5 In a Survery of 130 people 80 claimed to be CDO partisans and 60 claimed to be Anc partisan. If 30 of them are both ANC and CDO how many people are none of these two parties​

a. There are 15,600 ways to select a president, a vice president, and a secretary from a class of 26 members.

b. There are 14,950 ways to form a 4-person committee from a class of 26 members.

a. To select a president, a vice president, and a secretary from a class of 26 members, we can use the concept of permutations.

For the president position, we have 26 choices. After selecting the president, we have 25 choices remaining for the vice president position. Finally, for the secretary position, we have 24 choices left.

The total number of ways to select a president, a vice president, and a secretary is obtained by multiplying the number of choices for each position:

Number of ways = 26 * 25 * 24 = 15,600

Therefore, there are 15,600 ways to select a president, a vice president, and a secretary from a class of 26 members.

b. To form a 4-person committee from a class of 26 members, we can use the concept of combinations.

The number of ways to choose a committee of 4 people can be calculated using the formula for combinations:

Number of ways = C(n, r) = n! / (r!(n-r)!)

where n is the total number of members (26 in this case) and r is the number of people in the committee (4 in this case).

Plugging in the values, we have:

Number of ways = C(26, 4) = 26! / (4!(26-4)!)

Calculating this expression, we get:

Number of ways = 26! / (4! * 22!)

Using factorials, we simplify further:

Number of ways = (26 * 25 * 24 * 23) / (4 * 3 * 2 * 1) = 14,950

Therefore, there are 14,950 ways to form a 4-person committee from a class of 26 members.

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The Peterson family used their sprinkler for 30 hours, while the Stewart family used theirs for 15 hours.

Let's assume that the Peterson family used their sprinkler for a certain number of hours, which we'll denote as x, and the Stewart family used their sprinkler for the remaining hours, which would be 45 - x.

The water output rate for the Peterson family's sprinkler is given as 35 L per hour. Therefore, the total water output for the Peterson family can be calculated by multiplying the water output rate (35 L/h) by the number of hours they used the sprinkler (x): 35x.

Similarly, for the Stewart family, with a water output rate of 40 L per hour, the total water output for their sprinkler is given by 40(45 - x).

According to the problem, the combined total water output for both families is 1,650 L. Therefore, we can write the equation:

35x + 40(45 - x) = 1,650.

Simplifying the equation, we get:

35x + 1,800 - 40x = 1,650,

-5x = 1,650 - 1,800,

-5x = -150.

Dividing both sides of the equation by -5, we find:

x = -150 / -5 = 30.

So, the Peterson family used their sprinkler for 30 hours, and the Stewart family used theirs for 45 - 30 = 15 hours.

Therefore, the Peterson family used their sprinkler for 30 hours, while the Stewart family used theirs for 15 hours.

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Answer:

First, the graph is overall decreasing with two local maximums and two local minimums.

Second, it has 5 zeros, since there is one intersection and two touching points with the x-axis.

Considering the above observations we can state that:

I agree with both Priya's and Han's equations.

To determine if either Priya or Han equation is correct, we can substitute the coordinates of the given point (1,2) into each equation and check if the equation holds true.

For Priya's equation, y - 2 = (1/3)(x - 1), substituting x = 1 and y = 2:

2 - 2 = (1/3)(1 - 1)

0 = 0

The equation holds true, so Priya's equation is correct.

For Han's equation, 3y - x = 5, substituting x = 1 and y = 2:

3(2) - 1 = 5

6 - 1 = 5

5 = 5

The equation also holds true, so Han's equation is correct.

Both Priya's and Han's equations are valid equations of the line with a slope of 1/3 passing through the point (1,2). The equations have different forms, but they are algebraically equivalent and represent the same line. Therefore, I agree with both Priya's and Han's equations.

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Answer:

12

Step-by-step explanation:

[tex]\frac{3}{4}[/tex](x - 3) - [tex]\frac{1}{2}[/tex] = [tex]\frac{2}{3}[/tex]

We are looking at the denominators of 4, 2 and 3.  We are looking for the least common multiple.  If we listed out the multiples of the 3 numbers, we are looking for the lowest number that is in all three lists.

4,8,12

2,4,6,8,10,12

3,6,9,12

the lowest number that we see on all three lists is 12.

(a) Using Newton's method, the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex] correct to six decimal places, are approximately -1.084, -0.581, -0.214, 0.580, and 1.279.

(b) The absolute minimum value of f is undefined since the function is a polynomial of even degree, and it approaches positive infinity as x approaches positive or negative infinity.

