Which equation has a vertex at (0, 5) and focus of (three-halves, 5)?

The probability P(x > 18) is equal to 1 minus the probability P(x < 18) for a normally distributed variable x with mean μ = 100 inches.

In a normal distribution, the area under the curve represents the probability of observing a certain value or a range of values. The probability P(x > 18) represents the probability of observing a value greater than 18 for the variable x. Conversely, the probability P(x < 18) represents the probability of observing a value less than 18 for the variable x.

Since the total area under the normal distribution curve is equal to 1, we can say that the sum of the probabilities of all possible events is equal to 1. Therefore, the probability of an event occurring (P(x > 18)) plus the probability of the event not occurring (P(x < 18)) is equal to 1.

Mathematically, we can express this relationship as:

P(x > 18) = 1 - P(x < 18)

So, the probability P(x > 18) is related to P(x < 18) by subtracting the latter from 1.

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Answer:

3487

Step-by-step explanation:

Answer:

5 months

Step-by-step explanation:

100 105 110 115 120 125

75   85 95  110 115  125

Here is the set up:

A = area of rectangular garden = 6/7.

Let l = length = 3/5.

Let w = width

A = lw

6/7 = (3/5)w

Solve for w.

Hence, the answers are:a. Sensitivity of the test is 12.37%.b. Specificity of the test is 97.18%.c. False-positive fraction of the test is 2.86%.d. False-negative fraction of the test is 87.63%.

Sensitivity of a screening testSensitivity of the screening test is the probability of obtaining a positive screening test result among people with the disease. It is calculated as follows:Sensitivity = True positive / (True positive + False negative)From the given table,True positive = 12False negative = 85Total number of people with the disease = True positive + False negative = 12 + 85 = 97Sensitivity = 12 / (12 + 85) = 0.1237 = 12.37%Therefore, the sensitivity of the test is 12.37%.Specificity of a screening testSpecificity of the screening test is the probability of obtaining a negative screening test result among people who do not have the disease. It is calculated as follows:Specificity = True negative / (True negative + False positive)From the given table,True negative = 204False positive = 6Total number of people without the disease = True negative + False positive = 204 + 6 = 210Specificity = 204 / (204 + 6) = 0.9718 = 97.18%Therefore, the specificity of the test is 97.18%.False-positive fractionFalse-positive fraction is the proportion of healthy people who get a positive result out of the total number of healthy people. It is calculated as follows:False-positive fraction = False positive / (False positive + True negative)From the given table,False positive = 6True negative = 204False-positive fraction = 6 / (6 + 204) = 0.0286 = 2.86%Therefore, the false-positive fraction of the test is 2.86%.False-negative fractionFalse-negative fraction is the proportion of sick people who get a negative result out of the total number of sick people. It is calculated as follows:False-negative fraction = False negative / (False negative + True positive)From the given table,False negative = 85True positive = 12False-negative fraction = 85 / (85 + 12) = 0.8763 = 87.63%Therefore, the false-negative fraction of the test is 87.63%.Hence, the answers are:a. Sensitivity of the test is 12.37%.b. Specificity of the test is 97.18%.c. False-positive fraction of the test is 2.86%.d. False-negative fraction of the test is 87.63%.

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Answer:

there isn't a slope, because this line isn't even a function, because it is a vertical line... so it doesn't pass the vertical line test...

Step-by-step explanation:

Answer:

undefined

Step-by-step explanation:

the equation for the slope of the line is (y2-y1)/(x2-x1)

here are the given points: (-6,-8) and (-6,12)

label the points:

x1=-6

y1=-8

x2=-6

y2=12

now substitute into the equation (m is slope)

m=(12--8)/(-6--6)

m=(12+8)/(-6+6)

m=20/0

m=undefined

the slope is undefined because you cannot divide by 0

Hope this helps!

1- SHM stands for Simple Harmonic Motion.

In SHM, an object oscillates back and forth about an equilibrium position, with a motion that can be described by a sinusoidal function. The symbols commonly used in SHM are:

y: Displacement from the equilibrium position

t: Time

k: Spring constant or restoring force constant

m: Mass of the object

c₁ and c₂: Constants determined by initial conditions

2- Hooke's law relates the force exerted by a spring to the displacement of the object attached to it. It is represented by the second-order differential equation my" + ky = 0, where m is the mass of the object and k is the spring constant. The solution to this equation is given as y = c₁ cos(√(k/m) * t) + c₂ sin(√(k/m) * t). To determine the values of c₁ and c₂, initial conditions are needed.

