at a gathering of 30 people, there are 20 people who all know each other and 10 people who know no one. people who know each other hug, and people who do not know each other shake hands. how many handshakes occur within the group?

Answer:

13 ft

Step-by-step explanation:

The formula to find the length of the diagonal of a rectangle =

Diagonal² = Length² + Width²

Diagonal = √Length² + Width²

Length = 12 ft

Width = 5ft

Diagonal = √12² + 5²

Diagonal = √144 + 25

Diagonal = √169

Diagonal = 13 ft

The length of the diagonal of the rectangle = 13 ft

Answer:

The radius of the inner circle is 14 ft. Since the outer circle is 3 ft more than the inner circle, its radius is 17 ft. The circumference formula is 2(pi)radius (or 2(22/7)17 in this case). The circumference of the outer circle is 106.85 ft (or 106.9 if rounding). To find the difference, you would subtract the smallest FROM the greatest:

106.85 - 88 = 18.85 ft (or 18.9 if rounding)

The measure of the two angle is = 47 degree and 79 degree

What is Angle?

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.

Given ,

the grocery tore is located is (2x 15)⁰

the measure of the angle where the book tore is located is (3. 5x – 4. 5)⁰

Then angle a+ b+c+d = 90⁰

as the angle of the square  is 90 degree for all the side

= x⁰ + ( 2x-15)⁰ + (3.5x-4.5)⁰ = 90⁰

= 7.5x⁰ +19.5⁰ = 90⁰

= 7.5x⁰ = 90⁰ -19.5⁰

x = 70.5⁰/7.5⁰

x= 9.4⁰

Therefore,

angle a = 9.4⁰

angle b = 9.4* 2 -15

b = 3.8⁰

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Answer:

15%

Step-by-step explanation:

You add up all the frequencies and divide by 9 (the amount 6 was rolled).

It adds up to 60. Divide 9 by 60 and you have 15%.

The initial-value is  x(t)=F0/2w^2 (sin wt-wt cos wt)

An initial-value hassle is a differential equation wherein is an open set of, together with a point within the domain called the initial situation. A technique to an initial cost hassle is a function that is a technique to the differential equation and satisfies.

Inside the discipline of differential equations, preliminary cost trouble (additionally called Cauchy trouble by using a few authors) is a normal differential equation collectively with a detailed fee, called the preliminary situation, of the unknown function at a given factor in the domain of the solution.

In multivariable calculus, an initial-value hassle is a normal differential equation collectively with a preliminary circumstance that specifies the fee of the unknown characteristic at a given factor in the area. Modeling a system in physics or different sciences often amounts to fixing an initial cost problem.

Consider a differential equation x+x=F, sin wt, x(0) = 0,X(0) = 0

Apply Laplace transformation on both sides, and we get

(s²L{x(t)}-sy(0)-y'(0)) + w²L {x(t)} =·

Fow

Fow

(s² + w² ) { x(t)} = 3 + w²

L{x(t)}=

Fow

(5²+w²)²

x(t)=FwL

[(s² + w²)²]

Fow

x(t)=(sin wt-wt coswt)

2w

x(t)=

Fo

wtcos

2w (sin wt-wt cos wt),

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Using it's concept, it is found that there is a 0.8606 probability that the driver was not intoxicated.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Researching the problem on the internet, it is found that there are 62 + 76 + 254 + 598 = 990 deaths, of which 254 + 598 = 852 did not involve an intoxicated driver, hence the probability is given by:

p = 852/990 = 0.8606

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Answer: B

I took the quiz

Answer:

(−3, 2); 2 ≤ y < ∞

Step-by-step explanation:

I literally took the test hours ago

Step-by-step explanation:

so, for x = 0, y = 30.5

that means the first answer is out.

for x = 1, y = 21.35

so, only

y = 30.5(0.7)^x

can be right.

all other functions have an y-value of way over 30.5 (because the factor of 30.5 is larger than 1).

and to verify :

30.5 × 0.7¹ = 30.5 × 0.7 = 21.35

correct.

Answer:

\(x=-9\)

Step-by-step explanation:

\(5x+12=-33\)

Subtract 12 from both sides. The left side cancels:

\((5x+12)-12=(-33)-12\\5x=-45\)

Divide both sides by 5. The left side cancels:

\((5x)/5=(-45)/5\\x=-9\)

The value of x is -9.

