Adding and subtracting fractions
1 These diagrams show the distances four cyclists have cycled.
Write a calculation of the total distance each cyclist cycled.
a -
7/8 km
9/10 km
3/2km​

The decimal expansion of the following fraction 1/3 would be; 0.33

A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.

We need to find the expression of  1 divided by 3.

A negative divided by a negative is positive, then;

1/3 = 0.33

Therefore, The value of expression 1/3 would be; 0.33

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Answer:

D. 4x² - x / x² - x - 2

Step-by-step explanation:
First cross multiply then sum the results:

cross:

x(x + 2) = x² + 2x

3x(x - 1) = 3x² - 3x

sum the results of the cross:

x² + 2x + 3x² - 3x

4x² - x (this goes at the top)

Then multiply the bottom:

(x - 1 )(x + 2)

x² + 2x - x - 2

x² - x - 2 (this stays at the bottom)

Fraction ends up like:

4x² - x / x² - x - 2

Step-by-step explanation:

2y+y=180(Sum of supplementey angle)

3y=180

y=180\3

The Range  and standard deviation of the set of data 11, 8, 5, 11, 25 is 20 and 7.68 respectively.

What is mean ?

Mean can be defined as the ratio sum of the observations and total number of observations.

Given

set of data,

11, 8, 5, 11, 25

we have to find the range and standard deviation,

We know that,

range = max - min

here max = 25

min = 5

range = 25-5

range = 20

Standard deviation ,

= √( ( Σx^2 - (Σx)^2 / n ) / (n-1)  )

= √( ( Σ11^2+8^2+5^2+11^2+25^2 - (Σ60)^2 / 5 ) / (5-1)  )

= √( ( 956 - (3600)^2 / 5 ) / (5-1)  )

= √( ( 956 - 720) / 4  )

= √( 59 )

=  7.68

Hence, The Range  and standard deviation of the set of data 11, 8, 5, 11, 25 is 20 and 7.68 respectively.

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Answer:

A is ST, PR, and UV

B is rays SQ and QT

C is point Q

D is Points S, Q, and T

Answer: Samantha bought 7 tickets for a concert

Step-by-step explanation:

$11.00 + $9.00 + $8.00 = 28

$196 / 28 = 7

The door frame is not rectangular.

If the door frame is rectangular, the sum of the square of the height and the width would be equal to the square of the diagonal.

Height² + width = diagonal²

213² + 92²

45,369 + 8,463 = 53,833

231² = 53,361

53,833 ≠ 53,361

The door frame is not rectangular because the sum of the height and the width is not equal to the diagonal.

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The measure of diagonal in a rectangular pool is 13.9 meters. Therefore, option A is the correct answer.

Given that, a rectangular pool is 7 meters wide and 12 meters long.

What is the Pythagoras theorem?

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

We know that, measure of each angle in a rectangle is 90°.

Let the length of diagonal of rectangular pool be x

So using Pythagoras theorem, we get

x²=12²+7²

⇒ x²=144+49

⇒ x²=193

⇒ x=√193

⇒ x=13.89

≈13.9 meters

The measure of diagonal in a rectangular pool is 13.9 meters. Therefore, option A is the correct answer.

The probability that a Dutch male is taller than 195 cm is  0.2525

Out of a random sample of 1000 Dutch men, people taller than 190 cm are 253 in number using statistics.

Mean = 183 cm

SD = 10.5 cm

Z score = ( Value - Mean ) /SD

Dutch male is shorter than 175 cm

Z score = ( 175 - 183)/10.5  = -0.762

from z score table   probability is  0.223

Dutch male is taller than 195 cm

Z score = ( 195 - 183)/10.5  = 1.143

from z score table   probability is  0.8735 for shorter than 195 cm

Hence probability that a Dutch male is taller than 195 cm = 1 - 0.8735

= 0.1265

Dutch male is between 173 and 193 cm  

Z score = ( 173 - 183)/10.5  = -0.952        =>  0.1705Z score = ( 193 - 183)/10.5  =  0.952         => 0.8295

0.8295 -  0.1705  =0.659

taller than 190 cm

Z score = ( 190 - 183)/10.5  = 0.6667

taller than 190 cm  = 1 -  0.7475   =  0.2525

Hence in 1000  = 252.5  = 253

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The complete question is :

Height of Dutch Men. Males in the Netherlands are the tallest, on average, in the world with an average height of 183 centimeters (cm) (BBC News website). Assume that the height of men in the Netherlands is normally distributed with a mean of 183 cm and standard deviation of 10.5 cm.a.What is the probability that a Dutch male is shorter than 175 cm?b.What is the probability that a Dutch male is taller than 195 cm?c.What is the probability that a Dutch male is between 173 and 193 cm?d.Out of a random sample of 1000 Dutch men, how many would we expect to be taller than 190 cm?

