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Decide if the events A and B are mutually exclusive or not mutually exclusive. A person is selected at random.
A: Their birthday is in the fall.
B: Their birthday is in October.
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The subsets of the set {e, n, t} are given as follows:

{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.

Considering a set with n elements, the number of subsets in the set is the nth power of 2, that is:

\(2^n\)

The set for this problem is given as follows:

{e, n, t}

The cardinality is given as follows:

n = 3.

Hence the number of subsets is given as follows:

2³ = 8.

The subsets are given as follows:

{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.

In which {} is the empty set.

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Answer:

45 are pink 55 are not pink

Step-by-step explanation:

a) The number of pink seashells is A = 45

b) The number of seashells that are not pink = 55

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let the total number of seashells be = 100

Let the percentage of the seashells that are pink = 45 %

If 45% of the 100 seashells are pink, then the remaining 55% must be not pink. We can find the number of pink shells by multiplying 100 by 45%:

Number of pink shells = 100 x 0.45 = 45

To find the number of shells that are not pink, we can subtract the number of pink shells from the total number of shells:

Number of shells not pink = 100 - 45 = 55

Hence , there are 55 seashells that are not pink and 45 seashells that are pink.

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The standard error represents the average deviation of the sample means from the true population mean. Rounding this value to four decimal places, the standard error of X¯¯¯ is approximtely 0.6500 mpg.

A smaller standard error indicates that the sample means are more likely to be close to the population mean.To calculate the standard error of X¯¯¯, the mean from a random sample of 25 fill-ups by one driver, we can use the formula:

Standard Error (SE) = σ / sqrt(n),

where σ is the standard deviation and n is the sample size.

In this case, the standard deviation (σ) is given as 3.25 mpg, and the sample size (n) is 25.

Plugging in these values into the formula, we have:

SE = 3.25 / sqrt(25).

Calculating the square root of 25, we get:

SE = 3.25 / 5.

Performing the division, we find:

SE ≈ 0.65.

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Answer:

x = - 1

Step-by-step explanation:

P = \(\frac{x-2}{x+1}\)

the denominator of the rational function cannot be zero as this would make it undefined. Equating the denominator to zero and solving gives the value that x cannot be.

x + 1 = 0 ( subtract 1 from both sides )

x = - 1

P is undefined when x = - 1

Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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The base is 7 units and the height is 3 units of the rectangle.  Then the correct option is D.

Let one point be (x, y) and another point be (h, k).

Then the distance between the points will be

D² = (x - h)² + (y - k)²

On a coordinate plane, a rectangle has points (2, 2), (2, 5), (negative 5, 2), and (negative 5, 5).

Then the base of the rectangle will be

D² = (2 + 5)² + (2 - 2)²

D² = 7²

D = 7 units

Then the height of the rectangle will be

D² = (2 - 2)² + (5 - 2)²

D² = 3²

D = 3 units

Then the correct option is D.

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Answer:

A. The base is 5 units and the height is 3 units.

Step-by-step explanation:

dont listen to the person above

Answer:  first choice is correct

Step-by-step explanation:

\(\sqrt{10} = 3.16\\\\ \sqrt{13} = 3.6\)

22/9 = 2.44

Therefore Point A is 22/9, Point B is \(\sqrt{10}\),  Point C is \(\sqrt{13}\)

Answer:

3= 25 4= 20 25= 5

Step-by-step explanation:

its a pattern. the top goes up by ones and the bottom goes up by fives.

Answer:

661,068.8j

Step-by-step explanation:

The car has 661068.8 J of potential energy at a height of 62 m having a mass of 1088 grams.

Potential energy is a form of stored energy that is dependent on the relationship between different system components. When a spring is compressed or stretched, its potential energy increases.

We know, The gravitational constant is 9.8 m/s².

From the given information, m = 1088 grams, h = 62 meters.

Therefore, The amount of potential energy the car has is,

PE = mgh.

PE = 1088×9.8×62 J.

PE = 661068.8 J.