(a) To find the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex]  we can use Newton's method by finding the derivative of the function and solving for the values of x where the derivative is equal to zero.

First, let's find the derivative of f(x):

f[tex]'(x) = 6x^5 - 4x^3 + 12x^2 - 2[/tex]

Now, let's apply Newton's method to find the critical numbers. We start with an initial guess, x_0, and use the formula:

[tex]x_{(n+1)} = x_n - (f(x_n) / f'(x_n))[/tex]

Iterating this process, we can approximate the values of x where f'(x) = 0.

Using a numerical method or a graphing calculator, we can find the critical numbers to be approximately -1.084, -0.581, -0.214, 0.580, and 1.279.

Therefore, the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex] correct to six decimal places, are approximately -1.084, -0.581, -0.214, 0.580, and 1.279,

(b) To find the absolute minimum value of f(x), we need to analyze the behavior of the function at the critical numbers and the endpoints of the interval.

Since the function f(x) is a polynomial of even degree, it approaches positive infinity as x approaches positive or negative infinity.

Therefore, there is no absolute minimum value for the function.

Hence, the absolute minimum value of f is undefined.

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Answer:

Percent error is calculated using the formula:

   Percent Error = ( |Predicted Value - Actual Value| / Actual Value ) * 100%

Plugging in Brianna's prediction and the actual number of puppies sold:

   Percent Error = ( |16 - 9| / 9 ) * 100%

The absolute value of (16 - 9) is 7, so the calculation becomes:

   Percent Error = ( 7 / 9 ) * 100%

This is approximately 77.78%, which is Brianna's percent error in her prediction.

Part 1- The lower class boundary for the first class is 100.

Part 2- Approximately 75% of students take exactly two courses.

Part 1:

To find the lower class boundary for the first class, we need to consider the given class intervals. The lower class boundary is the smallest value within each class interval.

Given the class intervals:

100 - 104

105 - 109

110 - 114

115 - 119

120 - 124

125 - 129

130 - 134

The lower class boundary for the first class interval (100 - 104) would be 100.

So, the lower class boundary for the first class is 100.

Part 2:

To determine the percentage of students who take exactly two courses, we need to calculate the relative frequency for that particular category.

Given the data:

of Courses Frequency Relative Frequency Cumulative Frequency

1 23 0.4423 23

2 - 39

3 13 0.25 -

We can see that the cumulative frequency for the second class (2 courses) is 39. To find the relative frequency for this class, we need to divide the frequency by the total number of students surveyed, which is 52.

Relative Frequency = Frequency / Total Number of Students

Relative Frequency for 2 courses = 39 / 52 ≈ 0.75 (rounded to 4 decimal places)

To convert this to a percentage, we multiply the relative frequency by 100.

Percentage of students taking exactly two courses = 0.75 * 100 ≈ 75%

Therefore, approximately 75% of students take exactly two courses.

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Question

Part 1.

Data was collected for 300 fish from the North Atlantic. The length of the fish (in mm) is summarized in the GFDT below.

Lengths (mm) Frequency

100 - 104 1

105 - 109 16

110 - 114 71

115 - 119 108

120 - 124 83

125 - 129 18

130 - 134 3

What is the lower class boundary for the first class?

class boundary =

Part 2

In a student survey, fifty-two part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below:

Please round your answer to 4 decimal places for the Relative Frequency if possible.

# of Courses Frequency Relative Frequency Cumulative Frequency

1 23 0.4423 23

2   39

3 13 0.25

What percent of students take exactly two courses? %

The value of x in the diagram given in the question is 6

From the question given above, the following data were obtained:

The value of x can be obtained using cos ratio.

Cos θ = Adjacent / Hypotenuse

Cos 60 = 3 / x

Cross multiply

x × Cos 60 = 3

Divide both sides by Cos 60

x = 3 / Cos 60

= 3 / 0.5

= 6

Thus, the value of x is 6

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Answer:

Step-by-step explanation:

A rectangular tin measure 20cm by 10cm by 10cm. What's it's capacity in litres

20 * 10 * 10 = 2000cm^3

1000 cm^3 = 1 Litres

​2000 cm^3 = 2 Litres

Answer:

He needs to study for an additional 30 minutes - 12 minutes = 18 minutes before taking a break.

Step-by-step explanation:

To determine how many more minutes Mason needs to study before taking a break, we can calculate the remaining study time.

Mason plans to study for 1 and 1-half hours, which is equivalent to 90 minutes.

