If M = {Prime integers between 1 and 11} and N = { factors of 12}. Find:
The members of M
The members of N
M∪N;
M∩N.

Please show working

The slope of the line passing through the given points is 0.4 or 2/5.

From the table given below, we have (2, 23) and (5, 24.3).

Use the slope formula to find the slope of a line given the coordinates of two points on the line. The slope formula is m=(y2-y1)/(x2-x1), or the change in the y-values over the change in the x-values.

Put the points (2, 23) and (5, 24.3) in the slope formula and find the slope.

That is, m=(24.3-23)/(5-2)

=1.3/3

=0.4

=4/10 = 2/5

Put m=2/5 and the coordinate points (2, 23) in y=mx+c.

That is, 23=2/5 (2)+c

⇒23 - 4/5 =c

⇒111/5 = c

⇒ c=22.2

Now, equation is y=0.4m+22.2

Therefore, the slope of the line passing through the given points is 0.4 or 2/5.

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Driving to the supermarket is Joshua. He covers 7.5 miles since he goes an average of 0.56 miles per minute.

By dividing the entire specific number by sum of all the values, the average can be obtained. A mean may indeed be calculated by adding all of the values in a sample of data. In other terms, a means is also known as the arithmetic mean. The average is referred to as having a mean.

The provided function is

d(t) = 0.5t

Simply substitute it to get the figure set t = 15

7.5 miles are equal to d (15) 0.5 (15).

To get the distance, use the range equations d = st, which says "distance equals force times time." Rate and speed are equivalent because they both indicate a specific length of distance per unit time, such like km/h or kilometers per hour. R = s = d/t is true if clip r and mobility s are equal.

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Answer:

moderate since the lines are similar

Intersection of angle of triangle known as incenter is equidistant from the sides of the triangle.

An angle of a triangle is divided into two congruent angles by a straight line known as the angle bisector.

The incenter is the location where the intersection of the three angle bisectors of a triangle occurs.

In the figure , I is incenter of ΔPQR.

The sides of the triangle are equally distance from the incenter.

Meaning, PI=QI=RI. The triangle's inscribed circle is a circle that contacts all three sides and has the incenter as its center and a radius equal to this distance.

The triangle can accommodate only one circle larger than this one.

An equilateral triangle will have an identical incenter and circumcenter.

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Answer: 78

Step-by-step explanation:

Answer:

6.98

Step-by-step explanation:

The answer would be 6.98 after subtracting 8.92 from the 15.9 after applying arithmetic operation.

The study of numbers and their operations, which are relevant to all other fields of mathematics, is part of the discipline of arithmetic operations. Addition, subtraction, multiplication, and division are the basic operations that make up this system.

It is given that:

The number expression is:

= 15.9-8.92

As we know from the definition of the arithmetic operation: Addition, subtraction, multiplication, and division are the basic operations that make up this system.

In the expression subtract 8.92 from the 15.9

After applying the arithmetic operation:

= 6.98

Thus, the answer would be 6.98 after subtracting 8.92 from the 15.9 after applying the arithmetic operation.

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The equation with a complex solution with a real component of 4 is given by:

A. x² - 8x + 16 = -21.

A complex number is a number that has two parts, a real part and an imaginary part.

The general definition of a complex number is given as follows:

z = a + bi.

In which:

A quadratic function is defined as follows:

y = ax² + bx + c.

For a complex solution, the real component is defined as follows:

-b/2a.

Hence the equation in which the solution has a real component of 4 is given by:

x² - 8x + 16 = -21.

As the coefficients a and b are given as follows:

a = 1, b = -8.

Hence the real component of the solution is of:

-b/2a = -(-8)/2 = 4.

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Step-by-step explanation:

for the perimeter you have to say two brackets live plus height plus with plastic

16 bit strings of length five either start with two zeros or end with two zeros are there; 32 bit strings of length six either do not start with two zeros or do not end with two zeros are there; 16 bit strings of length seven either start with four ones or end with four ones are there and 256

bit strings of length eight do not start with a one or do not end with a one are there.

A string is a combination which is made up of only two characters, either 1 or 0.

So, the combinations of the string can be found,

If the length of the bit string is 5, it means it will have 5 characters.

If this string either start with two zeroes or end with two zeroes. It mean there are only three positions are remaining which have two choices available for each place.

So, the total bit strings possible are,

= 2×(1×1×2×2×2)

= 16

16 such bit strings are possible.

If the length of the bit string is 6, it means it will have 6 characters.

If this string either do not start with two zeroes or do not end with two zeroes. It mean there are only four positions are remaining which have two choices available for each place.

So, the total bit strings possible are,

= 2×(1×1×2×2×2×2)

= 32

So, 32 such strings are possible.

Now, If the length of the bit string is 7, it means it will have 7 characters.

If this string either start with four ones or end with four ones. It mean there are only three positions are remaining which have two choices available for each place.

So, the total bit strings possible are,

= 2×(1×1×1×1×2×2×2)

= 16

So, 16 such strings are possible.

If the length of the bit string is 8, it means it will have 8 characters.

