Determine whether the arguments are valid or invalid.
A ). She will go to school or she will get a job. She will not get a job. Therefore, she will go to school.
B). If Cathy is a gambler, then she lives in Marine. Cathy lives in Marine and she loves horses. Therefore, if Cathy does not love horses, she is not a gambler.

So overall, you can expect to make a profit of $166.67 if you play the game 100 times.

What is probability ?

Probability can be defined as the ratio of number of favourable outcomes and total number of outcomes.

To determine how much you expect to win or lose if you play the game 100 times, we need to calculate the expected value of each round and then multiply it by the number of rounds.

Let X be the random variable that represents the amount you win in one round of the game. The possible outcomes of X are winning $14, winning $12, or losing $10. We can calculate the expected value of X using the following formula:

E(X) = P(win $14) × $14 + P(win $12) × $12 + P(lose $10) × (-$10)

To calculate the probabilities, we can use the fact that there are 5 red balls, 3 green balls, and 4 yellow balls in the bag. The probability of drawing a red ball is therefore 5/12, the probability of drawing a green ball is 3/12, and the probability of drawing a yellow ball is 4/12.

So we have:

E(X) = (5/12) × $14 + (4/12) × $12 + (3/12) × (-$10)

E(X) = $5/3

This means that on average, you expect to win $5/3 per round. Over 100 rounds, you can expect to win:

100 × $5/3 = $166.67

However, it's important to note that this is just an average - in reality, you may win more or less than this amount depending on the luck of the draw.

Therefore, overall, you can expect to make a profit of $166.67 if you play the game 100 times.

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The range of heights for lots in New York City is:

1776 feet - 0 feet = 1776 feet.

Height is a mathematical term that refers to the vertical distance between an object's top and base. On sometimes, it has the designation "altitude." The measurement of an item along the y-axis in coordinate geometry is referred to as height in geometry.

The range of heights for lots in New York City is the difference between the tallest and shortest lots.

The tallest lot is 1 World Trade Center, which is 1776 feet tall.

The shortest lot is empty and 0 feet tall.

Therefore, the range of heights for lots in New York City is:

1776 feet - 0 feet = 1776 feet

So, the answer is A. 1776 feet.

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The equations; T = 2c + 43 and T = 3c + 33 for the total cost for the cakes indicates;

Part 1

The number of cupcakes for which the cost would be the same is the option;

In the solution, the x-value represents the A number of cupcakes and the y-value represents the B total cost

An equation is an statement of equivalence between two expression or values by joining them with an '=' sign.

Dolphin Bake Shop charges

Amount charged for each cup cake = $2

Amount charged for the large cake = $43

Total charge, T = 2·c + 43

Make A Splash Bakery

Amount charged for the large cake = $33

Amount charged for each cup cake = $3

Charges total, T = 3·c + 33

Part 1

The number of cupcakes that makes cost for the two options to be the same is found as follows;

The equivalent cost is the point where the equations for the total cost are also equivalent, therefore;

When the cost are the same; T = T and 2·c + 43 = 3·c + 33

2·c + 43 = 3·c + 33

3·c - 2·c = 43 - 33 = 10

c = 10

The number of cupcakes that makes the cost the same is 10 cup cakes

When the costs are the same; T = 2·c + 43, c = 10, therefore;

T = 2 × 10 + 43= 63

The charges at each store when the cost are the same is $63

The point on the graph of both equations at which the charges are the same is therefore the point (x, y) = (10, 63), which is the solution of the system of equations.

x-value is 10, which is the number of cupcakes

y-value is 63, which is the total cost

The correct option is therefore;

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The solution to  to log subscript 2 baseline (2 x cubed minus 8) minus 2 log subscript 2 baseline xx = 1x = 2x = 3x = 4 is 2 log₂ (x³ - 8) - 2 log₂ x = -2.

A logarithm expression is an expression in which the unknown value is expressed as the power to which a base number must be raised to produce a given number. For example, the equation log₂ 8 = 3 can be expressed as 2³ = 8.

A logarithm function is a type of mathematical function that calculates the logarithm of a given number. Logarithm functions are commonly used in mathematics, engineering, and science to simplify calculations. Logarithm functions can also be used to convert between different units of measurement.

