PLEASE HELP ME
You are given below as well as the following information:
m9 = 110 degrees
m8 =70 degrees
p || q

What is m6?
100 degrees
70 degrees
110 degrees
80 degrees

The probability that it will require between 13.7 and 17.3 minutes to perform the task is (6.5 / 7.5) - (2.9 / 7.5).

To find the probability that it will require between 13.7 and 17.3 minutes to perform the task, we can use the formula for calculating the probability of a range within a uniform distribution.
First, we need to find the total range of completion times, which is 18.3 - 10.8 = 7.5 minutes.
Next, we calculate the probability of the task taking less than 13.7 minutes by finding the difference between 13.7 and 10.8, which is 2.9 minutes.

Then, we divide this by the total range, 7.5 minutes.
So, the probability of the task taking less than 13.7 minutes is 2.9 / 7.5.
Similarly, we calculate the probability of the task taking less than 17.3 minutes by finding the difference between 17.3 and 10.8, which is 6.5 minutes.

Then, we divide this by the total range, 7.5 minutes.
So, the probability of the task taking less than 17.3 minutes is 6.5 / 7.5.
Finally, to find the probability of the task taking between 13.7 and 17.3 minutes, we subtract the probability of the task taking less than 13.7 minutes from the probability of the task taking less than 17.3 minutes.
Therefore, the probability that it will require between 13.7 and 17.3 minutes to perform the task is (6.5 / 7.5) - (2.9 / 7.5).

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Using the Laws of Detachment and Syllogism, the conclusions can be described as follows:

1. Invalid.

2. Law of Syllogism.

3. Law of Detachment.

4. Invalid.

For item 1, the events are given as follows:

Neither of the laws are reached in the conclusion, hence we have an invalid conclusion.

For item 2, the transitive property was applied correctly, hence the Law of Syllogism was used.

For item 3, p and p -> q are true, then we concluded that q is true, hence the Law of Detachment was used.

For item 4, we have an invalid conclusion, as we have p -> q and q, but no conclusion can be reached regarding p.

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The differential equation dx/dt = x^2/14 with the initial condition x(0) = 2 has a particular solution given by x(t) = -1/(t/14 - 1/2).

To solve the separable differential equation dx/dt = x^2/14 and find the particular solution satisfying the initial condition x(0) = 2, follow these steps,

1. Identify the differential equation: dx/dt = x^2/14
2. Separate the variables: dx/x^2 = dt/14
3. Integrate both sides: ∫(1/x^2) dx = ∫(1/14) dt
4. Evaluate the integrals: -1/x = t/14 + C₁
5. Solve for x: x = -1/(t/14 + C₁)
6. Apply the initial condition x(0) = 2: 2 = -1/(0 + C₁)
7. Solve for C₁: C₁ = -1/2
8. Substitute C₁ back into the equation for x: x(t) = -1/(t/14 - 1/2)

The particular solution to the differential equation dx/dt = x^2/14 with the initial condition x(0) = 2 is x(t) = -1/(t/14 - 1/2).

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Answer:

68

Step-by-step explanation:

Use the formula provided...

6 and 11 are b1 and b2, and 8 is h.

So, 6+11 = 17

17/2 = 8.5

8.5*8 = 68

Answer:

3$

Step-by-step explanation:

Let x be t-shirts and y socks.

4x + 3y= $37

2y + 5x= $41

x= (37 - 3y) ÷ 4

2y + 5((37-3y)÷4)=41

y=3

the solution of equation problem is estimated distance of the gold medal winning discus throw in 1980 is approximately 65.03 meters. The answer is option C.

An equation is a statement that says two things are equal. It can contain variables, which can take on different values. Equations are used to solve problems and model real-world situations by expressing relationships between variables.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Here,

5 and 13 are expressions for 2x.

