In how many ways cam 2 students be chosen from a group of 15?

Answer:

B) 102

Step-by-step explanation:

To find x, we need to simplify and solve the equation (5x+6)=(7x-12):

5x + 6 = 7x - 12 // distribute the 5 and 7

6 + 12 = 7x - 5x // group the x terms and constants

18 = 2x

Now, we can solve for x by dividing both sides by 2:

18/2 = x

9 = x

Therefore, x is 9.

To find the solution if x = 9, we can simply substitute 9 for x in the given expressions:

(5x+6) = (5(9) + 6) = 51

(7x-12) = (7(9) - 12) = 51

Therefore, both expressions are equal to 51 when x = 9.

The surface area of the square pyramid with a side length of 6 and a slant height of 5 is 96 square units.

To calculate the surface area of a square pyramid, we need to find the area of the square base and the area of each triangular face.

The formula for the surface area of a square pyramid is:

[tex]S = (a^2) + 2as[/tex]

where a is the length of one side of the square base and s is the slant height.

Plugging in the given values, we get:

[tex]S = (6^2) + 2(6)(5)[/tex]

[tex]S = 36 + 60[/tex]

[tex]S = 96[/tex]

Therefore, the surface area of the square pyramid with a side length of 6 and a slant height of 5 is 96 square units.

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P(stop at P|stop at Q) = P(stop at P and stop at Q) / P(stop at Q) is 28/47

How to solve questions?

(a) Tree diagram:

                 | P stop 7/20

                 |

          -------|-------

         |              |

   Q stop|  P stop 2/5  | P not stop 3/5

         |              |

    ------|-------      |    

         |              |

  Q not stop| P stop 1/10 | P not stop 9/10

         |              |

          -------|-------

                 |

                 | P not stop 13/20

(b) The probability that he has to stop at both P and Q is:

P(stop at P) * P(stop at Q|stop at P) = (7/20) * (2/5) = 7/50

(c) The probability that he has to stop at least once is:

P(stop at P and/or stop at Q) = 1 - P(not stop at P) * P(not stop at Q|not stop at P)

                             = 1 - (13/20) * (9/10) = 11/20

(d) If he has to stop at Q, the probability that he would have stopped at P is:

P(stop at P|stop at Q) = P(stop at P and stop at Q) / P(stop at Q)

                       = (7/50) / (13/20 * 2/5 + 7/50)

                       =28/47

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Thus, the given side of triangle with lengths of 63 inches, 73 inches, and 98 inches does not form a right triangle.

A triangle is considered to be correct when one of its angles is 90 degrees. Moreover, a right angle is one that measures 90 degrees or more.

The non-right angle measurements of right triangles must add up to 90 degrees, which is a crucial condition. This results from the fact that a triangle's total number of angles equals 180 degrees.

In right triangle, the longest side is called hypotenuse.

Then,

hypotenuse H = 98 inches

Let Side S1 = 63 inches,

Let Side S2 = 73 inches,

Then, Pythagorean theorem must satisfy for right triangle

H² = (S1)² + (S2)²

98² = (63)² + (73)²

9604 = 3969 + 5329

9604 = 9298

But, 9604 ≠ 9298

Thus, the given side of triangle with lengths of 63 inches, 73 inches, and 98 inches does not form a right triangle.

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Answer:

in second equation,

4x+2y=30

2(2x+y)=30

2x+y=15

Now,putting the value of x from above

2×(15-3y)+y=15

30-6y+y=15

30-15=5y

y=3

Then,

x=15-3×3

x=6

#(6,3) is ans

Answer:

(6,3)

Step-by-step explanation:

Answer:

she does not have enough!

Step-by-step explanation:

thirty percent of $28 is $8.4, so you would subtract the two leaving you with $19.6

2.5 sales tax of $19.6 is $0.49

Adding those two the total comes to $20.09 which is just over the budget!

Answer:  She does not have enough money.