3- If the initial conditions are y(0) = 0 and y'(0) = 0, which means the object starts at equilibrium with zero displacement and zero velocity, we can substitute these values into the solution equation and solve for c₁ and c₂. In this case, we find that c₁ = 0 and c₂ = 0.

4- To show that the sum of the solutions c₁ cos(w₀t) and c₂ sin(w₀t) is also a solution of the SHO (Simple Harmonic Oscillator) differential equation, we substitute the sum into the differential equation and demonstrate that it satisfies the equation. By taking the derivatives and substituting, we can show that the sum of the solutions satisfies the equation, thus confirming that it is also a solution.

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A. IQR or B. IQR is the correct response since Sunny Town is symmetrical or Sunny Town is asymmetrical.

The pattern of data distribution across various values or intervals is referred to as a distribution. The form, centre, and dispersion of a set of data can be described and examined in this manner.

We need to measure the fluctuation of the temperature data in both locations in order to decide which place has the most stable temperature. The interquartile range (IQR), which quantifies the spread of the middle 50% of the data, is the ideal measure of variability for this application.

As a result, depending on how the distributions are shaped, the answer is either A. IQR because Sunny Town is symmetric or B. IQR because Sunny Town is skewed. The IQR would be a suitable tool to gauge the data's spread if Sunny Town's temperature data were symmetric. The IQR would also be useful to measure the spread of the data if Sunny Town's temperature data were skewed. Therefore, the range would not be a suitable indicator of variability if the temperature data from either location were not skewed.

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Answer:

8m x 7m x 8m = 448m

Answer:

41/24 or 1 17/24

Step-by-step explanation:

2 3/8=19/8

-2/3+19/8

-16/24+57/24

41/24

Answer:

It would be -1/2

Step-by-step explanation:

-2--3/0-2=-1/2

Answer:

1. D (9/12)

2. B (1/4)

3. C (2^4x3x5)

Step-by-step explanation:

Hope this helps

Answer:

1) D 9/12

2) B 1/4

3) C 2^4 * 3 * 5

Step-by-step explanation:

1)

1/2 = 6/12

5/6 = 10/12

6/12 < 9/12 < 10/12, this is true.

2)

Although the visual representation doesn't give us exactly what the portion of each slice is, we can determine that the pizza is split into four equal slices. One of the slices is cut down even further, however, that doesn't change the fact that each of the other three pizza slices is 1/4. So the greatest pizza slice is equivalent to 1/4 of the pizza.

3)

Factor out 240:

240 = 120 x 2

120 = 60 x 2

60 = 30 x 2

30 = 15 x 2

15 = 5 x 3

2 x 2 x 2 x 2 x 3 x 5

Multiple the 2's together to get the following equation:

\(2^{4} * 3 * 5\)

My graph of the linear inequality 4y ≤ 5x is correct when compared to the answer key in the textbook (T1) for exercise number 270 of section 3.4. I verified that the graph represents the solution region for the given inequality.

To graph the linear inequality 4y ≤ 5x, we start by converting it to slope-intercept form, y ≤ (5/4)x. This form helps us understand the slope and y-intercept of the line. In this case, the slope is 5/4, which means the line rises 5 units for every 4 units it moves to the right. The y-intercept is 0 since there is no constant term.

To graph the inequality, we draw a dotted line with a slope of 5/4 passing through the origin (0,0). We use a dotted line because the inequality includes the "less than or equal to" symbol, indicating that points on the line are included in the solution.

Next, we determine which side of the line represents the solution region. We can choose a test point not on the line, such as (0,1), and substitute its coordinates into the inequality. If the inequality holds true, the region containing the test point is part of the solution. In this case, when substituting (0,1) into the inequality, we get 4(1) ≤ 5(0), which simplifies to 4 ≤ 0. Since this is false, the solution region is on the other side of the line.

Finally, we shade the region below the line to indicate the solution. This region represents all the points (x, y) that satisfy the inequality 4y ≤ 5x. Comparing this graph to the answer key in the textbook, it should match the solution region depicted there.

By following these steps, I ensured that my graph accurately represented the solution to the given linear inequality.

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We get that the radius is 3 ft and the length is 29 ft so the volume is

the approximate value is:

The value of p in the given equation is -1.

Given is an equation p-3 = -4, we need to find the value of p,

So,

p-3 = -4

p = -4+3

p = -1

Hence, the value of p in the given equation is -1.

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Answer: 3.7

Step-by-step explanation: In this case you're just multiplying by (10) usually this is done to make a decimal to a whole number

There are ten centimeters in one decimeter. How many decimeters are in thirty seven centimeters?

Divide 37/10=3.7

Another way is 3. 7*10=37

Expanding the equation gives us the final quadratic equation is 5x^2 - 15x - 30 = 0.

