Please help me with the following question.

The total number of outcomes that are possible are given as follows:

48 outcomes.

The number of outcomes for each case is obtained using the Fundamental Counting Theorem, with the multiplication of the number of outcomes for each trial.

The number of outcomes in each step is given as follows:

Hence the total number of outcomes that are possible are obtained as follows:

N = 6 x 8

N = 48.

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Answer:

300

Step-by-step explanation:

do 20 times 15 and you get 300 length times width = area

Answer:

300

Step-by-step explanation:

First of all, a square's side lengths must be the same for it to be correctly labeled as a square.

The quadrilateral we need to find the area for here is a rectangle.

The area of a rectangle is defined as length × width. So, to answer this question, all we need to do is multiply the given dimensions.

20 × 15

= (2 + 10) × 15

= (2 × 15) + (10 × 15)

= 30 + 150

= 300

Answer:

99.08

Step-by-step explanation:

169.95*(1-45%)*(1+6%) = 99.08

Answer:

400.33

Step-by-step explanation:

haul price= 377.67

tax=22.66

377.67+22.66=400.33

The measure of AC is 12 units.

The measure of AC' is 6 units

The measure of C'B' is 10.5 units.

The midsegment of a triangle is a line connecting the midpoints between two sides of a triangle. Therefore, the segment is parallel to the third side and half of it.

Therefore, applying mid segment principle,

C'B' = 1 / 2 (21)

C'B' = 21 / 2

C'B' = 10.5 units

Hence, using mid segment principle

AC' = CC' = 6

Therefore,

AC = 6 + 6 = 12 units

using mid segment principle,

AC' = 6 units

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If during her first week of work, a physical therapist estimated that therapy sessions would last about 30 minutes each. The time the physical therapist expect to spend at a therapy session is: about 45 minutes.

In order to find the expected duration of a therapy session, you can calculate the mean (average) of the durations for the five sessions.

The mean is calculated by adding the durations of all the sessions and then dividing by the number of sessions.

Mean = (47+53+32+50+45) / 5

Mean = 227/5

Mean = 45 minutes

Therefore the physical therapist should expect to spend about 45 minutes on average for each therapy session.

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Answer:

Answer:

It is a well-known fact that for any natural number k, there are no non-zero integers x, y, and z that satisfy x^3 + y^3 + z^3 = k, unless k = 1 or k = 8. This is known as Fermat's Last Theorem.

However, for k = 1, we have the solution (x, y, z) = (1, 0, 0) and for k = 8, we have the solution (x, y, z) = (2, −1, 1)

It's important to note that this problem is a complex mathematical problem, which was solved only by Andrew Wiles in 1994 using advanced mathematical theories such as Iwasawa theory and Galois representations.

The value of vector (2u + v) is -5i +8k +5j and the value of u.v is -7.

Geometrical objects with magnitude and direction are called vectors. A line with an arrow pointing in its direction can be used to represent a vector, and the length of the line corresponds to the vector's magnitude.

As a result, vectors are depicted as arrows and have starting and ending points.

The value of the vector (2u + v) is calculated as:-

E = (2u + v)

E = 2 ( -i + 5k) +( -3i + 5j -2k)

E = -2i +10k -3i +5j -2k

E = -5i + 5j + 8k

The value of u.v will be:-

u.v = ( -i +oj + 5k).(-3i +5j -2k)

u.v = 3 - 10

u.v = -7

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Answer:

$10.22

Step-by-step explanation:

The total amount Kendra needs for the bead is $2.87 more than the amount she currently has in her purse, which is $7.35. Therefore, x = $7.35 + $2.87 = $10.22.

The inequality that represents this situation is:

x ≥ $7.35 + $2.87

x ≥ $10.22

Another way to represent this would be:

x - $7.35 ≥ $2.87

x ≥ $10.22

Both of these inequalities represent the same thing, that x (the total amount Kendra needs for the bead) must be greater than or equal to $10.22.

Using the permitted $110 for travel, the businessperson can cover 291 miles.

We need to deduct the daily rate of $37.33 from the permitted money, then divide the sum by the per-mile rate of 25 cents to get how many miles a businessperson can travel with $110.