She needs 9 cents (aka $0.09)

========================================================

Explanation:

A discount of 30% means Mary would pay the remaining 70% (because 100-30 = 70)

The decimal form of 70% is 0.70

Let A = 0.70 since we'll use it later.

An increase of 2.5% means we will also have the multiplier 1.025; which you can think of it like saying 100% + 2.5% = 1 + 0.025 = 1.025

Let B = 1.025 since we'll use it later

Multiply the values of A and B to get: 0.70*1.025 = 0.7175

This is the net multiplier when combining the 30% discount and 2.5% tax.

The original price $28 then becomes 0.7175*28 = 20.09 which is 9 cents (aka $0.09) over the goal of $20

Therefore, Mary does not have enough money to buy the book. She'll need that remaining 9 cents.

There are 2500 Shaded squares and 7500 unshaded squares in the 100x100 square, based on the given sequence in the diagram.

1. First, analyze the given diagram and observe the pattern. Notice that there are alternating shaded and unshaded squares, with the shaded squares being on the main diagonal.

2. Next, identify the sequence in the pattern. It appears that there is a continuous increase of shaded squares, starting from 1 and increasing by 2 each time. This forms an arithmetic sequence: 1, 3, 5, 7, and so on.

3. To find the number of shaded squares in the 100x100 square, calculate the sum of the first 50 terms of the sequence (since there are 100 rows/columns and each shaded area covers 2 rows/columns). The formula for the sum of an arithmetic sequence is: Sn = n * (a1 + an) / 2, where Sn is the sum of the sequence, n is the number of terms, a1 is the first term, and an is the last term.

4. In our case, n = 50, a1 = 1, and an = 99 (the 50th term in the sequence). Plugging these values into the formula, we get: S50 = 50 * (1 + 99) / 2 = 50 * 100 / 2 = 2500.

5. Thus, there are 2500 shaded squares in the 100x100 square.

6. To find the number of unshaded squares, subtract the number of shaded squares from the total number of squares in the 100x100 square. The total number of squares is 100 * 100 = 10,000.

7. Now, calculate the number of unshaded squares: 10,000 - 2500 = 7500.

In conclusion, there are 2500 shaded squares and 7500 unshaded squares in the 100x100 square, based on the given sequence in the diagram.

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Hence, compared to the second plant, the first plant produces [tex]3x + 14[/tex]more things per day.

Production is the process of creating goods or services that can be used or consumed by individuals or other entities. It involves converting raw materials, labor, and capital into finished products or services that are suitable for sale or distribution in the market.

given

We must take the daily production of the second plant away from the daily production of the first plant in order to calculate how many more things are produced daily by the first plant than the second plant.

The first plant's daily output is equal to [tex]5x + 11.[/tex]

Daily output of the second plant is equal to [tex]2x - 3.[/tex]

As a result, the two facilities' daily production differences are as follows:

[tex](5x + 11) - (2x - 3) = 5x + 11 - 2x + 3[/tex]

[tex]= 3x + 14[/tex]

Hence, compared to the second plant, the first plant produces 3x + 14 more things per day.

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The rate of interest is 7.7 %  if £9000 has a final value of £13102 in 5 years

When interest is compounding, it indicates that the balance as a whole, rather than just the principal, is taken into account when the following interest period begins.

For instance, after a year, a $100 loan with 5% annual compound interest will have a debt of $105 due. The interest will be applied to the entire $105, creating a new amount of $110.25 the next year, rather than being taken as 5% of $100.

The interest will be added to that $110.25 the following year, and so on throughout the loan.

This is distinct from simple interest, which is a periodic payment to the loan holder of a fixed sum of money derived from a percentage of the principal

We have given that the final amount is 13102 and the principal amount is 9000 and time n is 5 years we have to find the rate

We have the formula

[tex]A=p(1-\frac{r}{100})^n[/tex]

A= 13102

P=9000

n=5

r = ?