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Answer:

To one decimal place,

y = 16.3 m

Step-by-step explanation:

Using SOHCAHTOA,

In this case we need to use CAH,

WE know the angle = 25 and the hypotenuse H = 18,

so,

y = adjacent

\(cos(angle) = y/H\\y = (18)(cos(25))\\y = 16.3135\\y = 16.3\)

Answer: 16.3 in.

Step-by-step explanation:

use SOH CAH TOA

cos x = adj/hyp

cos 25  = y/18

18 cos 25  = y

y= 16.3

Answer: (1/6)^2

Step-by-step explanation:

Answer:

The third answer is correct

Step-by-step explanation:

Use the properties of degrees:

1)

\( {( \frac{1}{108} })^{3} = \frac{ {1}^{3} }{ {108}^{3} } = \frac{1}{6561} \)

\( \frac{1}{6561} ≠ \frac{1}{36} \)

.

2)

\( ({ \frac{1}{9} })^{3} = \frac{ {1}^{3} }{ {9}^{3} } = \frac{1}{729} \)

\( \frac{1}{729} ≠ \frac{1}{36} \)

.

3)

\( ({ \frac{1}{6} })^{2} = \frac{ {1}^{2} }{ {6}^{2} } = \frac{1}{36} \)

\( \frac{1}{36} = \frac{1}{36} \)

The reason for the difference between these two percentages is given as follows:

Random error; the numbers were different due to variability inherent in sampling.

Sampling is a technique for when a group of elements from a population is taken to represent the entire population.

This group of elements has to be representative of the entire population, as to lead to correct conclusions, and thus the information gathered from the sample could be generalized to the entire population.

In this problem, the samples are representative, as all types of blood are expected to be present in an hospital, thus constituting a random sample, meaning that this is more than likely a random error.

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The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

add the numbers together, then divide by how many numbers appear

Step-by-step explanation:

8, 5, 2, 13, 6, 6, 4, 10, 0= 54/9 =6

Answer:

t = 21d

Step-by-step explanation:

Here tension and distance are denoted t by d  and  respectively. Since  t varies directly with d , then the relation between  t and d is k=td Given that, for the tension 42 pounds, the spring is stretched 2 inches. Substituting  t = 42 and d= 2 into  t = kd find the value of k . Therefore,

42= K (2)

\(K=\frac{42}{2}\)

K= 21

Thus the relationship is t = 21d

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The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.

option B.

The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;

The solution of the graph,

x > -4 and x < 1

The first equation with "≥" is ruled out because the graph doesn't have a thick dot.

Let's simplify the second expression;

x² + 3x - 3 < 0

solve using quadratic formula;

x > -3.79 or x < 0.79

The third expression is ruled out since its solution will be complex.

For the last expression;

x² + 3x - 3 > 0

x < -3.79 or x > 0.79

Thus, the correct inequality expression is x² + 3x - 3 < 0.

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Answer: 803.84cm3

Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.

To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.

4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.

Now, we have the area of the circle. 50.24cm squared!

The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,

16cm x 50.24cm squared = 803.84cm cubed.

The volume of the can of soup is 803.84cm cubed.

Answer:

\(x = 12.5\) degrees

Step-by-step explanation:

Since lines a and b are parallel, we have that angles 3 and 5 are congruent, that is, they have the same measure.

We have that:

\(m<3 = 10x\)

\(m<5 = 12x - 25\)

Value of x:

Since they are congruent:

\(m<3 = m<5\)

\(10x = 12x - 25\)

\(-2x = -25\)

\(2x = 25\)

\(x = \frac{25}{2}\)

\(x = 12.5\) degrees

Answer:

\(A = 6\).

Step-by-step explanation:

Let \(a\) denote a constant (a number, rather than a variable like \(x\).)

Let \(f(x)\) denote an expression about \(x\) (for example,

By the factor theorem, if \((x - a)\) is a factor of \(f(x)\), then \(f(a) = 0\). In other words, if all mentions of \(x\) in the expression \(f(x)\!\) are replaced with \(a\), then the expression should evaluate to zero.

\((x + 3)\) is equivalent to \((x - (-3))\). That is: \(a = -3\).