If this string either do not start with one and do not end with one. It mean there are only seven positions are remaining which have two choices available for each place.

So, the total bit strings possible are,

= 2×(1×2×2×2×2×2×2×2)

= 256

So, 256 such strings are possible.

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The number 32 can be written as a power with a base of 2 as 2^5

The index form of a number is defined as that number represented as an exponential expression, or even a single number raised to another number.

Example;

2^n

3^3

From the information given, we have to determine the index form of 32

It is expressed in the base of 2 as;

32 = 2 × 2 × 2 × 2 × 2

32 = 2^5

Thus, the number 32 can be written as a power with a base of 2 as 2^5

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The probability that at least one of the two adults believes most famous people make good role models be 0.436.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

A) The likelihood that both adults believe that most famous people make good role models would be = (199/800) × (198/799) = 39402/639200 = 0.062

B) We're looking for the likelihood that neither adult believes that most famous people make good role models.

Today that 199 people out of 800 believe that most famous people make decent role models.

The percentage of people who disagree that most celebrities make for good role models = 800 - 199 = 601

The probability that neither adult thinks most celebrities exists good role models. would be = (601/800) × (600/799)= 180300/319600 = 0.564

C) We're looking for the likelihood that at least one of the two adults believes that most celebrities make for positive role models.

Now that we know that neither of them believes that the majority of famous people are good role models, we can simply deduct that probability from 1.

The likelihood that at least one of the two adults believes most famous people make good role models = 1 - 0.564 = 0.436

The complete question is;

​In a sample of 800 U.S.​ adults, 199 think that most celebrities are good role models. Two Two U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S.​adults, complete parts​ (a) through​ (c).

(a) Find the probability that both adults think most celebrities are good role models. The probability that both adults think most celebrities are good role models is ________?(Round to three decimal places as​ needed.)

​(b) Find the probability that neither adult thinks most celebrities are good role models. The probability that neither adult thinks most celebrities are good role models is _______?(Round to three decimal places as​ needed.) ​

(c) Find the probability that at least one of the two adults thinks most celebrities are good role models. The probability that at least one of the two adults thinks most celebrities are good role models ______? (Round to three decimal places as​ needed.)

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To find the number of points at which the graph of the function intersects the x-axis, we need to find the roots of the equation:

4x^2 - 9x + 9 = 0

We can use the quadratic formula to find the roots:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 4, b = -9, and c = 9, so:

x = (-(-9) ± sqrt((-9)^2 - 4(4)(9))) / 2(4)

x = (9 ± sqrt(81 - 144)) / 8

x = (9 ± sqrt(-63)) / 8

Since the discriminant is negative, the roots are complex and the graph does not intersect the x-axis. Therefore, the answer is b. 0.

Therefore, the annual annuity payment can be approximately $6,069,727.

To calculate the size of the annual annuity payment, we can use the present value formula for an ordinary annuity. The formula is given by:

PMT = PV / [(1 - (1 + r)⁻ⁿ) / r]

Where:

PMT = Annual annuity payment

PV = Present value of the annuity

r = Annual interest rate

n = Number of periods

Given:

PV = $230 million

r = 8% = 0.08

n = 40 years

Using the formula, we can calculate the annual annuity payment:

PMT = 230,000,000 / [(1 - (1 + 0.08)⁻⁴⁰) / 0.08]

PMT ≈ $6,069,727

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Answer:

ok what do you want help with?

Step-by-step explanation:

The polynomial expression 2x⁶ - 12x⁴ in GCF factored form is 2x⁴(x² - 6).

The greatest number that can divide the numbers in equal parts.

It is called as greatest common factor.

Given:

A polynomial expression,

2x⁶ - 12x⁴.

To factor the polynomial using GCF:

The GCF of 2x⁶ and 12x⁴,

= 2x⁴.

So, the polynomial is,

2x⁶ - 12x⁴ = 2x⁴(x² - 6)

Therefore, the GCF form of the polynomial is 2x⁴(x² - 6).

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The measurement m angle Q and m angle R of Quadrilateral PQRS is 72°.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Area: base × height

Perimeter: 2 x (sum of lengths of adjacent sides)

Number of vertices: 4

Number of edges: 4

We are given that;

Angle P= 72

Since PQRS is a parallelogram, opposite angles are equal. So:

m∠Q = m∠P = 72°

Similarly,

m∠R = m∠S

Also, the sum of the angles of a parallelogram is 360°. Therefore:

m∠P + m∠Q + m∠R + m∠S = 360°

Substituting the given value, we get:

72° + 72° + m∠R + m∠S = 360°

Simplifying:

144° + m∠R + m∠S = 360°

m∠R + m∠S = 216°

Since PQRS is a parallelogram, opposite angles are equal, so:

m∠R = m∠P = 72°

Therefore,

m∠R = 72°

m∠Q = m∠P = 72°

So, the measures of parallelogram angles  Q and R are both 72°.

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Answer:

8 weeks per painting

Step-by-step explanation:

1/4 of a painting in 2 weeks

Multiply everything x 4

4/4 or 1 painting in 8 weeks

He has eaten \(\frac{5}{8}\) pizza altogether.The total pieces of pizza was 8.Marco ate 3 for lunch and 2 for dinner.So, he ate 5 pieces of pizza out of 8.