He will take a break once he has studied for 1-third of the planned time, which is 1/3 * 90 minutes = 30 minutes.

Mason has already studied for 12 minutes.

Therefore, he needs to study for an additional 30 minutes - 12 minutes = 18 minutes before taking a break.

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Answer:

when substituting x = -0.5, 0, and 1 into the equation, we get the results -8, -7, and -5, respectively.

Step-by-step explanation:

Part A:

To solve the equation 5 + x - 12 = 2x - 7, follow these steps:

Combine like terms on each side of the equation:

-7 + 5 + x - 12 = 2x - 7

-14 + x = 2x - 7

Simplify the equation by moving all terms containing x to one side:

x - 2x = -7 + 14

-x = 7

To isolate x, multiply both sides of the equation by -1:

(-1)(-x) = (-1)(7)

x = -7

Therefore, the solution to the equation is x = -7.

Part B:

Now let's substitute the given values of x and evaluate the equation:

For x = -0.5:

5 + (-0.5) - 12 = 2(-0.5) - 7

4.5 = -1 - 7

4.5 = -8

For x = 0:

5 + 0 - 12 = 2(0) - 7

-7 = -7

For x = 1:

5 + 1 - 12 = 2(1) - 7

-6 = -5

Answer:

PO = 12

Step-by-step explanation:

given a tangent and a secant from an external point to the circle then

the product of the measures of the secant's external part and the entire secant is equal to the square of the measure of the tangent , that is

OP × OQ = NO²

OP × 27 = 18² = 324 ( divide both sides by 27 )

OP = 12

The linear equation from the given table is expressed as:

y =  -1500x + 8350

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

y = mx + c

where:

m is slope

c is y-intercept

The formula for the equation of a line through two coordinates is:

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

We will take the two coordinates (1, 6850) and (2, 5350)

Thus:

(y - 6850)/(x - 1) = (5350 - 6850)/(2 - 1)

(y - 6850)/(x - 1) = -1500

y - 6850 = -1500x + 1500

y = -1500x + 1500 + 6850

y =  -1500x + 8350

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Answer:

x = 82

Step-by-step explanation:

x and 98 are same- side exterior angles. They are on the same side of the transversal and are outside the parallel lines.

same- side exterior angles sum to 180° , so

x + 98 = 180 ( subtract 98 from both sides )

x = 82

[tex]x[/tex] and [tex]98^{\circ}[/tex] are same side exterior angles which add up to [tex]180^{\circ}[/tex].

Therefore

[tex]x+98^{\circ}=180^{\circ}\\x=82^{\circ}[/tex]

i.  The position vector of X is 2b - a.

ii.  The position vector of Y is (3b + c)/4.

iii.  The ratio XY : Y Z is [tex]|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|[/tex]. Simplifying this expression will give us the final ratio.

i. To find the position vector x of point X, we can use the concept of vector addition. Since AB : BX = 2 : 1, we can express AB as a vector from A to B, which is given by (b - a). To find BX, we can use the fact that BX is twice as long as AB, so BX = 2 * (b - a). Adding this to the vector AB will give us the position vector of X: x = a + 2 * (b - a) = 2b - a.

ii. Similar to the previous part, we can express BC as a vector from B to C, which is given by (c - b). Since BY : YC = 1 : 3, we can find BY by dividing the vector BC into four equal parts and taking one part, so BY = (1/4) * (c - b). Adding this to the vector BY will give us the position vector of Y: y = b + (1/4) * (c - b) = (3b + c)/4.

iii. Z is the midpoint of AC, so we can find Z by taking the average of the vectors a and c: z = (a + c)/2. The ratio XY : YZ can be calculated by finding the lengths of the vectors XY and YZ and taking their ratio. Since XY = |x - y| and YZ = |y - z|, we have XY : YZ = |x - y|/|y - z|. Plugging in the values of x, y, and z we found earlier, we get XY : YZ =[tex]|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|[/tex].

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The triangles DEF and SRQ are not similar triangles

From the question, we have the following parameters that can be used in our computation:

The triangles in this figure are

DEF and SRQ

These triangles are not similar

This is because:

The corresponding angles in the triangles are not equal

For DEF, the angles are

50, 90 and 40

For SRQ, the angles are

51, 90 and 39

This means that they are not similar by any similarity statement

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The statement which is not true about the circle M is ∆ABM is isosceles.

The correct answer choice is option 2.

Based on the circle M;

diameter AC,

chords AB and BC,

radius MB

Isosceles triangle: This is a type of triangle which has two equal sides and angles.

