An oil tanker and a cruise ship leave port at the same time and travel straight-line at 32 mph and 46 mph, respectively. Two hours later, they are 63 miles apart. What is the angle between their courses?​

Answer:

Perpendicular refers to that which has a right angle in relation to the intersection of two lines or planes. ... As seen in the Cartesian plane, what defines a line as perpendicular is its point of intersection with another line.

Step-by-step explanation:

The most appropriate measure of central tendency for the variable of marital status would be the mode. In this case, the most appropriate measure of central tendency for the variable of marital status would be the mode.

The mode is the value or category that appears most frequently in a dataset. Since marital status is a categorical variable with different categories (married, divorced, separated, widowed, never married, cohabitating), finding the mode would identify the most commonly occurring marital status among the study subjects.

Using the mode as a measure of central tendency in this scenario makes sense because it provides information about the most prevalent category or group within the dataset. This can be valuable when studying demographic data, as it helps to identify the dominant marital status among the subjects.

On the other hand, the median and mean are measures of central tendency typically used for numerical data rather than categorical data. The median represents the middle value in an ordered dataset, while the mean is the arithmetic average. These measures would not be appropriate for a categorical variable like marital status, as it does not involve numerical values that can be added or averaged.

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There were 67 bicycles and 18 tricycles at the Bike & Trike race.

Let's use the variables b and t to represent the number of bicycles and tricycles, respectively.

From the problem statement, we know that:

b + t = 85 (equation 1: there are a total of 85 vehicles)

2b + 3t = 188 (equation 2: there are a total of 188 wheels)

We have two equations with two unknowns, so we can solve for b and t using any method. Let's use the substitution method:

Solve equation 1 for b:

b = 85 - t

Substitute this expression for b in equation 2:

2(85 - t) + 3t = 188

Simplifying and solving for t, we get:

170 - 2t + 3t = 188

t = 18

Substitute this value for t in equation 1 to find b:

b + 18 = 85

b = 67

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Step-by-step explanation:

distance / rate = time

216 mi / 72 mi/hr = 3 hours

Answer:

156, because the mean is 13, and the mean in equal to all of the numbers added up and divided by how many numbers there are.

Given the equation:

8x + 7y = -50

We will check the options to find which order pair is the solution of the equation

Point (-6 , -1)

8 * -6 + 7 * -1 = -48 - 7 = -55 ≠ -50

Point ( 0 , -6)

8 * 0 + 7 * - 6 = -42 ≠ -50

Point (-6, 0 )

8 * - 6 + 7 * 0 = -48 ≠ -50

Point (-1 , -6)

8 * -1 + 7 * -6 = -8 - 42 = -50

so, the order pair which is a solution for the equation is (-1 , -6 )

A check or quadrangle is defined by the intersection of pairs of diagonals of a parallelogram.

A parallelogram is a quadrilateral with two pairs of parallel sides. In a parallelogram, the opposite sides are parallel and have the same length. The opposite angles of a parallelogram are equal. A parallelogram is a unique type of quadrilateral with specific characteristics.

A quadrangle or check is defined as the intersection of pairs of diagonals of a parallelogram. In other words, it is the area inside the parallelogram that is divided into four triangles, each of which shares a common vertex in the center of the parallelogram.

The diagonals of a parallelogram are the line segments that connect the opposite vertices of a parallelogram. When these diagonals intersect, they form four triangles, which are also known as the parallelogram's "sub-triangles." The point where the diagonals intersect is called the center of the parallelogram, and it divides each diagonal into two equal parts.

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Answer:

358 and remainder of 3

Step-by-step explanation:

1. Divide it like any other problem

Hope this helps

By using permutation it can be inferred that

Total number of ways she can arrange the 4 pieces in the program = 24

What is permutation?

The mathematical technique that is used to determine the number of arrangements in a set when the order of arrangement is taken into account is called permutation

This is a concept of  permutation

A pianist plans to play 4 pieces at a recital.