$110 - $37.33 = $72.67

$72.67 ÷ $0.25 = 291 miles

It's crucial to remember that, regardless of how many kilometres the businessperson drives, the daily charge includes a fixed sum for the rental automobile. Each mile driven results in an additional fee known as the per-mile tariff. We may calculate the maximum number of miles the business person can travel without incurring additional costs by subtracting the daily rate from the permitted amount and dividing by the per-mile rate.

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The number of miles that the business person can travel  on the $110 is; 290.68 miles

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

The daily rate of $37.33 can be said to be the  y-intercept.

While 25 cents or $0.25 can be said to be the slope.

Thus, the equation of the line formed is;

y = 0.25x + 37.33

At a cost of $110, the number of miles is;

110 = 0.25x + 37.33

0.25x = 110 - 37.33

0.25x = 72.67

x = 72.67/0.25

x = 290.68 miles

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Answer: 4

Step-by-step explanation:

the measure of the angle x is c)30°

Answer:

30 degrees

Step-by-step explanation:

In the bottom triangle,

Both angles are 75 degrees, so their sum is 75 + 75 = 150 degrees
The remaining angle is 180 - (sum of the two other angles)
= 180 - ( 75 + 75)
= 30 degrees

As this angle is a the vertically opposite angle to x, it will be equal to x
∴ x = 30 degrees

The formula is: f(x) = 2 * sin(x * 5 / 2π) + 5

A = 5 - 3 = 2, the amplitude of the function.

Since (0,3) is the minimum, the midline is at y = 3 + 2 = 5, the average value of the maximum and minimum.

Let "c" be the shift, so the equation of the midline is y = 5 + c.

At x = 5, the function intersects its midline, so 5 = 5 + c.

Therefore, c = 0.

The period of the function is 2π / b, where b is the number of radians for one complete cycle.

Since the function intersects its midline at (5,5), b = 5.

Therefore, the period of the function is 2π / 5.

The formula of the sinusoidal function is:

f(x) = A * sin(b * (x - c)) + d,

where d = 5, the equation of the midline.

Therefore, the formula is:

f(x) = 2 * sin(x * 5 / 2π) + 5

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At the beginning of 2072 B.S., the population of the town was X.

Assuming the population growth rate is 10%, the population at the end of 2074 B.S. will be (X + 10% of X) + (X + 10% of X + 10% of X) = 1.1X + 1.1(1.1X) = 2.21X.

Therefore, the population of the town at the end of 2074 B.S. will be 2.21X. This is based on a linear population growth rate of 10% over two years. It is possible that the growth rate may not be constant, so the actual population may be slightly different.

In order to get a better estimate of the population at the end of 2074 B.S., it is important to consider other factors such as birth and death rates, migration, and economic and social factors.

For example, if the town is experiencing an influx of migrants, then the population growth rate may be higher than the estimated 10%. On the other hand, if the town faces an economic recession or job losses, then the population growth rate may be lower than the estimated 10%.

Overall, the population of the town at the end of 2074 B.S. is estimated to be 2.21X, based on a linear population growth rate of 10% over two years. However, this estimate may be slightly different depending on the other factors mentioned above.

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Answer:

The expression simplifies to:

[tex](\frac{3p^2 + 49}{42p})^2 -(\frac{3p^2 - 49}{42p})^2[/tex]

Using the difference of squares identity, the expression further simplifies to:

[tex]\frac{98p}{42p^2} = \frac{98}{42p}[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation: it just graph of y=-x

y+x=

4x+4y4y=

Answer:

Step-by-step explanation:

the error, based on the question, the eqution has 4 solution for the X

listed as (4, -4, -3, 1)

as X solution in verticial , put all the X value into the F(x) to find the Y valuein horizontal value

The Cadbury Report is a document that was produced by "The Committee on the Financial Aspects of Corporate Governance

The Cadbury Report, also known as Financial Aspects of Corporate Governance, is a document that was produced by "The Committee on the Financial Aspects of Corporate Governance," which was led by Sir Adrian Cadbury, the chairman of Cadbury.

It contains recommendations on how company boards and accounting systems should be set up to reduce the risks and failures associated with poor corporate governance. The Cadbury committee was established by the London Stock Exchange in 1991, and a draft of the report was released in May 1992. In December of that same year, it was released in its altered and complete form.