Answer:

i got 34:34:112

Step-by-step explanation:

sorry im bad at explaining things but i added a picture

Answer:

34, 34, 112

Step-by-step explanation:

(6x+10)+(x + 17)+(4x-34) = 180

=> 6x+x+4x = 180 -27+34

=> 11x = 187

=> x = 17

6(17) + 10= 112

17+17 = 34

4(17) -34 = 68 - 34 = 34

Please mark Brainliest if this helps!

Answer:

Option (B)

Step-by-step explanation:

In the graph attached,

Two lines graphed have the equations as,

y = 2x - 3 [A line having y-intercept as (-3)]

\(y=\frac{1}{3}x+4\) [Line having y-intercept as (4)]

Since both the lines have been represented by the dotted lines therefore, these lines will represent the inequalities [having the signs less than (<) or greater than (>)].

Now shaded region will decide the signs of the inequalities.

Since, shaded region of y = 2x - 3 is on the left side, inequality showing this region will be,

y > 2x - 3

Since, shaded region of \(y=\frac{1}{3}x+4\) is above the line, inequality showing this region will be,

\(y>\frac{1}{3}x+4\)

Therefore, Option (B) will be the answer.

Answer:

B

Step-by-step explanation:

Just is cuh

The following exponential rule is called the Product Rule.

What is exponential rule ?

Exponential rules are mathematical rules that govern the manipulation of exponential expressions, which involve terms that have a base raised to a power. Exponential rules are important in many areas of mathematics and science, particularly in algebra, calculus, and statistics.

According to the question:
The following exponential rule is called the Product Rule. It states that when multiplying two powers with the same base, you can add their exponents. The rule is:

\(a^m * a^n = a^(m+n)\)

For example, \(2^3 * 2^4 = 2^(3+4) = 2^7 = 128\). This rule is fundamental in simplifying expressions and solving equations involving exponential functions.

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There is a very small chance (less than 1%) that a randomly selected baby from this sample was born on Tuesday OR on Friday.

To find the probability that a randomly selected baby from this sample was born on Tuesday OR on Friday, we need to add the number of babies born on Tuesday to the number of babies born on Friday, and then divide by the total number of babies in the sample.

The number of babies born on Tuesday is 202020, and the number of babies born on Friday is 151515. Therefore, the total number of babies born on Tuesday or on Friday is 202020 + 151515 = 353535.

The total number of babies in the sample is 500500500. Therefore, the probability that a randomly selected baby from this sample was born on Tuesday OR on Friday is:

353535 / 500500500 = 0.0007061

It is interesting to note that the number of babies born on different days of the week varies in this sample. For example, there are more babies born on weekdays (Monday-Friday) than on weekends (Saturday and Sunday), and there are more babies born on Tuesday than on Wednesday or Thursday.

The number of scheduled deliveries is higher than the number of unscheduled deliveries overall, but there are some days (e.g., Friday and Saturday) where there are more unscheduled deliveries than scheduled deliveries. These patterns could be explored further to understand the factors that influence the timing and scheduling of deliveries.

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Answer:

3/5

Step-by-step explanation:

6 black marbles and 4 white marbles.= 10 marbles

P( black marble) = number of black marbles / total marbles

                            =6/10 = 3/5

Answer:

6/4 or 1 1/2

Step-by-step explanation:

because there is 6 black marbles and 4 white marbles

Circumference = 2× pie × r

Circumference = 6pie

Thus ;

2pie × r = 6pie

r = 3

____________________________________________

\(r = \frac{1}{2} \sqrt{ ({ - 6})^{2} + {2}^{2} - c} \\ \)

\(3 = \frac{1}{2} \sqrt{ 36 + 4 - c} \\ \)

\(6 = \sqrt{40 - c} \)

\(( {6})^{2} = ({ \sqrt{40 - c} })^{2} \)

\(36 = 40 - c\)

\(c = 4\)

1. The set of all points in a plane that are the same distance from a given point called Radius. So the option B is correct.

2. A straight line from the center to the circumference of a circle or sphere is Diameter. So the option A is correct.

The set of all points in the plane that are a fixed distance (the radius) away from a fixed point is referred to as a circle (the center).

Radius is the name for any distance that connects a point on a circle to its center. Any two radii have the same length when compared to the definition of a circle. Take note of the fact that the term "radius" is being used to describe both these intervals and their typical length.

The term "chord" refers to the space that connects two points on a circle.

The term "diameter" refers to a chord that runs through the center. Since a diameter is made up of two radii that are connected at their ends, each diameter has a length that is twice as long as its radius.