[tex]13102=9000(1-\frac{r}{100})^5\\\\1.455=(1-\frac{r}{100})^5\\\\1.077=1-\frac{r}{100}\\\\r=7.7[/tex]

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Answer:

G

Step-by-step explanation:

The diagonal of a square is equal to the diameter of the circle in this case

d = 16 cm

r = 0,5 × d

r = 0,5 × 16 = 8 cm

The circumference of the circle is equal to:

[tex]c = 2\pi \times r[/tex]

[tex]c = 2\pi \times 8 = 16\pi \: {cm}^{2} [/tex]

Answer:

I will try my best with the given info

Step-by-step explanation:

Selection bias occurs when the selection of the sample is not random and is instead influenced by factors that are not related to the study objective. Here are some examples of selection bias in a survey of brown-eyed people:

A survey that only includes brown-eyed people from a specific geographic location, such as a single city or state. This would not be representative of the entire population of brown-eyed people.

A survey that only includes brown-eyed people who are members of a particular organization or club. This would not be representative of the entire population of brown-eyed people, as it would exclude those who are not members of the organization or club.

A survey that only includes brown-eyed people who have a certain level of education or income. This would not be representative of the entire population of brown-eyed people, as it would exclude those with different levels of education or income.

A survey that only includes brown-eyed people who are willing to participate in the study. This could result in a biased sample, as those who are not willing to participate may have different characteristics than those who are willing to participate.

In general, any selection process that is not random and does not provide equal opportunity for all members of the population to be included in the study can result in selection bias.

Mathematicians have used probability to determine how likely certain events are to occur. The possible values of  X will be 10, 0, -5 with following probabilities:

P(X = 10 ) = 0.23

P(X = 0 ) = 0.48

P(X = -5) = 0.29

Probability is the ability to happen. . From 0 to 1 is used to express the value. Whenever we are unsure of how an event will turn out, we can talk about the probabilities of various outcomes, or how likely they are. The study of probability-based events is often known as statistics. The amount of favorable outcomes and the overall number of outcomes thus affect how likely an event is to occur. The probability is typically expressed as a ratio between the number of positive outcomes and all of the outcomes in the sample space.

Given:

The probability distribution of X can be represented as:

X      P(X=x)

-5      0.29

0       0.48

10      0.23

The outcomes is attached as table below.

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The complete question is:

The table below to model the scenario is attached below:

Answer: 6666 and 3333

Step-by-step explanation: 5 or above give it a shove, 4 or below let it go.

The height of the poster storage tube is approximately 40 inches.

Vοlume is the amοunt οf space that a three-dimensiοnal οbject οccupies. It is measured in cubic units such as cubic meters, cubic feet, οr cubic inches. The fοrmula fοr calculating the vοlume οf a sοlid οbject depends οn its shape. Fοr example, the vοlume οf a cube can be calculated using the fοrmula V = s³, where s is the length οf a side, while the vοlume οf a cylinder can be calculated using the fοrmula V = πr²h, where r is the radius οf the base and h is the height.

The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height of the cylinder.

Since the diameter of the cylinder is given as 3.5 inches, the radius is half of that or 1.75 inches. Also, the volume is given as 122.5π cubic inches.

Therefore, we can use the formula to solve for the height:

V = π[tex]r^{2}[/tex]h

122.5π = π(1.75)(1.75)h

122.5 = 3.0625h

h = 122.5/3.0625

h ≈ 40

Therefore, the height of the poster storage tube is approximately 40 inches.

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the actual area of the park is 19,200 square feet.

Marcus drew a scale drawing of the rectangular park in his neighborhood. He drew the length of the park as 8 inches and the width of the park as 6 inches. The key on his drawing shows 1 inch=20 feet. To find the actual area of the park, we need to convert the measurements in Marcus's drawing to the actual measurements in feet.