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3) The components of composition between two functions are [tex]f(n) = n^{2}+ 5^{n}[/tex] and g(n) = n² + 1.

4) The composition between functions g(n) = √(4 + n + √n) and h(n) = n⁴ + 8 is the function (g ° h)(n) = √[4 + n⁴ + 8 + √(n⁴ + 8)].

In this problem we find two cases of composition between functions, that is, a operation between two functions, so that the input of the first function (f(x)) is substituted by the entire second function (g(x)), that is:

f ° g(x) = f [g(x)]

Case 3 - If we know that [tex](f\,\circ \,g) (n) = (n^{2}+1)^{2}+5^{n^{2}+1}[/tex], then the components of the composition of functions are:

[tex]f(n) = n^{2}+ 5^{n}[/tex]

g(n) = n² + 1

Case 4 - If we know that g(n) = √(4 + n + √n) and h(n) = n⁴ + 8, then the composition between the two functions is:

(g ° h)(n) = √[4 + n⁴ + 8 + √(n⁴ + 8)]

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Answer: The acceleration of the stuntman is given by the second derivative of the height function, which is:

h''(t) = d²h/dt² = (-2 * 2 * t * 1000 + 1000 * -2) = -4000t + 1000

So, the acceleration is -4000t + 1000 ft/sec².

Step-by-step explanation:

(a) Verifying that y(x) = (x - c)^2 satisfies the differential equation y' = 2y:

To verify that the function y(x) = (x - c)^2 satisfies the differential equation y' = 2y, we can find the derivative y' and substitute it back into the equation:

y' = d/dx [(x - c)^2] = 2(x - c)

So, y' = 2y if and only if 2(x - c) = 2y, which can be simplified to x - c = y.

Therefore, y(x) = (x - c)^2 satisfies the differential equation y' = 2y for all x, including x = c.

(b) Values of b for which the initial value problem y' = 2/y, y(0) = b has no solution or a unique solution:

(i) No solution: If b = 0, the initial value y(0) = 0 and the denominator of the right-hand side of the differential equation y' = 2/y would be 0, making the equation undefined at that point. Therefore, the initial value problem y' = 2/y, y(0) = 0 has no solution.

(ii) Unique solution defined for all x: For all other values of b (b ≠ 0), the initial value problem y' = 2/y, y(0) = b has a unique solution that can be found using standard methods of solving initial value problems. This solution will be defined for all x.

The figure illustrating the fact that the initial value problem y' = 2/7, y(0) = 0 has infinitely many different solutions would show a family of curves that are all solutions to the differential equation y' = 2/7, with different starting values y(0) leading to different curves. This demonstrates that there are infinitely many different solutions to the initial value problem.

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Nominal categorical data is a categorical variable with two or more values, with no order. The examples of nominal categorical data here are the issue type, country, city.

Categorical data can be divided as two as per the variables. They are nominal and ordinal. In nominal categorical data, there will be two or more data points, but they are not ranked. The hair color can be red/blond/brown/black etc. But these cannot be ranked by taking one over the other.

In ordinal categorical data, there we can assign an order on the data points. Like grading system in marks of students, size comparison like large, medium, small. Here we could rank these in order.

Year can sometimes be nominal and sometimes ordinal. It is as per the context. If we are using it to calculate time it is ordinal.

So here we could not rank of variables in country, issue type, city. So all are nominal categorical data.

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For given arithmetic operations, matching is as:

Addition              - Subtraction

Multiplication      - Division

Square                - Square root

Cube                    - Cube root

Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.

These basic mathematical operations (+, -, ×, and ÷) we use in our everyday life. Whether we need to calculate the annual budget or distribute something equally to a number of people, for every such aspect of our life, we use arithmetic operations.

The four basic arithmetic operations in Maths, for all real numbers, are:

Addition (Finding the Sum; ‘+’)

Subtraction (Finding the difference;  ‘-’)

Multiplication (Finding the product; ‘×’ )

Division (Finding the quotient; ‘÷’)

As, inverse operations inverses the actual value

Addition                      - Subtraction

Multiplication              - Division

Square                        - Square root

Cube                           - Cube root

hence, they will be matched accordingly.

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Reversed Alternate Interior Angles.The theorem states that j || k.J and K converse different internal angles.

j and k angles.The Converse of Corresponding Angles Postulate leads to the expression j || k.