The quadratic equation with roots −3 and 6 can be written in the form:

(x - r1)(x - r2) = 0,

where r1 and r2 are the roots of the equation. Substituting the given roots, we have:

(x - (-3))(x - 6) = 0,

which simplifies to:

(x + 3)(x - 6) = 0.

To include the leading coefficient of 5, we can multiply both sides of the equation by 5:

5(x + 3)(x - 6) = 0.

Expanding the equation gives us the final quadratic equation:

5x^2 - 15x - 30 = 0.

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For per unit scoops of powdered 2 cups of Water is Needed.

It is a measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.

Given,  Ryan is making a fruit drink. The directions say to mix 3 cups of water with 1 1/2 scoops of powdered fruit mix.

We have to find how many cups of water should he use with 6 scoops of fruit mix

Let "n" be the number of cups required for 6 scoops of fruit mix

3 cups of water ⇒ 1.5 scoops of fruit mix.

Then, n cups of water ⇒ 6 scoops of fruit mi

So, by cross multiplication,

6 * 3 = n *1.5

n = 12

Ryan has to use 12 cups of water for 6 scoops.

thus,

For per unit scoops of powdered 2 cups of Water is Needed.

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Answer:

The diver is 29 ft below the water surface

Step-by-step explanation:

Here, we are interested in calculating the diver’s final depth before the surface of the water.

Firstly he descends 18 feet before ascending 7 feet. His depth would thus be;

18ft -7ft = 11 ft initially

It is at this point he descended a further 18 feet which makes his total feet of descent = 11 ft + 18 ft = 29 ft

This means he is 29 ft below the surface of the water

Answer:

-29

Step-by-step explanation:

The diver is 29 ft below the water surface

The function that describes the population of Martin is\(P(t) = 12,420 \times (1 + 0.016)^t\)

The predicted population of Martin in 2015 is 14557

The predicted  population of Martin in 2002 is 10,658

The function that describes the population of Martin as a function of the number of years t, since 2005, can be written as:

\(P(t) = 12,420 \times (1 + 0.016)^t\)

where P(t) is the population of Martin t years since 2005.

To predict the population of Martin in 2015, we need to substitute t = 10 into the equation:

P(10) = 12,420 × (1 + 0.016)¹⁰

= 14556.5

Therefore, the predicted population of Martin in 2015 is approximately 14556.5 people.

To predict the population of Martin in 2002, we need to find the number of years between 2005 and 2002, which is 3 years.

We can substitute t = -3 into the equation:

P(-3) = 12,420 × (1 + 0.016)⁻³)

= 10,658

Therefore, the predicted population of Martin in 2002 is approximately 10,658 people.

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Answer:

we need context to answer your question

Step-by-step explanation:

Answer:

(x-3)(x-9)

Step-by-step explanation:

first thing you need to do is move the -6 over. so we're going to add 6 to both sides (we add because it's negative 6 and we need 0 on the right side)

so you have: x^2-12x+27

now we need to come up with two numbers that add to -12 and multiply to 27.

the factors of 27 are 9 & 3 and 27 & 1. only 9 & 3 add to 12 so we are going to use those.

since the 12 is negative however, 9 and 3 should both be negative.

therefore we get: (x-3)(x-9)

*it doesn't matter which order you put them in!

To find the length of the curve described by the parametric equations, we use the formula. Therefore, the exact length of the curve described by the parametric equations is 16√17 - 2/3 units.

L = ∫[a, b] sqrt[(dx/dt)^2 + ( dy/dt)^2] dt

where a and b are the bounds of the parameter t.

Using the given parametric equations, we have:

x(t) = 8 + 3t^2

y(t) = 7 + 2t^3

Taking the derivatives with respect to t, we have:

dx/dt = 6t

dy/dt = 6t^2

Substituting these expressions into the formula for L, we get:

L = ∫[0,4] sqrt[(6t)^2 + (6t^2)^2] dt

= ∫[0,4] sqrt[36t^2 + 36t^4] dt

= ∫[0,4] 6t sqrt(1 + t^2) dt

To evaluate this integral, we use the substitution u = 1 + t^2, du/dt = 2t, and dt = du/2t. This gives:

L = ∫[1,17] 3 sqrt(u) du

= 2[u^(3/2)/3]∣[1,17]

= 2[(17^(3/2) - 1^(3/2))/3]

= 2(8√17 - 1/3)

Therefore, the exact length of the curve described by the parametric equations is 16√17 - 2/3 units.

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Answer:

The reasonable prediction for successful rolls is 4.