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So Katya's rectangular table is 1.6 meters long and 3/4 meters wide, with an area of 1 1/5 square meters.

Area is a measure of the size of a two-dimensional surface, such as the surface of a shape or object. It is usually measured in square units, such as square meters, square centimeters, square feet, or square inches. The area of a shape tells us how much surface area it covers, and is often used in a variety of fields, such as architecture, engineering, and physics. For example, the area of a room can help determine how much flooring is needed to cover it, the area of a building facade can help determine how much material is needed to cover it, and the area of a wing can help determine its lift and drag characteristics in aerodynamics.

Here,

Let's start by using the formula for the area of a rectangle:

A = lw

where A is the area, l is the length, and w is the width.

We are given that the width of the table is 3/4 meters, so we can substitute this value into the formula and simplify:

A = l(3/4)

l = (4/3)A

Next, we are told that the table has an area of 1 1/5 m^2. We can convert this mixed number to an improper fraction by multiplying the whole number by the denominator and then adding the numerator:

1 1/5 = (5*1 + 1)/5 = 6/5

So the area of the table is 6/5 m^2. Substituting this value for A in the formula above, we get:

l = (4/3)(6/5)

l = 8/5 m

Therefore, the length of the table is 8/5 meters, or 1.6 meters when converted to a decimal.

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Formula for the difference of cubes are,

⇒ x³ - y³ = (x - y) (x² + xy + y²)

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

To find the difference of cubes of two numbers.

Now, Let two numbers are x and y.

Hence, Formula for the difference of cubes of numbers x and y are,

⇒ x³ - y³ = (x - y) (x² + xy + y²)

Thus, Formula for the difference of cubes are,

⇒ x³ - y³ = (x - y) (x² + xy + y²)

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10352 grade point averages must be obtained. The solution has been obtained by using the concept of sample size.

What is sample size?

The sample size is the number of observations utilised to derive estimates for a certain population. By taking a sample from the population, the sample size was established. Sampling is the practise of selecting a subset of the population to infer characteristics about the complete population.

We know that for 99% confidence, the z- score is 2.5758

So, using this we get

N = (z * σ/E)²

N = (2.5758 * 0.79/0.02)²

N = 10351.86

Hence, 10,352 grade point averages must be obtained so that the sample mean is within 0.2 of the population mean.

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The solution is, the average speed of the boat relative to the water is 9 mph

Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

Speed = Distance/ Time

here, we have,

Let x represent the speed of the boat.

The rate of the current was 7 mph,

Assuming the boat travelled against the current while going upstream, the total speed would be x - 7

Assuming the boat in the direction of the current while going downstream, the total speed would be x + 7

Time = speed × time

Since she travelled 32 miles upstream and 32 miles downstream, then,

Time taken to go upstream = 32/(x -7)

Time taken to go downstream = 32/(x + 7)

Since the total time of the trip was 18 hours, then

32/(x -7) + 32/(x + 7) = 18

Cross multiplying by (x - 7)(x + 7), it becomes

32(x + 7) + 32(x - 7) = 18[(x - 7)(x + 7)

32x + 224 + 32x - 224 = 18(x² + 7x - 7x - 49

32x + 32x = 18x² - 882

18x² - 64x - 882 = 0

Dividing through by 2, it becomes

9x² - 32x - 441 = 0

9x² + 49x - 81x - 441 = 0

x(9x + 49) - 9(9x + 49) = 0

x - 9 = 0 or 9x + 49 = 0

x = 9 or x = - 49/9

Since the speed of the boat cannot be negative, then x = 9

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The key features of this rational function include the following:

Domain: (-∞, 2) ∪ (2, ∞)

Range: (-∞, -2) ∪ (-2, ∞)

Y-intercept: -7/2.

X-intercept: 7/2.

Vertical asymptote: x = 2.

Horizontal asymptote​: y = -2.

In Mathematics, a rational function simply refers to a type of function  which is expressed as a fraction. This ultimately implies that, a rational function is composed of two (2) main parts and these include the following:

Additionally, the horizontal extent of any graph of a rational function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left of the graph to the right.