The first position can be filled in 4 ways,

The second position can be filled in 3 ways

The third position can be filled in 2 ways

The fourth position can be filled in 1 day

Total number of ways she can arrange the 4 pieces in the program =

                                                                                          \(4 \times 3 \times 2 \times 1\)

                                                                                         = 24

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The value of x from the given diagram is -10

Two triangles are known to be similar if the ratio of their similar sides is equal. The diagram shown is similar to the required diagram.

Given the following parameters

<ABC = 2x

<BAC = 3x + 10

Equate the expression since both angles are equal. Substitute;

2x = 3x + 10

Subtract 3x from both sides

2x-3x = 3x-3x+10

-x = 10

x = -10

Hence the value of x from the given diagram is -10

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Answer:

r = 2

Step-by-step explanation:

4(3r + 4) - 6(r + 1) =22

12r + 16 - 6r - 6 = 22

6r = 12

r = 2

Answer:

the picture isnt showing up on mines

Answer:

(a) Because the confidence interval does not include includes 0​, it appears that there is not a significant difference between the mean level of hemoglobin in women and the mean level of hemoglobin in men.

(b) The correct option is (A).

(c) The correct option is (C).

Step-by-step explanation:

The 95% confidence interval for the difference between the two population​ mean hemoglobin level is:

CI = (-1.76 < μ₁ - μ₂ < -1.62)

(a)

The hypothesis to test the equality of the mean hemoglobin level in women and the mean hemoglobin level in​ men is:

H₀: The two population means are equal, i.e. μ₁ = μ₂.

Hₐ: The two population means are not equal, i.e. μ₁ ≠ μ₂.

The (1 - α)% confidence interval can be used to draw conclusion about the hypothesis test.

Decision rule:

If the (1 - α)% confidence interval does not consist of the null value then the null hypothesis will be rejected and vice-versa.

The 95% confidence interval for the difference between the two population​ means is:

CI = (-1.76, -1.62)

The 95% confidence interval does not consist of the null value, i.e. 0.

Thus, the null hypothesis will be rejected.

"Because the confidence interval does not include includes 0​, it appears that there is not a significant difference between the mean level of hemoglobin in women and the mean level of hemoglobin in men."

(b)

The (1 - α)% confidence interval for population parameter implies that there is a (1 - α) probability that the true value of the parameter is included in the interval.

Or, the (1 - α)% confidence interval for the parameter implies that there is (1 - α)% confidence or certainty that the true parameter value is contained in the interval.

So, the 95% confidence interval (-1.76, -1.62) implies that there is a 95% confidence that the above interval actually contains the value of the difference between the two population means, (μ₁ - μ₂).

The correct option is (A).

(c)

Now it is provided that the measures from men is denoted as population  1 and measures from women is denoted as population  2.

The confidence interval for the difference between two mean is:

\(CI=(\bar x_{1}-\bar x_{2})\pm MOE\)

According to the information:

\(\bar x_{1}=\bar x_{2}\\\\\bar x_{2}=\bar x_{1}\)

So, the new confidence interval will be:

\(CI=-(\bar x_{2}-\bar x_{1})\pm MOE\)

Then the confidence interval with measures from men being population

1 and measures from women being population  2 is:

\(CI=(1.62<\mu_{1}-\mu_{2}<1.76)\)

The correct option is (C).

The best description of the probability of drawing a king from the deck is 1 out of 13, or 1/13.

The probability of drawing a king from a standard deck of 52 playing cards can be determined by dividing the number of favorable outcomes (number of kings) by the total number of possible outcomes (total number of cards in the deck).

In a standard deck, there are 4 kings (one king for each suit: hearts, diamonds, clubs, and spades). Therefore, the number of favorable outcomes is 4.

The total number of possible outcomes is 52 (the total number of cards in the deck).

So, the probability of drawing a king is:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 4 / 52

Simplifying the fraction gives us:

Probability = 1 / 13

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Answer:

A

Step-by-step explanation:

The distance from the origin is determined by the position of the object, which cannot be determined from the graph of velocity.

The graph shows the velocity of an object as a function of time. When the velocity is positive, the object is moving to the right, and when the velocity is negative, the object is moving to the left. The velocity is decreasing because the slope of the graph is negative, but it is not necessarily moving towards the origin.