Step-by-step explanation:

Assuming the rolling cube  is a fair 6 sided cube, so the probability of success of one roll is given as

\(P(Success)=\dfrac{Number\ of\ successful\ events}{Number\ of\ total\ events}\)

\(P(Success)=\dfrac{1}{6}\)

The total success is given as

\(P(Total\ Success)=P(Success)\times Number\ of\ events\)

For 24 rolls it is given as

\(P(Total\ Success)=P(Success)\times Number\ of\ events\\P(Total\ Success)=\dfrac{1}{6}\times 24\\P(Total\ Success)=4\)

So the reasonable prediction for successful rolls is 4.

The present value of the annuity at the end of year 7 is approximately $47,069.08.

To calculate the present value of an ordinary annuity, we can use the formula:

PV = PMT * [(1 - (1 + r)⁻ⁿ) / r],

where PV is the present value, PMT is the annual payment, r is the interest rate per period, and n is the number of periods.

In this case, the annual payment is $4,500, the interest rate is 8%, and the number of periods is 16. However, the payments start at the end of year 8 and continue until the end of year 23, which means there is a delay of 7 years.

Using the formula, the present value at the end of year 7 can be calculated as:

PV = $4,500 * [(1 - (1 + 0.08)⁻¹⁶) / 0.08] = $47,069.08.

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The angle of c, denoted as angle(c), is the angle formed between the positive real axis and the line connecting the origin to c. To find the angle, we can use the arctan function: angle(c) = arctan(-2/(-9)).

c) The polar representation of a is r_a * e^(i * theta_a), where r_a is the modulus (magnitude) of a and theta_a is the argument (angle) of a.

d) The polar representation of c is r_c * e^(i * theta_c), where r_c is the modulus (magnitude) of c and theta_c is the argument (angle) of c.

e) To find the sum of a and the complex conjugate of c (c*), we add the real parts and imaginary parts separately. The sum is (a + c*) = (2 - 3j) + (-9 + 2j) = (-7 - j).

f) The complex conjugate of a (a*) is obtained by changing the sign of the imaginary part. So, a* = 2 + 3j.

g) The modulus (magnitude) of a, denoted as |a|, is the distance of a from the origin in the complex plane. |a| = sqrt((2^2) + (-3^2)) = sqrt(4 + 9) = sqrt(13).

h) The angle of a, denoted as angle(a), is the angle formed between the positive real axis and the line connecting the origin to a. To find the angle, we can use the arctan function: angle(a) = arctan(-3/2).

i) The angle of c, denoted as angle(c), is the angle formed between the positive real axis and the line connecting the origin to c. To find the angle, we can use the arctan function: angle(c) = arctan(-2/(-9)).

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We have the given equation for the remaining Tylenol in her body.

Where n represents the number of hours.

We need to find the remaining Tylenol in her body after 4 hours. Therefore, set n=4.

Replacing on the formula:

The value is rounded to the nearest hundredth.

Hence, Jane will have 14.99 mg's of Tylenol remaining in her body after 4 hours.

The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

To determine the upper and lower control limits for the sample means, we can use the formula:

Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))

Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))

In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.

For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.

Given:

Mean = 2.0 litres

Standard Deviation = 0.01 litres

Sample size (n) = 5

Using the formula, we can calculate the upper and lower control limits:

UCL = 2.0 + (1.96 * 0.01 / sqrt(5))

LCL = 2.0 - (1.96 * 0.01 / sqrt(5))

Calculating the values:

UCL ≈ 2.0018 litres

LCL ≈ 1.9982 litres

Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997

Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.

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The age of Barbra is 22 years.

The algebraic method for solving simultaneous linear equations is the substitution method. A quantity of one variable through one expression is replaced in the second equation, as the name implies.

Now, according to the question.

Let 'a' be the age of Alice.

Let 'b' be the age of Barbra

Let 'c' be the age of Carol.

The sum of age of all three sisters is 68 years.

Thus,  a + b + c = 68

Now, as Alice is three years younger than Barbra.

a = b - 3

and, Barbra is 5 years younger than Carol.

b = c - 5

c = b + 5

By substitution of values of a and c in total age.

(b - 3) + b + (b + 5) = 68

3b - 3 + 5 = 68

On solving the expression.

b = 22

Therefore, the age of Barbra is 22 years.

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The ratios for each pair of the data are the same, so the download time and the file size are proportional.

A proportional relationship is a linear function that has the following features.

Hence the output variable y is given by the multiplication of the input variable x and the constant of proportionality k, hence the equation is:

y = kx.

A set of data is only proportional if the division of the output by the input is the same for all pairs of values.

For this set of data, this division is given as follows:

Same ratios, hence the measures are proportional.

The data is given by the image at the end of the answer.

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