These two expressions are joined together by the sign "="

To estimate the distance of the gold medal winning discus throw in 1980 using the line of best fit, we need to first calculate the value of x for the year 1980

x = 1980 - 1920 = 60

Now, we can substitute x=60 into the equation of the line of best fit to find the estimated distance:

y = 0.34x + 44.63

y = 0.34(60) + 44.63

y = 20.4 + 44.63

y ≈ 65.03

Therefore, the estimated distance of the gold medal winning discus throw in 1980 is approximately 65.03 meters. The answer is option C.

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Answer:

Its number C

Step-by-step explanation:

Looked it up and it was correct

Answer:  We can use the Pythagorean theorem to find the length of the hypotenuse (c) of a right triangle, which is given by:

c^2 = a^2 + b^2

where a and b are the lengths of the legs.

In this case, a = 4 and b = 6. Substituting these values into the formula, we get:

c^2 = 4^2 + 6^2

c^2 = 16 + 36

c^2 = 52

Taking the square root of both sides, we get:

c = sqrt(52)

Simplifying, we can factor out a 4 from under the radical:

c = sqrt(4 * 13)

c = 2 sqrt(13)

Therefore, the exact length of the hypotenuse is 2 sqrt(13) units.

Step-by-step explanation:

The function of the graph shown is option A. g(x) = -(x-6) ^2.

The function is a type of relation, or rule, that maps one input to specific single output.

We have been given a graph of a function, we need to find the function g(x).

So, we can see that the graph is intersecting the x-axis at ( 6, 0), then the function which satisfies the coordinate will be the function of g(x).

A. g(x) = -(x-6) ^2

put x = 6

g(x) = -(6-6) ^2

g(x) = - (0)

LHS = RHS

Thus, The function of the graph shown is option A. g(x) = -(x-6) ^2.

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The equations of the tangent lines at the points (1, 12) and (2, 13) are:

\((i) y(x) = (10a - 6a^2)x + (6a^2 - 10a + 12)\\(ii) y(x) = (10a - 6a^2)x + (12a^2 - 20a + 13)\)

To find the slope of the tangent line to the curve at a specific point, we need to take the derivative of the curve equation with respect to x and evaluate it at that point.

Let's calculate the slope of the tangent line when x = a for the curve equation \(y = 9 + 5x^2 - 2x^3.\)

(a) Find the slope m of the tangent to the curve at the point where x = a:

First, we take the derivative of y with respect to x:

dy/dx = d/dx (\(9 + 5x^2 - 2x^3\))

= 0 + 10x - 6\(x^2\)

\(= 10x - 6x^2\)

To find the slope at x = a, substitute a into the derivative:

\(m = 10a - 6a^2\)

(b) Find equations of the tangent lines at the points (1, 12) and (2, 13):

(i) For the point (1, 12):

We already have the slope m from part (a) as \(m = 10a - 6a^2.\) Now we can substitute x = 1, y = 12, and solve for the y-intercept (b) using the point-slope form of a line:

y - y_1 = m(x - x_1)

y - 12 = (\(10a - 6a^2\))(x - 1)

Since x_1 = 1 and y_1 = 12:

\(y - 12 = (10a - 6a^2)(x - 1)\\y - 12 = (10a - 6a^2)x - (10a - 6a^2)\\y = (10a - 6a^2)x - (10a - 6a^2) + 12\\y = (10a - 6a^2)x + (6a^2 - 10a + 12)\)

(ii) For the point (2, 13):

Similarly, we substitute x = 2, y = 13 into the equation \(m = 10a - 6a^2\), and solve for the y-intercept (b):

\(y - y_1 = m(x - x_1)\\y - 13 = (10a - 6a^2)(x - 2)\)

Since x_1 = 2 and y_1 = 13:

\(y - 13 = (10a - 6a^2)(x - 2)\\y - 13 = (10a - 6a^2)x - 2(10a - 6a^2)\\y = (10a - 6a^2)x - 20a + 12a^2 + 13\\y = (10a - 6a^2)x + (12a^2 - 20a + 13)\)

Thus, the equations of the tangent lines at the points (1, 12) and (2, 13) are:

\((i) y(x) = (10a - 6a^2)x + (6a^2 - 10a + 12)\\(ii) y(x) = (10a - 6a^2)x + (12a^2 - 20a + 13)\)

These equations are specific to the given points (1, 12) and (2, 13) and depend on the value of a.