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The complete question is:

1. The set of all points in a plane that are the same distance from a given point called

1. Center

2. Radius

C. Surface area

D. Circumference

2. A straight line from the center to the circumference of a circle or sphere is

A. Diameter

B. Radius

C. Surface area

D. Circumference

Answer:From the given information, we know that after sailing for 2 hours, Alvin and his friends are 10 miles from shore. This can be written as y = 10 when x = 2.

Since there is a proportional relationship between x and y, we can write an equation using this information: y = kx, where k is the proportionality constant.

Substituting the known values, we get: 10 = k * 2

Solving for k, we get: k = 10/2 = 5

So, the equation relating x and y is: y = 5x

To find their distance from shore after sailing for 3 hours, we can plug in x = 3 into the equation:

y = 5x

y = 5 * 3

y = 15

So, after sailing for 3 hours, Alvin and his friends are 15 miles from shore.

Step-by-step explanation:

Yes , the integer k is divisible by 4 and statement (1) alone is sufficient to determine that k is divisible by 4.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

To determine if the integer k is divisible by 4, let's analyze the given statements:

Statement (1): 8k is divisible by 16.

This means that 8k is a multiple of 16. Since 16 is divisible by 4, we can conclude that k must be divisible by 4 as well. Therefore, statement (1) alone is sufficient to determine that k is divisible by 4.

8k = 16

k = 2

b)

This statement does not provide direct information about the divisibility of k by 4. While 12 is divisible by 4, the fact that 9k is divisible by 12 does not guarantee that k itself is divisible by 4.

9k = 12

k = 12/9

k = 4/3

So , it is not an integer

In conclusion, statement (1) alone is sufficient to determine that k is divisible by 4. Statement (2) is not sufficient on its own.

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The required area of the parallelogram and pentagon is 91 unit² and 75 unit².

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

A parallelogram in is shown in figure 1 with the dimensions height = 7 and base = 13,
Area of the parallelogram  = 13 × 7 = 91 unit²

Now,
A pentagon is shown in figure 2,
Area of the pentagon = 5 [1/2 × height × side]
                                 = 5 [1/2 × 5 × 6]

                                 = 75 suqare units.

Thus, the required area of the parallelogram and pentagon is 91 unit² and 75 unit².

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The inequality solved to give a solution of x ≥ 1 and x ≤ -3 is |x + 1| ≥ 2.

b = 1, ≥

From the diagram, the solution to the inequality is x ≥ 1 and x ≤ -3

Hence:

|x + b| ≥ 2

x + b ≥ 2 or -(x + b) ≥ 2

x ≥ 2 - b or x ≤ -2 - b

2 - b = 1 and -2 - b = -3

b = 1

Hence |x + 1| ≥ 2

The inequality solved to give a solution of x ≥ 1 and x ≤ -3 is |x + 1| ≥ 2. b = 1, ≥

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a)  the vectors in b are linearly independent and span R^2, we can conclude that b is a basis for R^2.

(a) To prove that the set of vectors b = {(3, 4), (1, 2)} is a basis for R^2, we need to show two things: linear independence and spanning.

Linear independence: We need to show that the vectors in b are linearly independent, which means that there is no non-trivial linear combination of the vectors that equals the zero vector.

Let's assume that we have scalars a and b such that a(3, 4) + b(1, 2) = (0, 0). This leads to the following system of equations:

3a + b = 0

4a + 2b = 0

Solving this system, we find that a = 0 and b = 0. Since the only solution to the system is the trivial solution, the vectors (3, 4) and (1, 2) are linearly independent.

Spanning: We need to show that any vector in R^2 can be expressed as a linear combination of the vectors in b. In other words, we need to show that for any vector (x, y) in R^2, there exist scalars a and b such that a(3, 4) + b(1, 2) = (x, y).

Solving this system of equations, we find a = (2x - y)/5 and b = (3y - x)/5. This shows that any vector (x, y) in R^2 can be expressed as a linear combination of (3, 4) and (1, 2).