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The value of n(A) is 35 if n(B) = 35, n(A nB) = 15, and n(A U B) = 55.

A set is a collection of well defined objects.

We can use the formula: n(A U B) = n(A) + n(B) - n(A nB)

Substituting the given values, we get:

55 = n(A) + 35 - 15

Simplifying, we get:

55 = n(A) + 20

Subtracting 20 from both sides, we get:

n(A) = 35

Therefore, the value of n(A) is 35.

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The $500,000 and $350,000 invested by Mario and Luigi, and the $3 million profit from the business in the first year indicates;

a) The amount Luigi made a day is about $3,384.4

b) The amount Luigi made per hour is about $141

Profit is the revenue, less costs, expenses and tax.

The amount Mario invests = $500,000

Amount Luigi invests = $350,000

The ratio in which the profit was split after their first year = Within the same ratio of their initial investments

The amount of profit made by the business = $3 million

The ratio of their initial investment = 500,000 : 350,000 = 10 : 7

Therefore, the ratio in which the profit is split = 10 : 7

The amount Luigi received in a year = (7/(10 + 7)) × 3 = 1235294 2/17

The time unit conversion from year to day is presented as follows;

Number of days in a year = 365 days

The amount Luigi received peer day = (1235294 2/17)/365 = 3384 456/1241

3384 456/1241 ≈ 3384.4

b) The number of hours in a day = 24 hours

Amount Luigi received per hour = (3384 456/1241)/24 = 141 19/1241

141 19/1241 ≈ 141

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The Area of Trapezoid of figures given below.

The area of a trapezoid is found using the formula, A = ½ (a + b) h,

where 'a' and 'b' are the bases (parallel sides) and 'h' is the height (the perpendicular distance between the bases) of the trapezoid.

Given:

1. Area of Trapezoid

= 1/2 ( a+ b) x h

= 1/2 (22+ 11) x 12

= 33 x 6

= 198 m²

2. Area of Trapezoid

= 1/2 ( a+ b) x h

= 1/2 (38+ 24) x 26

= 806 mm²

3. Area of Trapezoid

= 1/2 ( a+ b) x h

= 1/2 (105 + 212) x 78

= 12363 Km²

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Answer:

A = 20 ft²

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 5 and h = 8 , then

A = [tex]\frac{1}{2}[/tex] × 5 × 8 = [tex]\frac{1}{2}[/tex] × 40 = 20 ft²

Answer:

The movie theater sold 85 large bags of popcorn and 204 small bags of popcorn.

Step-by-step explanation:

Let's use the following variables to represent the number of large and small bags of popcorn sold:

L: the number of large bags of popcorn sold

S: the number of small bags of popcorn sold

We can then write a system of equations based on the information given in the problem:

L + S = 289 (the total number of bags sold is 289)

4L + S = 544 (the total revenue from popcorn sales is $544)

To solve for L and S, we can use the method of substitution. Rearrange the first equation to solve for one variable in terms of the other:

L = 289 - S

Substitute this expression for L in the second equation and solve for S:

4(289 - S) + S = 544

1156 - 4S + S = 544

3S = 612

S = 204

Now that we know that 204 small bags of popcorn were sold, we can use the first equation to solve for L:

L + S = 289

L + 204 = 289

L = 85

Therefore, the movie theater sold 85 large bags of popcorn and 204 small bags of popcorn.

The exponential function that best matches the graph is given as follows:

E. y = 4^(x + 1).

An exponential function, with horizontal asymptote at y = 0, is defined as follows:

y = ab^x.

In which:

From the graph, when x = 0, y = 4, hence the parameter a is given as follows:

a = 4.

When x = -1, y = 1, meaning that when x increases by one, y is multiplied by 4, hence the parameter b is given as follows:

b = 4.

Hence the function is defined as follows:

y = 4(4)^x

y = 4^(x + 1).

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the area of the rectangle will be 1.5w².

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.

Area of rectangle is A = a*b

The given length of the rectangle is w

The width will be 1.5w

So the rectangle of the white figure is Area = w*1.5w = 1.5 w²

hence the area of the rectangle will be 1.5w².