Equilateral triangle is a triangle which has three equal sides and angles.

Hence, ∆ABM is equilateral triangle.

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Answer:

781250

Step-by-step explanation:

The sequence is has common ratio of 5 so the equation is 10*5^x-2 or 2*5^x so 2*5^8=781250

Answer:

ar⁷= 781,250

Step-by-step explanation:

a =10

ar =50

ar² = 250

8th term = ar⁷=?

r = ar/a

= 50/10

r =5

ar⁷ = 10 × 5 ⁷

=10 × 78125

= 781,250

There are 70 ways a person can order a two-course meal from the given restaurant.

To determine the number of ways a person can order a two-course meal from a restaurant that offers 10 appetizers and 7 main courses, we can use the concept of combinations.

First, we need to select one appetizer from the 10 available options.

This can be done in 10 different ways.

Next, we need to select one main course from the 7 available options. This can be done in 7 different ways.

Since the two courses are independent choices, we can multiply the number of options for each course to find the total number of combinations.

Therefore, the number of ways a person can order a two-course meal is 10 [tex]\times[/tex] 7 = 70.

So, there are 70 ways a person can order a two-course meal from the given restaurant.

It's important to note that this calculation assumes that a person can choose any combination of appetizer and main course.

If there are any restrictions or limitations on the choices, the number of combinations may vary.

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Answer:

Relative maximum at x=0; Relative minimum at x=8/3

Step-by-step explanation:

To find the relative maximums and the relative minimums, you must first find the first derivative of the function. The first derivative of this function is 6x^2-16x. Simply it and you get 2x(3x-8). X would be equal to 0 and 8/3. Next, make a number line where you put 0 and 8/3 have a value of zero.

        +                           -                                 +      

-------------------0----------------------------8/3-----------------------

Plug in a value of x<0 to get the region left of 0. Say we use -1, we get -2(-3-8), which is positive, meaning that it is increasing there. From 0 to 8/3, if we use 1, we get 2(3-8), which is decreasing. If we use 3, we get 6(9-8), which is increasing. From this, we can see that when x=0, the graph has a relative maximum. When x=8/3, the graph has a relative minimum.

Answer:

[tex]m = \frac{35 - 15}{4 - 0} = \frac{20}{4} = 5[/tex]

[tex]y = 5x + 15[/tex]

The functions y₁(t) = e^ãt cos(μt) and y₂(t) = e^ãt sin(μt) are a fundamental set of solutions because they are linearly independent and satisfy the given homogeneous linear differential equation, allowing for the formation of the general solution.

To show that y₁(t) = e^ãt cos(μt) and y₂(t) = e^ãt sin(μt) are a fundamental set of solutions, we need to demonstrate two things: linear independence and satisfaction of the given homogeneous linear differential equation.

First, let's consider linear independence. We can prove it by showing that there is no constant c₁ and c₂, not both zero, such that c₁y₁(t) + c₂y₂(t) = 0 for all t.

Now, let's verify that y₁(t) and y₂(t) satisfy the homogeneous linear differential equation. If the given differential equation is of the form ay''(t) + by'(t) + cy(t) = 0, we can substitute y₁(t) and y₂(t) into the equation and verify that it holds true.

Once we have established linear independence and satisfaction of the differential equation, we can state that the general solution to the homogeneous linear differential equation is given by y(t) = c₁y₁(t) + c₂y₂(t), where c₁ and c₂ are arbitrary constants. This general solution represents the linear combination of the fundamental set of solutions.

In summary, y₁(t) = e^ãt cos(μt) and y₂(t) = e^ãt sin(μt) form a fundamental set of solutions for the given differential equation, and the general solution is given by y(t) = c₁y₁(t) + c₂y₂(t).

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Answer:

x = - 5 , x = 2

Step-by-step explanation:

f(x) = x² + 3x - 10

to find the zeros let f(x) = 0 , that is

x² + 3x - 10 = 0

consider the factors of the constant term (- 10) which sum to give the coefficient of the x- term (+ 3)

the factors are + 5 and - 2 , since

5 × - 2 = - 10 and 5 - 2 = + 3 , then

(x + 5)(x - 2) = 0 ← in factored form

equate each factor to zero and solve for x

x + 5 = 0 ( subtract 5 from both sides )

x = - 5

x - 2 = 0 ( add 2 to both sides )

x = 2

the zeros are x = - 5 , x = 2

Answer:

The function given here is a quadratic function of the form f(t) = at^2 + bt + c, where a is -2, b is 8, and c is 300. The maximum value of a quadratic function occurs at its vertex. For a function in the form f(t) = at^2 + bt + c, the t-coordinate of the vertex is given by -b/(2a). We can use this to find the time at which the firework reaches its maximum height.