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Answer:

Look at the image I attached to my response.

Step-by-step explanation:

For proof #3, I did it according to the way I was taught how to do proofs in my state/school, so what you wrote could be correct.

If the cube and sphere both have volume as 512 cubic units, then the solid that has a greater surface area is Cube.

we first find the side length of the cube and the radius of the sphere.

The volume of the cube is 512 cubic units,

We have,

⇒ side³ = 512,

⇒ side = 8

So, the side length of the cube is 8 units.

Volume of sphere is also 512 cubic units,

We have,

⇒ (4/3)πr³ = 512,

On Simplifying,

We get,

⇒ r = 4.96 units.

So, radius of sphere is = 4.96 units.

Next we can find the surface area of each solid.

The surface-area of cube is = 6×(side)²,

⇒ 6(side²) = 6(8²) = 384 square units,

The surface area of the sphere is = 4πr²,

⇒ 4π(r²) = 4π(4.96²) ≈ 309 square units.

Therefore, the Cube has a greater surface area than the sphere.

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Answer:

1

Step-by-step explanation:

We can use the slope formula

m = (y2-y1)/(x2-x1)

    = (5-8)/(-8 - -5)

    = -3/(-8+5)

    = -3/-3

   = 1

Sam will be 12m behind when Robert crosses the finish line.

What does it mean to do speed?

I will assume the boys have all run at a constans speed right rom the beginning of the race.

When Robert has run 50, Sam has run 40 metres

so Sam has has run 4/5 as far as Robert.

If this ratio stays the same then when Robert has run 60m Sam will have run  4/5 of 60 = 48 metres.

So  that Sam will be 12m behind when Robert crosses the finish line.

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Answer:

a)~5572.45 (cm^3)

b)~1519.76 (cm^2)

Step-by-step explanation:

A volleyball has a diameter d = 22 cm

=> Its radius r is r = d/2 = 22/2 = 11 cm

a) Its volume is calculated by:

V = (4/3) x pi x r^3

with p = ~3.14 and r = 11 cm

=> V = (4/3) x 3.14 x 11^3 = ~5572.45 (cm^3)

b) Its surface area is calculated by:

A = 4 x pi x r^2

with p = ~3.14 and r = 11 cm

=> A = 4 x 3.14 x 11^2 = ~1519.76 (cm^2)

the statement is false. The correct probability is approximately 0.5567, not 0.0062.

To determine the truth value of the statements, we need to calculate the probabilities using the given normal distribution with a mean of 8 and a standard deviation of 16.

a. The probability of obtaining an X value greater than 12 can be calculated by finding the area under the normal curve to the right of 12. We can use the z-score formula to standardize the value:

z = (X - mean) / standard deviation

For X = 12, mean = 8, and standard deviation = 16:z = (12 - 8) / 16 = 0.25

Using a standard normal distribution table or a calculator, we can find that the probability of obtaining a z-value of 0.25 or greater is approximately 0.4013. Therefore, the statement is false. The correct probability is approximately 0.4013, not 0.16.

b. The probability of obtaining an X value between 12 and 14 can be calculated by finding the area under the normal curve between these two values. First, we standardize the values:

z1 = (12 - 8) / 16 = 0.25

z2 = (14 - 8) / 16 = 0.375

Using the standard normal distribution table or a calculator, we can find the area to the right of z1 and subtract the area to the right of z2:

(12 < X < 14) = P(z1 < Z < z2)

              = P(Z < z2) - P(Z < z1)

Using the table, we find P(Z < 0.375) = 0.6480 and P(Z < 0.25) = 0.5987.