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Answer:

C revenue

Step-by-step explanation:

The option is (B) The entire solution region is viable is correct when both the inequalities are solved.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

Let's first translate the given information into mathematical inequalities -

The perimeter of the tabletop to be no more than 28 feet -

Perimeter = 2(length + width) ≤ 28

The length of the tabletop to be greater than or equal to the square of 2 feet less than its width -

Length ≥ (Width - 2)²

We can combine these two inequalities to form the system -

2(length + width) ≤ 28

Length ≥ (Width - 2)²

Now, let's solve for y in terms of x (so that we can graph the solution region) -

2(y + x) ≤ 28

y ≥ (x - 2)²

Simplifying the first inequality -

y ≤ -x + 14

Now graph both the inequalities -

The viable solutions are the points that satisfy both inequalities, which lie in the shaded region above.

Therefore, there is no part of the solution region that includes negative length or negative width.

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a. The angle generated by P in time t is pi radians.

b. The distance traveled by P along the circle in time t is 16pi cm.

c. The linear speed of P is 2pi cm/sec.

What is angular speed ?

Angular speed, also known as rotational speed, is a measure of how fast an object is rotating around a fixed point. It is typically measured in radians per second and is denoted by the symbol "ω" (omega).

Angular speed is calculated as the change in angle (measured in radians) divided by the time it takes to make that change. In other words, it is the rate at which the angle is changing over time.

Angular speed is an important concept in physics and engineering, as it is used to describe the motion of rotating objects such as wheels, gears, and turbines. It is also used to calculate other important parameters such as linear speed, centripetal force, and torque.

The problem involves finding the properties of a point P that is rotating around a circle with a given radius r and angular speed omega. The problem provides the values of r, omega, and t and asks to find the angle generated by P in time t, the distance traveled by P along the circle in time t, and the linear speed of P.

(a) To find the angle generated by P in time t, we use the formula for angular displacement:

theta = omega * t

Here, omega is given as pi/8 radians per second and t is given as 8 seconds. We substitute these values to get:

theta = (pi/8) * 8 = pi radians

Therefore, the angle generated by P in time t is pi radians.

(b) To find the distance traveled by P along the circle in time t, we use the formula for arc length:

s = r * theta

Here, r is given as 16 cm and theta is calculated in part (a) as pi radians. We substitute these values to get:

s = 16 * pi = 16pi cm

Therefore, the distance traveled by P along the circle in time t is 16pi cm.

(c) To find the linear speed of P, we use the formula for tangential velocity:

v = r * omega

Here, r is given as 16 cm and omega is given as pi/8 radians per second. We substitute these values to get:

v = 16 * (pi/8) = 2pi cm/sec

Therefore, the linear speed of P is 2pi cm/sec.

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.

The cumulative frequency graph indicates that the percentage of the vehicles that go over the 30 mph speed limit is about 62.6% which more than the allowable 20%, therefore, a speed camera will have to be installed.

The cumulative frequency is the sum of the frequency up to an interval. The cumulative frequency indicates the total number of observations located above or below a value.

The cumulative frequency graph indicates the value of the sum of the number of vehicles travelling at a particular speed, therefore;

The cumulative frequency of cars traveling at 20 mph = 13

Cumulative frequency of cars traveling at 10 mph = 8

The cumulative frequency if the cars travelling at 30 mph = 50

Cumulative frequency of the cars travelling at 40 mph = 59

The cumulative frequency of the cars traveling at 50 mph = 60

Number of cars that go over the 30 mph speed limit = 59 + 60 = 119

Percentage of the cars that go over the 30 mph is therefore;

The percentage of cars that go over the 30 mph speed limit is 62.6% which is more than the 20%, therefore;

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let's say the segment with A(-5 , -8) and B(10 , 7) gets partitioned by point C

[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-5,-8)\qquad B(10,7)\qquad \qquad \stackrel{\textit{ratio from A to B}}{3:2} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{3}{2}\implies \cfrac{A}{B} = \cfrac{3}{2}\implies 2A=3B\implies 2(-5,-8)=3(10,7)[/tex]

[tex](\stackrel{x}{-10}~~,~~ \stackrel{y}{-16})=(\stackrel{x}{30}~~,~~ \stackrel{y}{21}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-10 +30}}{3+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-16 +21}}{3+2} \right)} \\\\\\ C=\left( \cfrac{ 20 }{ 5 }~~,~~\cfrac{ 5}{ 5 } \right)\implies C=(4~~,~~1)[/tex]

Answer:

( 4, 1 )

Step-by-step explanation:

The possible lengths of side AB as required to be determined in the task content are; 17.2, 15.59 and 8.