Answer: a. The equation using the information as it is given above that can be solved to answer this question is:

distance = speed x time

Let t be the amount of time Krystal spent driving from Houston to Philadelphia.

distance = 50t + 60(46 - 25 - t)

b. To find the distance between Houston and Philadelphia, we can substitute the known values into the equation and solve for t.

distance = 50t + 60(46 - 25 - t)

distance = 50t + 60(21) - 60t

distance = 50t + 1260 - 60t

distance = -10t + 1260

To find the total distance, we can set t = 25

distance = -10(25) + 1260

distance = -250 + 1260

distance = 1010

Therefore, Houston is 1010 miles from Philadelphia, to the nearest mile.

Step-by-step explanation:

The required area of the white part of the flag is 612 Square inches.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

We have,

Width = 8(1/2) = 17/2 In

Length = 72 In

Area of the white part of the flag is

= 17/2 ×  72

= 612 Square inches

Thus, required area is 612 Square inches.

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The white portion of the flag must have a 612 square inch area.

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Answer: The cost of both services is equal when h = 2 hours.

Step-by-step explanation: The shared point on the table is when the cost of the two services is equal, i.e. when C1 = C2, where C1 is the cost of Five Seconds of Summer's service and C2 is the cost of Fall Out Boy's service.

To graphically solve the system, we can plot the two equations on the same coordinate plane. The x-axis represents the number of hours and the y-axis represents the cost. The equation for Five Seconds of Summer's service would be y = 5 + 5x and the equation for Fall Out Boy's service would be y = 9 + 3x

We can then find the point of intersection of the two lines, which represents the point at which the cost of the two services is equal. We can label this point as (x, y) and our solution.

To solve the system algebraically using substitution, we can set C1 = C2 and solve for the number of hours (h) in terms of cost.

C1 = 5 + 5h = C2 = 9 + 3h

5 + 5h = 9 + 3h

2h = 4

h = 2

So, the cost of both services is equal when h = 2 hours.

From the above result, it is clear that Fall Out Boy's service is cheaper than Five Seconds of Summer's service. For 2 hours of tutoring, the cost of Fall Out Boy's service is $9 + 3(2) = $15 and the cost of Five Seconds of Summer's service is $5 + 5(2) = $15.

However, there could be scenarios where one service is cheaper than the other depending on the number of hours of tutoring required. For example, if a student requires more than 4 hours of tutoring, Five Seconds of Summer's service would be cheaper. And if a student requires less than 2 hours of tutoring, Fall Out Boy's service would be cheaper.

In conclusion, the best option would depend on the number of hours of tutoring required, and it is best to check both options and compare the cost before making a decision

Answer:

To compare the costs of the two tutoring services, we can set up a system of equations. Let x be the number of hours of tutoring.

Five Seconds of Summer's tutoring service:

y = 5 + 5x (base charge of $5 and $5 per hour)

Fall Out Boy's tutoring service:

y = 9 + 3x (base fee of $9 and $3 per hour)

We can make a table to compare the costs of the two services at different number of hours:

Hours (x) Five Seconds of Summer (y) Fall Out Boy (y)

0                                 5                          9

1                                 10                         12

2                                 15                         15

3                                 20                         18

4                                      25                         21

The shared point in the table is when x = 0, y = 5 for Five Seconds of Summer's tutoring service and y = 9 for Fall Out Boy's tutoring service.

We can graph the two equations to compare the costs:

[Graph would be here if I were able to create one]

From the graph we can see that for any number of hours greater than 0, Five Seconds of Summer's tutoring service is cheaper.

We can also solve the system algebraically using substitution.

y

The statement regarding ethical considerations in experimental designs that is not necessarily true is that it is  unreasonable for a study to knowingly cause harm to an individual, even if that individual has given consent.

Therefore the answer is option B. It is unreasonable for a study to knowingly cause harm to an individual, even if that individual has given consent.

This statement is not necessarily true because there are some situations where knowingly causing harm to a person may be ethical in the context of medical research, such as in the case of trials for life-threatening diseases where no other treatments are available. However, in such cases, strict ethical review and oversight is usually required to ensure that the risks are minimized and that the participants are fully informed of the risks involved.

In ethical considerations in experimental designs, it is generally accepted that participants should be fully informed of the risks involved in a study and should give their informed consent before participating. This means that they should be aware of what is going to happen during the experiment, what benefits and risks are associated with participating, and what their rights are as participants.

However, there are some situations where knowingly causing harm to a person may be considered ethical in the context of medical research, such as in trials for life-threatening diseases where no other treatments are available. In such cases, strict ethical review and oversight is usually required to ensure that the risks are minimized and that the participants are fully informed of the risks involved.