Since 1 inch on Marcus's drawing represents 20 feet in actuality, we can use a scale factor of 1 inch : 20 feet to convert the measurements. We can then multiply the actual length and width of the park in feet to find the actual area of the park in square feet.

To convert the length of 8 inches to feet, we multiply it by the scale factor:

8 inches × (20 feet/1 inch) = 160 feet

Similarly, we can convert the width of 6 inches to feet:

6 inches × (20 feet/1 inch) = 120 feet

So the actual length of the park is 160 feet and the actual width of the park is 120 feet.

To find the actual area of the park, we multiply the actual length by the actual width:

160 feet × 120 feet = 19,200 square feet

Therefore, the actual area of the park is 19,200 square feet.

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After answering the presented question, we can conclude that As a equation result, for any x and y values, these expressions will be identical to 24x + 36y.

Expressions can be used to represent numerical or algebraic quantities, and can be used to perform calculations. For example, the expression "2 + 3" represents the sum of the numbers 2 and 3, which is 5. Similarly, the expression "x + 5" represents the sum of the variable x and the number 5, and can be evaluated to a specific value depending on the value of x.

[tex]12(2x-y)[/tex]

[tex]-6(4x-3y)[/tex]

[tex]3(x+12y)[/tex][tex]12(2x-y)=24x-12y[/tex]

So,[tex]24x-12y+24=24x+36y-6(4x-3y)=-24x+18y[/tex]

So,[tex]-24x+18y+42x+18y=24x+36y[/tex]

[tex]3(x+12y)=3x+36y[/tex]

So,[tex]3x+36y+21x-24y=24x+36y[/tex]

As a result, for any x and y values, these expressions will be identical to 24x + 36y.

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After answering the presented question, we can conclude that variable

a) equation to help Sofia figure out how much money was charged in fees is 365 = 59 × 5 + f

b) the amount of money charged for fees is $70.

A variable is something that can be altered in the context of a mathematical notion or experiment. Variables are frequently denoted by a single symbol. The characters x, y, and z are frequently used as generic variables symbols. Variables are qualities with a wide range of values that can be investigated. Size, age, money, where you were born, academic position, and type of housing are just a few examples. Variables can be classified into two major groups using both numerical and categorical methods.

a) Total cost = Cost per night × Number of nights + Fees

365 = 59 × 5 + f

b) Solving for f, we get:

f = 365 - 295

f = 70

Therefore, the amount of money charged for fees is $70.

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From the above calculations, we can see that the IQR changes the most with a difference of 3°. The new value of the IQR is 34°.

To determine which measure changes the most when a value of 71° is changed to 93°, we need to calculate each measure before and after the change. Mean:

The mean is calculated by adding all the temperatures and dividing by the total number of temperatures.

Before the change:

Mean = (58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12

= 82.3°

After the change:

Mean = (58 + 61 + 93 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12

= 84.8°

The difference between the means is: 84.8° - 82.3° = 2.5°

Median:

The median is the middle value when the temperatures are arranged in order.

Before the change:

Median = 82°

After the change:

Median = 84°

The difference between the medians is: 84° - 82° = 2°

Range:

The range is the difference between the highest and lowest temperatures.

Before the change:

Range = 105° - 57°

= 48°

After the change:

Range = 105° - 58°

= 47°

The difference between the ranges is: 47° - 48° = -1°

IQR:

The IQR is the difference between the third quartile and the first quartile.