2Angles 2 and 5 make up the alternating inner angles of the lines j and k.Angle 2 equals Angle 5 if

Reversed Alternate Interior Angles.The theorem states that j || k.

J and K converse different internal angles.

3. Angle 3 also equals Angle 10.

The exterior angles of the lines l and m are, respectively, Angle 3 and

Angle 10.

The Converse of Alternate Exterior Angles Theorem states that angle 3 equals angle 10, so l || m.

Reversed Alternate Interior Angles.The theorem states that j || k.J and K converse different internal angles.

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According to the problem the volume of the solid generated by revolving the region is .

The amount of space a thing occupies is its volume, which is expressed in cubic units. It is a three-dimensional measure of an object's size, as opposed to its length and width, which are considered two-dimensional measures. Volume is commonly used to measure the capacity of containers, such as barrels, tanks, and boxes.

This is a solid of revolution generated by revolving the region bounded by the curves y=[tex]e^{(x-9)}[/tex] and y=0 and the lines x=9 and x=10 about the x-axis. To find the volume of this solid, we can use the method of washers.

The formula for the volume of a solid of revolution generated by revolving a region bounded by two curves about the x-axis is given by:

V = π∫[tex]b a [((f(x))^{2} - (g(x))^{2}] dx[/tex]

In this problem, f(x) = [tex]e^{(x-9)}[/tex] and g(x) = 0. Thus,

V = π∫10 9 [tex]e^{(2x-18)} dx[/tex]

Integrating, we get

V = π [tex][\frac{e^{(2x-18)}}{2}] 10^{9}[/tex]

V = π(157.087 - 1.1102)/2

V = 78.488π [tex]cm^{3}[/tex] equal to the integral of the area of the region over the interval [9, 10] with respect to x.

The area of the region is equal to the integral of y from 9 to 10. Thus, the volume of the solid generated by revolving the region is equal to the double integral:

V = ∫[tex]9^{10}[/tex] ∫[tex]0^{e^{(x-9)} } dy dx[/tex]

Evaluating the integral yields:

V =∫ [tex]9^{10} e^{(x-9)} dx[/tex]

[tex]= \frac{e^{(x-9)} }{9^{10} }\\ =e^{1} -1\\ =2.718-1 =1.718[/tex]

Therefore, the volume of the solid generated by revolving the region is 1.718.

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Answer:

$2.88

Step-by-step explanation:

formula → 3.6 × (1 - 20%)

→ 3.6 × (1 - 0.2)

calculate sum or difference

→ 3.6 × 0.8

→ = 2.88

Using their concepts, we have that the mean will be increased and the median will remain constant.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile, which is the middle value of the distribution.

The largest value is the 7th observation, therefore it will be included in the calculation of the mean.

Since this observation have an increased value, the sum of all observations will be increased while the number of observations remains constant,

So the mean will be increased.

Hence, for a distribution of 7 observations, we have that:

The first three observations are the first half.

The 4th observation is the median.

The last three observations are the second half.

Here only the last observation changes, not the fourth, hence the median remains constant.

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Therefore , the solution of the given problem of inequality graph comes out to be  the graph of the inequality 2x - y ≤ -3 is a line that cuts through the x-y plane

An inequality graph is a graph that represents the solution set of an inequality, showing the values of the independent variable (usually represented on the x-axis) for which the inequality is true.

Here,

An inequality can be represented graphically by shading the region on a coordinate plane that satisfies the inequality. The direction of shading (above or below the line) depends on the inequality symbol.

The graph of the inequality 2x - y ≤ -3 in the x-y plane can be plotted by finding the boundary line for the inequality and shading the region that satisfies the inequality. To do this, we can start by setting the equation 2x - y = -3 and finding the x- and y-coordinates of the points on the line. Then we can plot these points and draw the line that connects them.

Next, we will determine which side of the line represents the solution set. To do this, we can pick a point that is not on the line and substitute its x- and y-coordinates into the inequality. If the inequality is true for the point, we shade the region that contains the point. If the inequality is false, we shade the region that does not contain the point.

So the graph of the inequality 2x - y ≤ -3 is a line that cuts through the x-y plane and is shaded on one side. The shaded region represents all the x- and y-coordinates that satisfy the inequality.

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