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The gallons consumed when car A travels 300 mi of city driving plus 100 mi of highway driving is 12.66 gallons

The gallons consumed when car B travels 300 mi of city driving plus 100 mi of highway driving is 13.37 gallons

The gallons consumed when car A travels 100 mi of city driving plus 300 mi of highway driving is 13.74 gallons

The gallons consumed when car B travels 100 mi of city driving plus 300 mi of highway driving is 12.54 gallons

Gallons consumed when car A travels 300 mi of city driving plus 100 mi of highway driving = (300 / 33) + (100 / 28)

= 9.09  + 3.57 = 12.66 gallons

Gallons consumed when car B travels 300 mi of city driving plus 100 mi of highway driving = (300 / 29) + (100 / 33)

= 10.34 + 3.03 = 13.37 gallons

Gallons consumed when car A travels 100 mi of city driving plus 300 mi of highway driving = (100 / 33) + (300 / 28)

= 3.03 +  10.71 =13.74 gallons

Gallons consumed when car B travels 100 mi of city driving plus 300 mi of highway driving = (100 / 29) + (300 /33)

= 3.45 + 9.09 = 12.54 gallons

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Answer: Income Statement:

Revenue: _________

Expenses: _________

Net Income: _________

Statement of Stockholders' Equity:

Beginning Balance:

Common Stock: $550,000

Retained Earnings: $46,000

Total: $596,000

Additions:

Common Stock: $32,000

Total: $628,000

Deductions:

Dividends: $24,000

Total: $604,000

Ending Balance:

Common Stock: $550,000

Retained Earnings: $50,000

Total: $600,000

Note: I've left the Revenue, Expenses and Net Income section in the income statement blank as it is not provided in the question. It is also important to note that these are just examples and the numbers may not match with the actual financial statement.

Step-by-step explanation:

Answer: In a real-life representation of the multiplication problem "15 (2/5) = 6," we can imagine a bag of 15 items, each of which is 2/5 of a whole. To find out how many whole items are in the bag, we can multiply 15 (the number of items) by 2/5 (the fraction of each item that is a whole).

The result of 6 represents the number of whole items in the bag.

Step-by-step explanation:

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By multiplying the mean of random variable X by two to four, the random variable Y's mean is calculated to be 20. (5). By dividing the X standard deviation (25), by 4, the standard deviation of Y is equal to 102.

The random variable X has a mean of 5 and a standard deviation of 25. A normal distribution's mean serves as its nucleus, and the standard deviation quantifies how much the values deviate from the mean. Y = 2 + 4X is the definition of the random variable Y. By adding 2 to the mean of X (5), we can determine the mean of Y, which equals 20. By dividing the standard deviation of X (25), by 4, we can determine the standard deviation of Y, which yields a standard deviation of 102 for Y. As a result, the standard deviation is 102 and the mean of Y is 20.

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A compound event is a combination of multiple simple events that can occur simultaneously or independently. When talking about coin flipping, the sample space is the set of all possible outcomes of the experiment, which in this case is flipping a coin 3 times. In this case, the sample space is {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}.

Option A, You get exactly 2 tails, is a compound event because it consists of three simple events, THT, HTH, and TTH. These events can happen independently of one another and therefore, it is a compound event.

Option B, You get exactly 3 tails, is not a compound event because it only consists of one simple event, TTT. This event is not a combination of other simple events and is, therefore, not a compound event.

Option C, This is not an event, is not a valid option as it is not a possible outcome.

Option D, You get exactly 3 heads, is also a compound event because it consists of one simple event, HHH. This event can happen independently of other simple events and it is, therefore, a compound event.

Hence, options A and D are compound events as they are a combination of multiple simple events that can happen independently or simultaneously.

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The exponential equation that represents the relationship between the air pressure and the elevation above the Earth's surface is

y = 14.7 x 0.827^x

The air pressure at the top of Mount Everest, elevation 29,000 feet is approximately 1.931 psi

To write an exponential equation for the relationship between the air pressure and the elevation above the Earth's surface, we can use the form y = a x b^x,

where y is the air pressure,

x is the elevation,

and a and b are constants.

We can use the data given in the problem to find the values of a and b.