It follows from the task content that the length measures which are possible for side AB be determined.

By the triangle inequality theorem;

AB < 7 + 12; AB < 19

and

AB > 12 - 7; AB > 5

On this note, 5 < AB < 19.

Consequently, the possible lengths of side AB as required are; 17.2, 15.59 and 8.

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Answer:

x=-15, y=26

Step-by-step explanation:

The equation is  (4.5-0.7)/5 and length of each piece is 0.74

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

He has a piece of wood that is 4.5 feet long.

After cutting five equal pieces of wood from it, he has 0.7 feet of wood left over

an equation that could be used to determine the length of each of the five pieces of wood he cut

legth of each piece is = (4.5-0.7)/5

The total length is 4.5  and the leftover is 0.7, so used wood is total minus left ove

Length of each piece is used woof by number if pieces

(4.5 - 0.7)/5 = 3.7/5 = 0.74

Therefore, the equation is  (4.5-0.7)/5 and legth of each piece is 0.74

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$5

$5 is the y intercept, so that would be the delivery fee. Also, each pizza costs $10

Using the Hamilton's method of apportioning of seats, the five countries will get the following number of seats:

Adams = 7

Grant =7

Colton= 11

Davis= 5

Hayes= 2

Total = 7+7+11+5+2 = 32 seats

To calculate the number of seats, first find the Standard Divisor (SD). That is: SD = Total population / Number of seats available

Total population = 213,000+225,000+351,000+158,000+70,000 = 1,017,000

Then divide the total population by number of seats available (32).

That is: SD = 1,017,000/32

SD = 31,781.25

Find the Standard Quota (SQ) for each county by using the formula;

SQ = County population / SD

Adam's SQ = 213,000/31,781.25 = 6.70

Grant's SQ = 225,000/31,781.25 = 7.08

Colton's SQ = 351,000/31,781.25 = 11.04

Davis's SQ = 158,000/31,781.25 = 4.97

Hayes's SQ = 70,000/31,781.25 = 2.20

Find the Lower Quota for each county and find the total number of occupied seats:

Adams = 7

Grant =7

Colton= 11

Davis= 5

Hayes= 2

Total = 7+7+11+5+2 = 32 seats

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Answer:

1. The wholesale cost of the bike is $93.75.

2. Andre will pay $100 before tax.

Answer:

The probability that the couple have two girls and then a boy is 1/8 (12.5%).

Step-by-step explanation:

Tree diagrams show probabilities for sequences of two or more independent events.

To draw a tree diagram showing the given information:

See the attachment for the tree diagram.

To find the probability that the couple have two girls and then a boy, multiply along the branches representing those events.

Therefore, the probability that the couple have two girls and then a boy is:

[tex]\sf P(girl)\;and\;P(girl)\;and\;P(boy)=\dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2}=\dfrac{1}{8}=12.5\%[/tex]

Answer:

1/8 or 0.125 (12.5%).

Step-by-step explanation:

Using the tree diagram, we can see that there are 8 possible outcomes for the gender of the three children: BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG. Since each outcome is equally likely, the probability of any one outcome is 1/8.

The outcome we are interested in is GGB, which has a probability of 1/8. Therefore, the probability that the family has two girls, and then a boy is 1/8 or 0.125 (12.5%).

V = r²h where,

V is the volume of the cylinder

r is the radius of the cylinder

h is the height of the cylinder

in this case, h is the value we want to find, h, r is 3m and V is 155.43m³ !!

155.43 = × (3)² × h

17.27 = × h

h = 5.4972117...

= 5.50m (3.s.f) = height of cylinder

hope this helped, if you have any questions feel free to ask !! :D