Replace all mentions of \(x\) in \(x^3 - x^2 - 10\, x + A\) by \((-3)\) to get:

\((-3)^3 - (-3)^2 - 10\times (-3) + A\).

That should evaluate to zero. Therefore: \(-27 - 9 + 30 + A = 0\). Solve for \(A\) to get \(A = 6\).

The salary for a given period depends on the salary unit rate and the

duration of the period under consideration.

Responses:

1. A) $903.85

2. G) $25,680

3. H) $48,450

4. C) $29.54

5. D) $26,822.40

1. The weekly salary = Annual salary ÷ 52

Which gives;

Sally's weekly salary = $47,000 ÷ 52 ≈ $903.85

2. Annual salary = Weekly salary × 12

Which gives;

Justin's annual salary = $2,140 × 12 = $25,680

3. Annual salary = Number of credit hours × Salary per credit hour

Which gives;

Annual salary = $950 × 51 = $48,450

4. Hourly rate = Annual income ÷ Number of hours worked

Number of hours worked = 205 days × 8 hours/day = 1,640 hours

Marc's annual income = $48,445.60

Which gives;

Hourly rate = $48,445.60 annually ÷ 1,640 hours/annum = $29.54

Marc's hourly rate = $29.54

5. Annual salary = Hourly rate × Number of hours worked per year

Number of hours worked per year = 254 × 8 = 2032

Which gives;

David's annual salary = $13.20/hour × 2032 hours = $26,822.4

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The measure of angle x of the quadrilateral inscribed in a circle is x = 31°

Given data ,

Let the quadrilateral be ABCD inscribed in a circle

Now , the measure of angles of the quadrilateral are

Opposite angles are supplementary: A + C = 180° and B + D = 180°.

Adjacent angles are supplementary: A + B = 180°, B + C = 180°, C + D = 180°, and D + A = 180°

And , the sum of opposite angles is always equal to 180°

So , the measure of 118° + 2x° = 180°

On simplifying , we get

2x = 62

Divide by 2 on both sides , we get

x = 31

Hence , the angle is solved and x = 31

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Answer: 19

Step-by-step explanation: The best way is to set this up with synthetic division (as the attached image).

Hope this helps!

Answer:

73°

Step-by-step explanation:

This equation uses two supplementary angles. Supplementary angles are two angles that add up to 180 degrees.

The triangle has two angles implied, 30 degrees and (180-137) degrees.

(180 - 137) = 43 degrees

Now that we have two angles inside the triangle, we subtract them from 180 to find the last angle.

180 - 43 - 30 = 107

The angle with a measure of 107 degrees and angle 3 are supplementary

180 - 107 = 73 degrees

Answer:73.4° Fahrenheit.

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

Answer:

and

Step-by-step explanation:

A conjunction is formed when two statements join with the connector and.

The symbol used for a conjunction is:

∧

to mean AND.

For example, when you have two statements :

p : It will rain today.

q : I will fetch water.

You can connect the statements to form a compound statement :

It will rain today and i will fetch water. ( p ∧ q ).

Answer:

Ask that bleep Jocelyn, its her money she always wants us to answer for her ugh shes so selfish

Step-by-step explanation:

Triangles ABC and MNO are congruent with each other using Side Side Side Rule of Congruency.

There are four rules of congruency of two triangles.

The rules are:

RHS: where in two right angled triangles, right angle, hypotenuse and another length of side are equal, so they are said to be congruent.

SSS: where in any two triangles if each three sides of a triangle are equal to corresponding sides of another triangle then that triangles are called congruent.

SAS: In two triangles, two sides and angle between them are equal for one triangle to another, so the triangles are said to congruent,

AAS: In two triangles, two angles and one side are equal for one triangle to another, so the triangles are said to congruent,

Here in the picture given that, in triangle ABC and triangle MNO,

AC = MO

AB = NO

BC = MN

So the triangles ABC and MNO are congruent with each other using Side Side Side Rule of Congruency.

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Answer:

$50

Step-by-step explanation: