula.

P-value from Z-Table

Multiply by 100 to find the percentage.

Final answer:

27 % of the time will the police take 4 minutes or less to arrive.

Let x and y be the two numbers.

Their sum is 140, so

x + y = 140

Twice the first number x is 2x. 5 more than this is 2x + 5. This is the value of the second number, so

y = 2x + 5

Substitute this into the first equation and solve for x :

x + (2x + 5) = 140

3x + 5 = 140

3x = 135

x = 135/3 = 45

Then

y = 2*45 + 5 = 95

The segments can form a Triangle.

The Pythagorean theorem, or Pythagorean theorem, illustrates the relationship between the three sides of a right-angled triangle. The square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle, according to the Pythagorean theorem.

We have Three segments as:

AB = 12 unit, BC = 9 unit, AC = 7 unit

The longest segment is 12 unit

So, AB² = 12² = 144

and, BC² + AC²

= 9² + 7²

= 81 + 49

= 130

So, a right angles triangle is not possible.

Now, using Triangle Inequality

12+ 9 >7

12 + 7>9

9 + 7> 12

Thus, a Triangle can be possible but not Right angles Triangle.

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The maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.

Acceleration is directly proportional to the force acting on an object. In simple terms, if the force on an object is greater, then it will undergo more acceleration. However, there are limitations to the acceleration that can be tolerated by the human body. At about 5 g (49.0 m/s2) for more than a few seconds, an average person starts to lose consciousness. Let's use this information to answer the given question.

Let the maximum burn rate |ΔM/Δt| that the engine could reach before the ship's acceleration exceeded 5 g be x.

Let the mass of the spaceship be m and the exhaust speed of the engine be v.

Using the formula for the thrust of a rocket,

T = (mv)e

After substituting the given values into the formula for thrust, we get:

T = (3.00 × 104)(2.50 × 103) = 7.50 × 107 N

Therefore, the acceleration produced by the engine, a is given by the formula below:

F = ma

Therefore,

a = F/m= 7.50 × 107/3.00 × 104= 2.50 × 103 m/s²

The maximum burn rate that the engine could reach before the ship's acceleration exceeded 5 g is equal to the acceleration that would be produced by a maximum burn rate. Therefore,

x = a/5g= 2.50 × 103/(5 × 9.8)≈ 51.0 kg/s

Therefore, the maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.

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When three or more parallel lines intersect two transversals, they cut off the transversals proportionally.

It should be noted that parallel lines are the lines in a plane that are the same distance apart.

In this case, when three or more parallel lines intersect two transversals, they cut off the transversals proportionally.

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In 286 ways are there to distribute seven identical apples and six identical pears to three distinct people.

There are 7 identical apples and 6 identical pears.

So total number of fruits here = 7+6 = 13 identical fruits

The number of ways to distribute 13 fruits in three distinct people is given by \(=^{13}C_3=286\) ways.

Hence the number of ways is 286.

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