What is fraction?

A fraction is a numerical value that is a part of whole number.In this numerator divided by denominator .In simple term both are integers.The word fraction means to break.

there are many types of fraction.Proper fraction, improper fraction,mixed fraction,whole fraction, like fraction, unlike fraction and unit fraction.

Total pieces of pizza =8

Marco ate for lunch =3

He ate for dinner =2

Total he ate =3+2

                     =5

Now remaining pieces of pizza=8-5

                       =3

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Answer:

5/8

Step-by-step explanation:

There are approximately 3.72 x 10⁴¹ ways that Anna can hand out 1 treat to each of the 36 children who come to her door.

Anna has 2 dozen Rollo bars, which is equivalent to 2 x 12 = 24 Rollo bars.

She also has 1 dozen apples, which is equivalent to 1 x 12 = 12 apples.

So, Anna has a total of 24 + 12 = 36 treats to hand out.

Now, she needs to hand out 1 treat to each of the 36 children who come to her door.

This can be thought of as selecting 1 treat from the total of 36 treats for each child, without replacement, as each child can only receive 1 treat.

The number of ways to do this is given by the concept of permutations, denoted by "nPr", which is calculated as;

nPr = n! / (n - r)!

where n is the total number of items (treats) to choose from, and r is the number of items (treats) to choose.

In this case, n = 36 (total number of treats) and r = 36 (number of children).

Plugging in the values, we get;

36P36 = 36! / (36 - 36)! = 36! / 0! = 36!

Since 0! (0 factorial) is equal to 1, we can simplify further:

36! / 1 = 36!

36! ≈ 3.72 x 10⁴¹

So, there are 3.72 x 10⁴¹ ways that Anna can hand out 1 treat to each of the 36 children who come to her door.

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The type of sampling technique used in this scenario is a Simple Random Sample.

A simple random sample is a sampling technique in which every member of the population has an equal chance of being selected for the sample.

This means that each member of the population is assigned a number, and then a random number generator is used to select the members of the sample.

There are several ways to conduct a simple random sample, such as drawing names out of a hat or using a computer program to randomly select participants.

In the given scenario, a sample frame is developed with all possible items from the population, and then a sample is drawn in such a way that every item in the frame has the equal chance of being selected.

This means that each item in the population has an equal chance of being selected for the sample, and the sample is therefore a simple random sample.

Therefore,

The type of sampling technique used in this scenario is a Simple Random Sample.

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Answer:

33/5

Step-by-step explanation:

I believe this is the answer

Answer:

\(7\frac{1}{5} + \frac{ - 3}{5} = \frac{36}{5} + \frac{3}{5} = \frac{39}{5} \)

I HOPE IT IS HELPFUL

Answer:

-3

Step-by-step explanation:

Based on his weekly salary and commission, we can calculate that Mr. Randall sold goods worth $1,800.

In the formula given, sales is represented as s. To find the total sales, you can solve the equation:

300 + 0.07s = 426

0.07s = 426 - 300

s = 126 / 0.07

= $1,800

In conclusion, Mr. Randall sold $1,800 worth of goods.

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The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

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The equation x(x - 3) = 4 has two solutions: x = 4 and x = -1, which can be found using the quadratic formula x = (-b ± √(b² - 4ac)) / (2a).

Let's first rewrite the equation in standard quadratic form: x² - 3x - 4 = 0. Here, a = 1, b = -3, and c = -4.

Using the quadratic formula, we can substitute these values into the formula and solve for x:

x = (-(-3) ± √((-3)² - 4(1)(-4))) / (2(1))

 = (3 ± √(9 + 16)) / 2

 = (3 ± √25) / 2.

Now, evaluating the square root, we have: x = (3 ± 5) / 2.

This gives us two possible solutions:

1. When x = (3 + 5) / 2 = 8 / 2 = 4.

2. When x = (3 - 5) / 2 = -2 / 2 = -1.

Therefore, the equation x(x - 3) = 4 has two solutions: x = 4 and x = -1.

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Answer:

Corresponding Angles; x=35

Step-by-step explanation:

These are corresponding angles.

To solve this, make the two angles equal to each other.

4x+7 = 6x-63

Push the variables to one side and the numbers to the other

4x-4x+7+63= 6x-4x-63+63

7+63=6x-4x

70 = 2x

x=35

Now, plug it into one of the angles. It does not matter which, both angles are the same.

4(35)+7 = 147

(It was at this point i realize that you were looking for the x value, not the angles, but I guess this is a bit extra.)

Answer:

Step-by-step explanation:

-3y = -2x + 4

3y = 2x - 4

y = 2/3x - 4/3

perp; -3/2

y + 3 = -3/2(x - 4)

y + 3 = -3/2x + 6

y = -3/2x + 3

Answer:

a = 7/2

Step-by-step explanation:

Step 1: Write equation

6a - (2a + 4) = 11 - 3(a - 2)

Step 2: Solve for a