P(12 < X < 14) = 0.6480 - 0.5987 = 0.0493

Therefore, the statement is false. The correct probability is approximately 0.0493, not 0.09.

c. The probability that an X value is more than 2.5 standard deviations from the mean can be calculated using the z-score:

z = (X - mean) / standard deviation

For X = 8 + 2.5 * 16:

z = (8 + 2.5 * 16 - 8) / 16 = 0.15625

Using the standard normal distribution table or a calculator, we can find the probability of obtaining a z-value of 0.15625 or greater. The value is approximately 0.5567, not 0.0062.

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The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.

The sample variance is a measure of how much the individual data points in a sample vary from the mean.

It is calculated by finding the average of the squared differences between each data point and the mean.

To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:

Calculate the mean (average) of the data set:

Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90

Subtract the mean from each data point and square the result:

(93 - 90)^2 = 9

(89 - 90)^2 = 1

(91 - 90)^2 = 1

(87 - 90)^2 = 9

(91 - 90)^2 = 1

(89 - 90)^2 = 1

Calculate the sum of the squared differences:

9 + 1 + 1 + 9 + 1 + 1 = 22

Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):

Variance = 22 / 5 = 4.4

It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.

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The normal approximation can be used in a two-sample test of proportions when the sample sizes are sufficiently large.

The rule of thumb is that each sample should have at least 10 successes and 10 failures. When these conditions are met, the sampling distribution of the difference in sample proportions can be approximated by a normal distribution with a mean equal to the difference in population proportions and a standard deviation calculated from the sample proportions. This approximation allows us to calculate probabilities and make inferences using the standard normal distribution. It is important to note that this approximation may not be accurate for small sample sizes, in which case exact methods such as the Fisher's exact test should be used instead. In summary, the normal approximation can be used in a two-sample test of proportions when the sample sizes are large enough and the conditions are met.

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Answer:1380

Step-by-step explanation:

Answer:

9:45 AM

Step-by-step explanation:

To get to work in the morning, Amanda cycles for 10 miles at the rate of 12 mph.

Time (hours) = Distance/speed

Hence, the time she spends cycling = 10mile/12 mph

= 0.8333333333 hour

Converting to minutes:

1 hour = 60 minutes

0.8333333333 hour =

0.8333333333 hours × 60 minutes/1 hour

= 50 minutes.

Hence, she spends 50 minutes cycling

She makes a 10 minutes stop for a cup of coffee, and then rides a bus for 15 minutes. The speed of the bus is 45 mph.

The total number of minutes she spends to get to work is calculated as:

(50 + 10 + 15)minutes

= 75 minutes.

It takes Amanda 75 minutes to get to work.

At what time will Amanda get to work if she leaves home at 8:30 AM?

= 8:30AM + 75 minutes

= 8:30 AM + 1 hour 15 minutes

= 9:45 AM

Answer:

3/5 works

Step-by-step explanation:

its in between 1/2 and 5/8

Answer:

it's 9/16 it is in between 1/2 and 3/4

The probability of A and B occurring simultaneously (P(A ∩ B)) is c. 0.00.

In this scenario, A and B are stated to be mutually exclusive events. Mutually exclusive events are events that cannot occur at the same time. This means that if event A happens, event B cannot happen, and vice versa.

Given that P(A) = 0.4 and P(B) = 0.5, we can deduce that the probability of A occurring is 0.4 and the probability of B occurring is 0.5. Since A and B are mutually exclusive, their intersection (A ∩ B) would be an empty set, meaning no outcomes can be shared between the two events. Therefore, the probability of A and B occurring simultaneously, P(A ∩ B), would be 0.

To further clarify, let's consider an example: Suppose event A represents flipping a coin and getting heads, and event B represents flipping the same coin and getting tails. Since getting heads and getting tails are mutually exclusive outcomes, the intersection of events A and B would be empty. Therefore, the probability of getting both heads and tails in the same coin flip is 0.