(b) To perform the Gram-Schmidt orthonormalization process on the set of vectors b = {(3, 4), (1, 2)}, we can follow these steps:

Step 1: Normalize the first vector:

u1 = (3, 4) / ||(3, 4)|| = (3, 4) / 5 = (0.6, 0.8)

Step 2: Subtract the projection of the second vector onto the first vector:

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The part of the figure marked ? is solved to be

113 degrees

The part of the circle marked by a question mark is solved using the relation as shown below

given angle formed by the tangents = 180 degrees - minor arc GE

information given in the problem includes

given angle formed by the tangents = 67 degrees

minor arc GE = ?

plugging in these values results to

67 degrees = 180 degrees - ?

rearranging the equation

? = 180 degrees - 67

? = 113

hence the required side is 113 degrees

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Answer:

3(14+4)+28+64 = 54+92 = 146 gm/mol

Step-by-step explanation:

Name of elements : 1) Nitrogen

2) hydrogen

3) phosphorus

4) oxygen

The theorem that explains why ∠4 ≅ ∠8 is the Alternate Interior Angles Theorem. The same side interior angles pair are ∠3 and ∠5, and ∠4 and ∠8.

Alternate Interior Angles theorem states that if two parallel lines are intersected by a transversal, then the alternate interior angles formed are congruent.

The same-side interior angles are the angles that are on the same side of the transversal and inside the two parallel lines. In the given diagram, the same-side interior angle pairs are ∠3 and ∠5, and ∠4 and ∠8.

All the angle pairs formed by the intersection of the two parallel lines and the transversal are

Corresponding angles are ∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8

Alternate interior angles are ∠3 and ∠5, ∠4 and ∠8

Alternate exterior angles are ∠1 and ∠7, ∠2 and ∠6

Vertical angles are ∠3 and ∠4, ∠5 and ∠6, ∠1 and ∠2, ∠7 and ∠8

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Answer:

Kai will walk 8 miles

Step-by-step explanation:

Have a gr8 day!

Therefore, in a 2x2 table, the pattern of cell frequencies that would indicate independence is d. All cell frequencies are exactly the same.

In a 2x2 contingency table, the expected cell frequencies under the null hypothesis of independence are equal for all cells. If the observed cell frequencies in the table are approximately equal to the expected cell frequencies, then we can conclude that there is no significant association between the two variables being studied. In other words, the pattern of observed cell frequencies is consistent with the null hypothesis of independence. Therefore, if all cell frequencies are exactly the same, it suggests that the variables are independent, as each cell has an equal chance of being filled by any observation regardless of the value of the other variable.

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Answer:

Is the dilation an enlargement or reduction?

Reduction

The point of dilation is about what coordinate?

0,0

What is the scale factor?

1/3

Step-by-step explanation:

The dilation is a reduction. The point of dilation is about coordinate (0,0).  The scale factor is 1/3.

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

On a coordinate plane, the pre-image rectangle has points (0, 0), (6, 0), (6, -3), and (0, -3).

The image has points (0, 0), (2, 0), (2, -1), and (0, -1).

The required figure has been attached below which represents the dilation.

As we can see that the dilation is a reduction.

The point of dilation is about coordinate (0,0).

This result of dilating a given triangle with a scale factor is 1/3.

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Answer:

f(1) = -3 f(n) = 2 f(n - 1) + 1 f(2)

Alternate form:

{f(n) = -f(1)/3, f(n - 1) = f(1)/2 - f(2)/2}

Answer:

f = -3

Step-by-step explanation:

F(1)=-3

Re-order the terms so constants are on the left

f . 1 = -3

1 f = -3

multiply by 1

1 f = -3

f = -3

Answer:

I'll need a picture of it, and/or the options to help you out.

Step-by-step explanation:

Angle CBD or k is equal to 70 degrees.

Angles are formed when two rays, known as the sides of the angle, share a common endpoint, called the vertex of the angle. The size of an angle is measured in degrees or radians. In a geometric plane, angles are usually denoted by a symbol that indicates the vertex, with the vertex being the middle letter, and the two rays are represented as line segments originating from the vertex.

Angles can be classified in different ways, including by their size or magnitude, by their position or direction, and by their relationships with other angles. Some common types of angles include acute angles (less than 90 degrees), right angles (exactly 90 degrees), obtuse angles (greater than 90 degrees but less than 180 degrees), straight angles (exactly 180 degrees), and reflex angles (greater than 180 degrees). Angles can also be complementary (adding up to 90 degrees), supplementary (adding up to 180 degrees), or congruent (having the same size).

We know that the sum of the angles in a triangle is 180 degrees. Let's use that fact to solve for k.

Angle ABD + angle CBD + angle ABC = 180 degrees

Substituting the given values, we get:

30 + k + 80 = 180

Combining like terms, we get:

k + 110 = 180

Subtracting 110 from both sides, we get:

k = 70

Therefore, angle CBD or k is equal to 70 degrees.

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