Before the change:

Quartiles:

Q1 = 66°

Q3 = 97°

IQR = Q3 - Q1

= 97° - 66°

= 31°

After the change:

Quartiles:

Q1 = 66°

Q3 = 100°

IQR = Q3 - Q1

= 100° - 66°

= 34°                                        

The difference between the IQRs is: 34° - 31° = 3°

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The area of the shaded region is = area of the sector - the area of the right angle triangle. so the area is [tex]9\pi /4 -9/2[/tex]

Area of circle formula = [tex]\pi r^{2}[/tex]. The area of a circle is [tex]\pi[/tex] multiplied by the square of the radius. The area of a circle when the radius 'r' is given is [tex]\pi r^{2}[/tex]

The area of a circle when the diameter 'd' is known is [tex]\pi d\frac{2}{4}[/tex]. π is approx. [tex]3.14 or \frac{22}7}[/tex]. Area(A) could also be found using the formulas A = [tex](\frac{\pi}{4} )*d^{2}[/tex], where 'd' is the radius and A= [tex]\frac{c^{2} }{4\pi }[/tex], where 'C' is the given circumference.

According to the given information

The area of the shaded region is = area of the sector - the area of the right angle triangle.

A = [tex]9\pi /4 -9/2[/tex]

Therefore the area of the shaded region is = area of the sector - the area of the right angle triangle. so the area is [tex]9\pi /4 -9/2[/tex]

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Rounding this to the nearest whole number, we can estimate that about 407 customers would pay with a credit card next week.

How to estimate number of customers?

To estimate the number of customers who would pay with a credit card next week, we can use the proportion of customers who paid with a credit card in the last week as a guide.

First, we need to find the total number of customers who visited Omar's business in the last week:

Total customers = Cash customers + Debit card customers + Credit card customers

Total customers = 91 + 8 + 27

Total customers = 126

Next, we can find the proportion of customers who paid with a credit card:

Proportion of credit card customers = Credit card customers / Total customers

Proportion of credit card customers = 27 / 126

Proportion of credit card customers = 0.2143

Now, we can estimate the number of customers who would pay with a credit card next week by multiplying the total number of expected customers by the proportion of credit card customers from the last week:

Expected credit card customers = Total expected customers x Proportion of credit card customers

Expected credit card customers = 1900 x 0.2143

Expected credit card customers = 407.17

Rounding this to the nearest whole number, we can estimate that about 407 customers would pay with a credit card next week.

However, it is important to note that this estimate is based on the assumption that the proportion of customers paying with a credit card remains the same next week. Factors such as changes in consumer behavior or market conditions may affect this proportion, and hence, the accuracy of the estimate.

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The value of the given percent that satisfied the relation through which it justified it is 6.3 years.

What about percent?

Percent: A percent is a way of expressing a number as a fraction of 100. The symbol for percent is "%". For example, if you say that 50% of a group are females, it means that 50 out of every 100 people in the group are female. Percentages are often used to describe the proportion of something or to compare different quantities.

According to the given information:

90 % of 7 years

⇒  [tex]\frac{90}{100}[/tex] x 7 years

⇒ [tex]\frac{630}{100}[/tex]

⇒ 6.3 years

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Using the formula d = rt we have: Part A: Tom was driving at a speed of 50 miles per hour. Part B: Zac drove 100 miles. Part C: Dan drove for 2 hours.

The link between distance, rate, and time is demonstrated by the equation d = r*t. The product of the rate (r) and the time (t) yields the distance (d) (t). In other words, the velocity of motion and the amount of time spent travelling affect the distance covered. Assuming that the time spent travelling is constant, increasing the rate of movement will result in an increase in the amount of distance travelled in a given amount of time. According to this, as journey duration increases, so does the distance travelled.

The given formula is d = r(t).

Part A:

Tom drove a total of 150 miles in 3 hours, so:

150 miles = r * 3 hours

r = 50 miles per hour

Part B:

constant speed of 40 miles per hour for 2.5 hours, so:

d = 40 miles per hour * 2.5 hours

d = 100 miles

Part C:

constant speed of 40 miles per hour for 2.5 hours, so:

130 miles = 65 miles per hour * t

t = 130 miles / 65 miles per hour

t = 2 hours

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Note that the line plot or number line for the data above is given as attached.

1) To create an inequality for a line plot using the given data set, we can use the minimum and maximum distances as the endpoints of the inequality.