In this case, since events A and B are mutually exclusive, the probability of their intersection, P(A ∩ B), is 0.

Therefore, the correct answer is: c. 0.00

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Answer:

Find the radius

Square the radius

Multiply by pi

Round to nearest hundredth

The ounces of the watermelon sugar scrub per dollars is 1.1 ounces per dollars.

The store charges $12.65 for a 14 oz container of watermelon sugar scrub. The amount in ounces of watermelon sugar scrub per dollars can be calculated as follows:

12.65 dollars = 14 ounces

1 dollars = ?

cross multiply

Hence,

amount of ounces of watermelon sugar scrub per dollars  = 14 × 1 / 12.65

amount of ounces of watermelon sugar scrub per dollars  = 14/ 12.65

amount of ounces of watermelon sugar scrub per dollars  = 1.10671936759

amount of ounces of watermelon sugar scrub per dollars  = 1.1 ounces per dollars

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The area of the rectangle changing at the instant when the other side is cm and increasing at cm per minute is k²/min

Let's start by defining the variables:

Let x be the length of the rectangle (in cm).

Let y be the width of the rectangle (in cm).

Let A be the area of the rectangle (in cm²).

We know that one side of the rectangle (y) is constant, so its derivative with respect to time is zero:

dy/dt = 0

We also know that the other side of the rectangle (x) is increasing at a rate of dx/dt = cm/min.

We can use the formula for the area of a rectangle to express A in terms of x and y:

A = x×y

To find how fast the area of the rectangle is changing with respect to time, we can take the derivative of both sides with respect to time:

dA/dt = d/dt (x×y)

Using the product rule of differentiation, we get:

dA/dt = x × dy/dt + y × dx/dt

Since dy/dt = 0 (as we established earlier), we can simplify the equation to:

dA/dt = x × 0 + y × dx/dt

Plugging in the given values for y and dx/dt, we get:

dA/dt = (cm) × (cm/min) = k²/min

Therefore, the area of the rectangle is increasing at a rate of k²/min at the instant when one side is cm and increasing at cm per minute.

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The complete question is :

A rectangle has one side of "k" cm. how fast is the area of the rectangle changing at the instant when the other side is cm and increasing at cm per minute?

Functions are used to represent graphs, and vice versa.

The function represented by the graph is \(f(x) =- |x + 4| + 3\)

The graph (see attachment) is an absolute value graph.

An absolute value graph is represented as:

\(f(x) =a |x - h| + k\)

Where

\(Vertex = (h,k)\)

The vertex is the minimum or the maximum point on the graph.

So, we have:

\(Vertex = (-4,3)\)

The function becomes

\(f(x) =a |x + 4| + 3\)

The function also passes through the point (-1,0).

So, we have:

\(0 =a |-1 + 4| + 3\)

\(0 =a |3| + 3\)

Remove the absolute bracket

\(0 =3a + 3\)

Subtract 3 from both sides

\(3a =- 3\)

Divide both sides by 3

\(a =- 1\)

Substitute -1 for (a) in \(f(x) =a |x + 4| + 3\)

\(f(x) =- |x + 4| + 3\)

Hence, the function represented by the graph is \(f(x) =- |x + 4| + 3\)

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The value of x , y and z in the parallel line is 50 degrees.

When parallel lines are crossed by a transversal line, angle relationships are formed such as vertically opposite angles, alternate interior angles, alternate exterior angles, adjacent angles, corresponding angles etc.

Therefore, let's use the angle relationships to find the angle, x, y and z as follows:

Therefore,

x = 360 - 310(sum of angles in a point)

x = 50 degrees

Therefore,

x = y(alternate interior angles)

Alternate interior angles are congruent.

Hence,

y = 50 degrees

Therefore,

x = z(alternate interior angles)

z = 50 degrees.

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