The distance from the origin is determined by the position of the object, which cannot be determined from the graph of velocity.The object is moving towards the origin means the displacement from the origin is decreasing.

As time passes by, the object is moving towards the origin at a decreasing velocity. As the velocity is decreasing, the slope of the line decreases, and eventually the velocity becomes zero when the object reaches the origin.

The graph is showing the velocity of an object as a function of time. When the velocity is positive, the object is moving to the right, and when the velocity is negative, the object is moving to the left. The velocity is decreasing because the slope of the graph is negative, but it is not necessarily moving towards the origin.

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Answer:

B

Step-by-step explanation:

Apply the Pythagorean Theorem to determine whether or not the given triplets represent right triangles or not:

I. 5 feet and 13 feet:  5^2 + 12^2 = 13^2 is TRUE

II.  9 ft and √63 ft:  9^2, 63, 12^2:  63 + 81 do add up to 144  TRUE

III.  2, 10, 12^2:  2 + 10 do NOT add up to 144.  FALSE

Answer B is correct

After considering the given data we conclude that the example for the given function are a) \(f(x) = x/(x+2)\), b) \(f(x) = sin^2(\pi x/2)\), c) \(f(x) = x/(x+1).\)

Now let us proceed to solving the sub questions
a. An example of a continuous function defined on (0,1) with range (0,1) is \(f(x) = x/(x+2)\). This function is continuous on(0,1)  and its range is (0,1).
b. An example of a continuous function defined on (0,1) with range is \(f(x) = sin^2(\pi x/2)\). This function is continuous on (0,1) and its range is (0, 1)
c. An example of a continuous function defined on (0,1] with range (0,1) is \(f(x) = x/(x+1)\). This function is continuous on (0,1] and its range is (0,1).
We have to keep in mind  that it is possible to prove the existence of such functions using the Intermediate Value Theorem, which projects that if a function is continuous on a closed interval [a,b], therefore it takes on every value between f(a) and f(b) at least once. But, the theorem does not provide a way to construct such functions explicitly.
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The simplified value of the expression √900 + √0.09 + √0.000009 is 30.303.

To simplify the given expression, let's evaluate the square roots individually and then perform the addition.

√900 = 30, since the square root of 900 is 30.

√0.09 = 0.3, as the square root of 0.09 is 0.3.

√0.000009 = 0.003, since the square root of 0.000009 is 0.003.

Now, we can add these simplified values together

√900 + √0.09 + √0.000009 = 30 + 0.3 + 0.003 = 30.303

Therefore, the simplified value of the expression √900 + √0.09 + √0.000009 is 30.303.

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Answer:

a cycle is a sequence of non-repeated vertices and the degree of a graph is the number of neighbors the vertex has.

Answer:

x = 60  (Answer C)

Step-by-step explanation:

Ambiguous.  I will assume that you meant:

x+4-7=1  =>  √(x + 4) - 7 = 1

This latter result simplifies to

√(x + 4) = 8

Squaring both sides, we get:  x + 4 = 64, or x = 60  (Answer C)

The value of x is 4.

Option A is the correct answer.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

√(x + 4 - 7) = 1

Square on both sides.

x + 4 - 7 = 1²

x + 4 - 7 = 1

Add 7 on both sides.

x + 4 = 1 + 7

x = 8

Subtract 4 on both sides.

x + 4 - 4 = 8 - 4

x = 4

Thus,

The value of x is 4.

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Answer:

14√2

Step-by-step explanation:

28/√2

Since you can't have a square root as the denominator of a fraction, we must multiply the denominator and the numerator to get rid of the square root.

Hence,

28 x √2 , √2 x √2

Your problem would now be:

28√2 / 2

Reduce the fraction by canceling out the common factor of 2

ANS = 14√2

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1. Yes, the relation ((0,0), (1,1), (2,4), (3,9)) is a function. A function is a relation in which each input (x-value) is associated with only one output (y-value). In this case, for every x-value, there is a unique y-value. For example, when x is 0, y is 0; when x is 1, y is 1; when x is 2, y is 4; and when x is 3, y is 9.