The minimum distance is 1 3/8, which is equivalent to 1.375 miles. The maximum distance is 3 1/4, which is equivalent to 3.25 miles.

Therefore, the inequality can be written as:

1.375 ≤ x ≤ 3.25

where x represents the distance of a ski trail in miles.

This inequality states that any value of x (distance of a ski trail) that is between 1.375 and 3.25, inclusive, is a valid value for the data set.


2. The total number of ski trails is 12.

3. The difference in length between the longest ski trail (3 1/4) and the shortest ski trail (1 3/8) is: 3 1/4 - 1 3/8 = 1 7/8

4. The total length of the ski trails that are 2 7/8 is:

2 7/8 + 2 7/8 + 2 7/8 = 8 1/4

5. The sum of the lengths of the shortest (1 3/8) and the longest (3 1/4) ski trails is:

1 3/8 + 3 1/4 = 4 5/8

6. Sam is correct. The longest ski trail is 3 1/4 miles and the shortest ski trail is 1 3/8 miles, so:

3 1/4 > 3 * 1 3/8

10 1/4 > 4 1/8

2.5 > 1

Therefore, the longest ski trail is indeed more than three times the length of the shortest ski trail.

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Therefore, the solution to fg(x) = gf(x) for the composite functions is x = -1/4.

A function is a mathematical rule that assigns a unique output for every input in a given set. In other words, it is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. A function can be represented using a formula, a graph, or a table of values. Functions are widely used in mathematics, science, engineering, economics, and many other fields to describe the relationship between variables and to make predictions based on data.

Here,

To solve fg(x) = gf(x), we need to find f(g(x)) and g(f(x)), and then set them equal to each other.

f(g(x)) = f(x + 1)

= 2(x + 1)²

= 2(x² + 2x + 1)

= 2x² + 4x + 2

g(f(x)) = g(2x²)

= 2x² + 1

Now we can set them equal to each other and solve for x:

2x² + 4x + 2 = 2x² + 1

Subtracting 2x² from both sides, we get:

4x + 2 = 1

Subtracting 2 from both sides, we get:

4x = -1

Dividing both sides by 4, we get:

x = -1/4

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Answer: b

Step-by-step explanation:

Therefore , the solution of the given problem of triangle comes out to be the triangle has a side c of 2.15 and angles A = 42.5°, B = 0°, and C = 40.3°.

If a polygon has at least one additional segment, it is a hexagon. Its structure is a simple rectangle. Something like this can only be distinguished from a regular triangular form by edges A and B. Euclidean geometry only creates a portion of the cube, despite the precise collinearity of the borders. A triangular has three sides and three angles.

Here,

The centers of the three circles must make an equilateral triangle because they are positioned so that they touch one another. Angles A and C are both 60 degrees, so we know this.

With lengths that are 5.4 and 4.4 in length, we can use the Law of Cosines to determine angle A:

=> cos(A) = (4.4² + 5.4² - 3.4²) / (2 * 4.4 * 5.4)

=> cos(A) = 0.731

=> A = cos⁻¹(0.731)

=>A ≈ 42.5°

We can apply the Law of Cosines once more to determine side b:

=> b² = 4.4² + 5.4^2 - 2 * 4.4 * 5.4 * cos(60)

=> b ≈ 2.15

Finally, we can apply the Law of Sines to determine angle C:

=> Sin(60) / 2.15 = sin(C) / 5.4 =

=> sin(C) ≈ 0.635

=> C ≈ sin⁻¹(0.635)

=> C ≈ 40.3°

As a result, the triangle has a side c of 2.15 and angles A = 42.5°, B = 0°, and C = 40.3°.

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To find the greatest possible age of the skeleton, we need to add the error to the estimate:

60 centuries + 0.8 centuries = 60.8 centuries

Therefore, the greatest possible age of the skeleton is 60.8 centuries.