Let y = air pressure (psi)

x = elevation (feet)

We know that at sea level (x = 0), y = 14.7 psi

At Denver, Colorado, elevation 5280 feet, y = 12.15 psi

We can use these two points to find the values of a and b in the equation y = a x b^x

12.15 = 14.7 x b^5280

b = (12.15/14.7)^(1/5280)

b = 0.827

a = 14.7

The exponential equation that represents the relationship between the air pressure and the elevation above the Earth's surface is

y = 14.7 x 0.827^x

b.) To find the air pressure at the top of Mount Everest, elevation 29,000 feet, we can substitute that value for x into the exponential equation.

y = 14.7 x  0.827^29000

y = 1.931 psi

The air pressure at the top of Mount Everest, elevation 29,000 feet is approximately 1.931 psi. It's worth noting that this is a very low air pressure and the human body is not able to survive with such low pressure without proper equipment.

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Answer: 14

Step-by-step explanation:

The two triangles are not congruent

According to the triangle congruency laws, triangles are considered congruent when their sides and angles are equal.

The rules include

Side - Side - Side = SSS

Side, Angle, and Side = SAS

Angle Side Angle = ASA

Angle, Angle, and Side. = AAS

Hypotenuse and one leg. = HL

In the problem no information is given about the sides and just one angle is given.

Even though, for the figure it can be deduced that one side is equal but the information is not enough to determine if the triangles are congruent

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The triangles are congruent by AAS (Angle-Angle-Side) and not by ASA (Angle-Side-Angle)

When the corresponding length of sides or measure of the internal angles of two or more triangles are equal, then the triangles are said to be congruent. The congruency can be expressed in terms angles, sides, or the combination of sides and angles. An example is the SAA (Side-Angle-Angle) property which implies that a side that is not an included angle and other angles are congruent.

Considering triangles ABC and CDE, it can be seen that two angles are congruent and a side of both are congruent. Since the congruent side is not an included angle, then the congruent relations is AAS (Angle-Angle-Side).

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Using slope of the graph, The average rate of change in dollars per year for this time period is -220.

You may determine the slope of the line by determining the rise and the run using two of the line's points. The rise and the run are terms used to describe changes in height between two points. Rise divided by Run gives you the slope. Rise/run on a slope Rise or run is a slope.

We have coordinates that represent the given information,

Let x = number of year,

Y = Change in income,

So, Our coordinates become = (0, 31560) and (13, 28700)

The average rate of change is defined as slope of the graph

Slope of graph = y2 - y1 / x2 - x1

⇒ 28700 - 31560 / 13 - 0

⇒ -2860 / 13

⇒ - 220

The value of slope is negative, which indicates depreciation.

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The triangles are congruent if two of one triangle's sides and its included angle are the same as the corresponding sides and angles of another triangle.

The complete question is,

To what extent can the congruence of the triangles be demonstrated?

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The area of triangle with three sides a,bc is equals to  

√[s × (s – a) × (s – b) × (s – c)].

What is triangle ?

Triangle can be defined as in which it consists of three sides, three angles and sum of the three angles are 180 degrees always.

Given

in the triangle with three sides a,b,c.

Let ABC be a triangle such that the length of the 3 sides of the triangle is AB = c, BC = a and CA = b.

The semi-perimeter of triangle ABC = s = (a + b + c)/2

Then, the area of triangle ABC = √[s × (s – a) × (s – b) × (s – c)].

Therefore, The area of triangle with three sides a,bc is equals to  

√[s × (s – a) × (s – b) × (s – c)].

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The intersection of equations y=2x-2 and y= -2x^2 +4x+ 3 is y = 3

The general formula for the equation of a line is expressed as;

y = mx + c

Where the parameters are;

From the information given, we have the equation of the lines as;

Now, equate the lines, we have;

2x - 2 = -2x² + 5x + 3

collect the like terms

2x -5x + 2x² - 2 - 3 = 0

add the iike terms

2x² -3x - 5 = 0

Factorize the quadratic equation

2x² - 5x + 2x - 5 = 0

Group in pairs

(2x² - 5x) + (2x-5) = 0

x(2x -5) + 1(2x - 5) = 0

The intersection for when  x = 5/2

y = 2x - 2

y = 2(5/2) - 2

y = 3

Hence, the value is 3

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Answer:true

Step-by-step explanation:

The Banzhaf power distribution of the weighted voting system will be 34, 31, and 30.

List all the victorious coalitions, then tally the crucial voters, to determine a voter's power using the Banzhaf index. A crucial voter is someone whose vote, if it were altered from yes to no, would result in the measure's failure. The percentage of all swing votes that a voter may cast is used to determine that person's influence.

[30: 18, 16, 13, 12]

P₁, P₂ = 18 + 16 = 34

P₁, P₃ = 18 + 13 = 31

P₁, P₄ = 18 + 12 = 30

P₂, P₃ = 16 + 13 = 29

P₂, P₄ = 16 + 12 = 28

P₃, P₄ = 13 + 12 = 25

The Banzhaf power distribution of the weighted voting system will be 34, 31, and 30.

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