Therefore, there is a clear and consistent mapping between the x-values and the y-values, satisfying the criteria for a function.
2. No, the graph of a circle cannot be considered a function. A function requires that each input (x-value) is associated with only one output (y-value). However, in the graph of a circle, for some x-values, there are multiple y-values or no y-value at all. This violates the definition of a function. For example, consider the equation of a circle: x^2 + y^2 = r^2. If we solve for y, we get two possible y-values for each x-value (except for the points where the circle intersects the x-axis). Therefore, the graph of a circle is not a function.
3. A real-world example of a relation that is not a function is a person's age and their height. While a person's age can be mapped to a single value, their height can vary. For example, a person who is 10 years old can have a height of 4 feet, but another person who is also 10 years old can have a height of 5 feet. This demonstrates that for a given age, there can be multiple possible heights, making it a relation that is not a function.

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The value of logm 4/m is 1.139 - 2 logm m. This means that we can express logm 4/m in terms of other logarithmic values without finding the exact value of m.

Given that logm 3 = 0.903, logm 4 = 1.139, and logm 7 = 1.599. We are to find logm 4/m.

Using the properties of logarithm, we have,

logm 4/m = logm 4 - logm m

               =1.139 - logm m               .....................................(1)

Again, using the properties of logarithm, we know that:

logm 4 = logm (2 × 2)  

        = logm 2 + logm 2

         = 1.139 = 2logm 2                    ..................................(2)

Substituting equation (2) into (1) gives:

logm 4/m = 2logm 2 - logm

           m = 2logm (2/m)          ..................................................(3)

Using the property of logarithm once again, we know that:

loga b = logc b / logc a                     ............................................(4)

Substituting equation (4) into equation (3), we have:

logm 4/m = 2 logm 2 - logm

m= logm [(2/m)² / m]                       .............................................(5)

Now, we are to find logm 4/m by substituting the given values.

Using equation (2), we have:

logm 2 = (1.139)/2

     = 0.5695

Using equation (5), we get:

logm 4/m = logm [(2/m)² / m]

logm 4/m = logm [4/m²m]

 logm 4/m = logm 4 - logm

logm 4/m = 1.139 - 2 logm m

Therefore, by using the properties of logarithm, we have found that logm 4/m = 1.139 - 2 logm m. This means that we can express logm 4/m in terms of other logarithmic values without finding the exact value of m.

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The length of the rectangle is 7 cm and the width is 5 cm.

The whole distance covered by the rectangle's borders or its sides is known as its perimeter. As we know the rectangle will have 4 sides then the perimeter of the rectangle will be equal to the total of its four sides. And the unit will be in meters, centimeters, inches, feet, etc.        

The formula for the Perimeter of the rectangle is given by

Here we have

The length of a rectangle is 2cm greater than the width of the rectangle

And perimeter of the rectangle = 24 cm

Let x be the width of the rectangle

From the given data,

Length of the rectangle = (x + 2) cm  

As we know Perimeter of rectangle = 2(Length+width)

=> Perimeter of rectangle = 2(x+2 + x) = 2(2x +2)

From the given data,

Perimeter of rectangle =  24cm

=> 2(2x +2) = 24 cm

=> (2x +2) = 12     [ Divided by 2 into both sides ]

=>  2x = 12 - 2

=>  2x = 10

=>   x = 5         [ divided by 2 into both sides ]  

Length of rectangle, (x+2) = 5 + 2 = 7 cm

Therefore,

The length of the rectangle is 7 cm and the width is 5 cm.

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Answer:

9 x + 8 y = 10   (I)

y = -4x + 7        (II)

One way is to rewrite the second as

4x + y = 7

Now multiply this equation by 8

32 x + 8 y = 56

9 x + 8 y = 10        and now subtract the equations

23 x = 46     this gives x as 2

From equation (II)  y = -4 (2) + 7  = -1

So our values are (2, -1)

Check:

(I) 9 x + 8 y = 10         9 * 2 - 8 = 10

(II)  4 x + y = 7       or 4 * 2 - 1 = 7

Or you can substitute equation (II) directly into equation (I)

Answer:

When it increases slowly with time