Given a = -2 and b = 8, we can calculate t = -b/(2a):

t = -8/(2*-2) = 2

We can then substitute this value back into the height equation to find the maximum height:

h(2) = -2(2)^2 + 8*2 + 300

h(2) = -8 + 16 + 300

h(2) = 308

So, the greatest height the fireworks reach is 308 feet.

Part A: The interest earned if the interest is compounded quarterly is $2,768.40.

Part B: The interest earned if the interest is compounded continuously is $2,695.92.

Part C: The difference in the amount of interest earned is approximately $72.48.

Part A: To calculate the interest earned when the interest is compounded quarterly, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^(^n^t^)[/tex]

Where:

A = the final account balance

P = the principal amount (initial investment)

r = the annual interest rate (4.75% or 0.0475 as a decimal)

n = the number of times the interest is compounded per year (4 times for quarterly)

t = the number of years (42 months divided by 12 to convert to years)

Plugging in the values:

A = $15,000(1 + 0.0475/4)^(4 * (42/12))

A = $15,000(1.011875)^(14)

A ≈ $15,000(1.18456005)

A ≈ $17,768.40

The interest earned is the difference between the final account balance and the principal amount:

Interest earned = $17,768.40 - $15,000

Interest earned ≈ $2,768.40

Part B: When the interest is compounded continuously, we can use the formula:

[tex]A = Pe^(^r^t^)[/tex]

Where:

A = the final account balance

P = the principal amount (initial investment)

e = the mathematical constant approximately equal to 2.71828

r = the annual interest rate (4.75% or 0.0475 as a decimal)

t = the number of years (42 months divided by 12 to convert to years)

Plugging in the values:

A = $15,000 * e^(0.0475 * 42/12)

A ≈ $15,000 * e^(0.165625)

A ≈ $15,000 * 1.179727849

A ≈ $17,695.92

The interest earned is the difference between the final account balance and the principal amount:

Interest earned = $17,695.92 - $15,000

Interest earned ≈ $2,695.92

Part C: Comparing the interest earned for each account, we find that the interest earned when the interest is compounded quarterly is approximately $2,768.40, while the interest earned when the interest is compounded continuously is approximately $2,695.92.

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The angular velocity of the object is 31.25 radians/second.

Angular velocity is defined as the change in angular displacement per unit of time. In this case, the object rotates a total of 25 radians in 0.8 seconds. Therefore, the angular velocity can be calculated by dividing the total angular displacement by the time taken.

Angular velocity (ω) = Total angular displacement / Time taken

Given that the object rotates 25 radians and the time taken is 0.8 seconds, we can substitute these values into the formula:

ω = 25 radians / 0.8 seconds

Simplifying the equation gives:

ω = 31.25 radians/second

So, the angular velocity of the object is 31.25 radians/second.

Angular velocity measures how fast an object is rotating and is typically expressed in radians per second. It represents the rate at which the object's angular position changes with respect to time.

In this case, the object completes a rotation of 25 radians in 0.8 seconds, resulting in an angular velocity of 31.25 radians per second. This means that the object rotates at a rate of 31.25 radians for every second of time.

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Note the translated question is:

An object that is rotated moves 25 radians in 0.8 seconds. what is the angular velocity of said object?

Third option is correct.The midpoint of WZ of WXYZ with the vertices W(0, 0), X(h, 0), Y(h,b), and Z(0, b) is (0, b/2).

To find the midpoint of segment WZ, we need to average the x-coordinates and the y-coordinates of the endpoints.

The coordinates of point W are (0, 0), and the coordinates of point Z are (0, b).

To find the x-coordinate of the midpoint, we average the x-coordinates of W and Z:

(x-coordinate of W + x-coordinate of Z) / 2 = (0 + 0) / 2 = 0 / 2 = 0

To find the y-coordinate of the midpoint, we average the y-coordinates of W and Z:

(y-coordinate of W + y-coordinate of Z) / 2 = (0 + b) / 2 = b / 2

Therefore, the midpoint of segment WZ is (0, b/2).

So, the correct answer is (0, b/2).

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Answer:

B. 7

Step-by-step explanation:

3/KL = 12/28

KL = 3/(12/28) = (28 x 3)/12 = 7